This paper presents a human visual quality criterion for still monochrome pictures. The main idea is based on the decomposition of the signal in tuned channels with respect to the location in the visual field, the orientation and the frequency. The specific sensitivity of each channel and the self-masking are taken into account to evaluate the quality of the picture.

This paper proposes a new method for image coding involving two steps. First, we use a 'Dual Recursive Wavelet' Transform in order to obtain a set of subclasses of images with better characteristics than the original image (lower entropy, edges discrimination, ... ). Second, according to Shannon's rate distortion theory, the wavelet coefficients are vector quantized using the Kohonen Self-Organizing Feature Maps. We compare this training method with the well known LBG algorithm.

Autonomous analysis of complex image data is a critical technology in today’s world of expanding automation. The growth of this critical field is slowed by problems in traditional image analysis methods. Traditional methods lack the speed, generality, and robustness that many modern image analysis problems require. While neural networks promise to improve traditional techniques, homogeneous neural network systems have difficulty performing all the diverse analysis required of an autonomous system. This paper proposes a dual-staged, heterogeneous neural network approach to image analysis; specifically, a way to solve the target cuing problem.

Bilevel quantization using dither is useful with coarse quantizers. So we study it from a statistical viewpoint, furthermore, physical energy theory known as Hopfield neural network or Ising spin system. These are equivalent internally and they should be related to the optimum convergence or minimum quantization error of dithering. In this paper, we show this relationship and theoretical improvements.

A new bidirectional neural network is proposed based on convex projection theory. The neurons in the network are divided into two classes, clamped and floating neurons. For clamped neurons their states are preassigned to some fixed values and provide the network stimulus. For floating neurons their states change in accordance to those of other neurons and provide the network response. Steady state solutions under synchronous operation are presented in a closed-form formula. An adaptive learning algorithm is discussed which does not need matrix inverse computation and thus saves much learning time. Experiments in storing and retrieving binary images are carried out on a data base composed of 26 uppercase and lower-case English characters.

A Neural Network Emulator named NNE-CA was implemented using five recently developed general purpose 56-bits Digital Signal Processor (DSP56001). The NNE-CA is a MIMD (Multiple Instruction and Multiple Data) type parallel processor having Ring-Star coupled 5 DSPs. Its host computer is MVME147, which uses VME bus. The vector quantization using self organized neural netwoik, the resistive net for shape from shading, and back- propagation algorithms are simulated on the NNE-CA.

This paper presents a pattern recognition system that self-organizes to recognize objects by shape as part of an Integrated Visual Network (IVN) for autonomous flight control. The system uses a multistaged hierarchical neural network that exhibits insensitivity to the location of the object in the visual field. The network's three layers perform the functionally disjoint tasks of preprocessing (dynamic thresholding), invariance (position normalization), and recognition (identification of the shape). The Preprocessing stage uses a single layer of elements to dynamically threshold the grey level input image into a binary image. The Invariance stage is a multilayered neural network implementation of a modified Walsh-Hadamard transform that generates a representation of the object that is invariant with respect to the object’s position. The Recognition stage is a modified version of Fukushima's Neocognitron that identifies the position normalized representation by shape. The inclusion of the Preprocessing and Invariance stages allows reduction of the massively replicated processing structures used for translation invariance in the Neocognitron. This system offers roughly the same translation invariance capabilities as the Neocognitron with a dramatic reduction in the number of elements and the network's interconnection complexity.

This paper proposes image compression using an advanced neural network in which a variable input-output function of a neural unit can be learnt as well as a weight coefficient of a neural connection corresponding to information source and application. Since the neural network has the improved learning capability for local nonlinearity of information source, its application to compression of nonlinear information such as image is investigated. A learning algorithm and adaptive controlling schemes of input-output functions are derived. Simulation results show that the neural network can achieve higher SNR and shorter learning time than a conventional network having only variable weights.

ASP modules constitute the basis of a parallel computing technology platform for the rapid development of a broad range of numeric and symbolic information processing systems. Based on off-the-shelf general-purpose hardware and software modules, ASP technology is intended to increase productivity in the development (and competitiveness in the marketing) of cost-effective low-MIMD/high-SIMD Massively Parallel Processor (MPPs). The paper discusses ASP module philosophy and demonstrates how ASP modules can satisfy the market, algorithmic, architectural and engineering requirements of such MPPs. In particular, two specific ASP modules, based on VLSI and WSI technologies, are studied as case examples of ASP technology; the latter reporting 1 TOPS/ft3, 1 GOPS/W and 1 MOPS/$ as ball-park figures-of-merit of cost-effectiveness.

As high-performance sequential and parallel computing systems become increasingly accessible to large portions of the computing community, how well these systems perform on particular applications becomes of greater interest.

The SCC-100 parallel processor utilizes a fully-programmable, 32-bit MIMD architecture optimized for image and signal processing. Applications include image registration, clutter suppression, velocity filtering, multispectral processing, medical imaging and computer vision research as well as radar and sonar signal processing. The first SCC-100 processor, with 19 nodes and a peak throughput in excess of 1 GFLOPS, was recently delivered. A micro-miniature version using hybrid wafer-scale integration is currently under development for space applications.

The MEGA Node is a loosely coupled, highly parallel computer, based on transputers. One of its main characteristics is its ability to change the topology of the network, using an electronic switch. It covers a range from 128 to 1024 "worker processors", delivering from 550 to 4400 Mflops peak performance. To achieve these performances, a hierarchical structure has been adopted. This highly parallel machine is issued from the Esprit I P1085 "Supernode" project. The software has to support a wide spectrum of users going from those who wish to obtain maximum performance from the machine to those who wish to use it as a general purpose multi-user parallel machine. This paper describes the different ways to use the MEGA Node and the software environments provided to satisfy all kind of users. The Helios environment is a good example to explain how an operating system can control this machine, particularly the networking management and the fundamental problem of mapping. The MEGA Node has already been used for a wide range of applications like signal/image processing (high and low level), image synthesis, scientific and engineering number-crunching, neural network simulation and logic simulation. Only a few of them are discussed in this paper: medical image analysis and vision and ray tracing.

In this paper several digital video signal processing algorithms that use the median operation are presented. Both numerical and visual evaluations of the resulting image sequences clearly show that the median operation has many desirable properties for digital image sequence processing applications.

Quincunx sub-sampling and interpolation techniques are widely used in many image and video signal bandwidth compression techniques, like HDTV transmission systems. In this paper we consider the basic quincunx interpolation problem: interpolation of the missing samples of an orthogonally sampled image after quincunx sub-sampling with a factor of two. New median-based nonlinear interpolation techniques are developed and compared with traditional linear designs. It is shown that nonlinear interpolators result in considerably lower hardware complexity than good quality linear designs and, in many respects, even better image quality can be achieved.

A new optimization theory for stack filters is presented in this paper. This new theory is based on the minimax error criterion rather than the mean absolute error (MAE) criterion used in [8]. In the binary case, a methodology will be designed to find the stack filter that minimizes the maximum absolute error between the input and the output signals. The most interesting feature of this optimization procedure is the fact that it can be solved using a linear program (LP), just like in the MAE case [8]. One drawback of this procedure is the problem of randomization due to the lost of structure in the constraint matrix of the LP. Several sub-optimal solutions will be discussed and an algorithm to find an optimal integer solution (still using a LP) under certain conditions will be provided. When generalizing to multiple-level inputs, complexity problems will arise and two alternatives will be suggested. One of these approaches assumes a parameterized stochastic model for the noise process and the LP is to pick the stack filter which minimizes the worst effect of the noise on the input signal.

In this paper we analyze the statistical properties of discrete morphological filters. These properties are important when we are applying morphological filters to noisy images. Analytical expressions for the output distribution of basic discrete morphological filters are derived using the theory of stack filters.

The construction of morphological filters, i.e., morphological operators which are increasing and idempo- tent, is an important problem in mathematical morphology. In this paper it is described how one can construct openings and closings and other morphological filters by iteration. It turns out that a sort of order continuity is required to guarantee that iteration leads to idempotence. An important class of operators which yield morphological filters after iteration are the so-called pointwise monotone operators. In the last section the abstract theory is illustrated by a number of concrete examples.

Median-based filtering techniques are compared by considering a test image which contains a central disk-shaped region with a step or a ramp edge against a uniform background. Free parameters are the amplitude of Gaussian noise added,'the edge slope, and the number of filtering iterations. The quantitative comparison measure is the normalized squared error between the filtered noisy image and the noise-free image, on the flat image regions and on the transition region separately.

FLIR images contain a high level of noise, mainly caused by the acquisition system. Different classical non linear filters have been proposed to reduce this noise. Here, those having the best performance have been selected, studied in depth, and evaluated using statistical and subjective criteria. The best filters were AM and DWMTM, on which a detailed comparison study was carried out, finally choosing the AM one.

In the lattice of the operators acting on a complete lattice, a link ? is the inf of an increasing and a decreasing mappings. The links generate a complete lattice, and are characterized, in case of complete distributivity, by the implication A ? X ? B ? ? (A) ^ ?(B) ? ?(X). They allow minimal representation of a large class of mappings by means of hit-or-miss. Special attention is devoted to the residuals, i.e. the set difference between the identity and increasing mappings. These particular links allow to provide a common form to skeletons, ultimate erosions and conditional bisectors.

To characterize optimal mean-square morphological filters, it is first necessary to interpret morphological operations in a functional manner appropriate to the theory of statistical estimation. The present paper takes such an approach in the case of digital N-observation grayscale filters, these being defined via the Matheron representation. Having obtained the optimality criterion, we are lead to the characterization of a minimal search space, the nodes of the space being potential erosion structuring elements. More precisely, there exists a set of structuring elements which will always contain elements forming the basis for an optimal MS filter. Moreover, the set, called the fundamental set, is minimal, in the sense that no element can be deleted from it without possibly yielding a set not containing the optimal structuring element for a single-erosion filter.

The notion of fractal image compression arises from the fact that the iteration of simple deterministic mathematical procedures can generate images with infinitely intricate geometries, known as fracial images [2]. The purpose of research on fractal—based digital image coding is to solve the inverse problem of constraining this complexity to match the real—world complexity of real—world images. In this. paper, we propose a fractal image coding technique based on a mathematical theory of iterated transformations [1, 2, 3, 7] which encompasses deterministic fractal geometry. Initial results were reported in [7, 8]. The main characteristics of this technique are that (i) it is fractal in the sense that it approximates an original image by a fractal image, and (ii) it is a block—coding technique which relies on the assumption that image redundancy can be efficiently exploited through blockwise self—iransformabiliiy. We therefore refer to it as fracial block—coding. The coding—decoding system is based on the construction, for each original image given to encode, of a specific image transformation which, when iterated on any initial image, produces a sequence of images which converges to a fractal approximation of the original. We show how to design such coders, and thoroughly describe the implementation of a system for monochrome still images. Extremely promising coding results were obtained.

The watershed transformation is a very powerful image analysis tool provided by mathematical morphology. However, most existing watershed algorithms are either too time consuming or insufficiently accurate. The purpose of this paper is to introduce a new and flexible implementation of this transformation. It is based on a progressive flooding of the picture and it works for n-dimensional images. Pixels are first sorted in the increasing order of their gray values. Then, the successive gray levels are processed in order to simulate the flooding propagation. A distributive sorting technique combined with breadth-first scannings of each gray level allow an extremely fast computation. Furthermore, the present algorithm is very general since it deals with any kind of digital grid and its extension to general graphs is straightforward. Its interest with respect to image segmentation is illustrated by the extraction of geometrical shapes from a noisy image, the separation of 3-dimensional overlapping particles and by the segmentation of a digital elevation model using watersheds on images and graphs.

The digitization of the skeleton is the source of many difficulties. The skeleton of a binary set can be defined as the set of crest points and their upstream on the distance function10, 12. The final result depends on the quality of the distance function which has been used. The result is particularly coarse with the hexagonal distance function. The use of an euclidean distance function yields a beautiful skeleton, once some subtle interactions with the grid have been solved.

In this paper we show how the classical morphological definitions for Euclidean space can be extended to the sphere, where the rotation group replaces the Euclidean translation group. The main problem to overcome is the non-commutativity of the rotation group. Some examples of morphological transformations on the sphere are given. To visualize the results we use a projection of the sphere onto a plane.

Noting that the skeleton is defined by means of the distance function to the nearest point, an analog notion named anti-skeleton is derived when substituting to that distance the distance to the farthest point. A complete parallel is constructed, concerning the mathematical definitions and properties of the skeleton and the anti-skeleton. An example of its use in image analysis is then presented.

The morphological pyramid is a new computationally efficient algorithm for generating multidimensional bandpass representation of an image. This image pyramid offers a flexible convenient multiresolution format that mirrors the multiple scales of processing in the human visual system. Here the morphological pyramid is used for image mosaic and smear removal by multiresolution interpolation, some image examples are illustrated to show the effectiveness of this approach.

An efficient subband image decomposition method by mathematical morphology is described in this paper, it decomposes the input signal spectrum into 4 subband images by using two separable structure elements, then each band image, can be decimated and coded effectively for data transmission. This subband pyramid scheme preserves the number of pixels as in the original image, also the data structure itself is very compact, the advantages of morphology over linear filtering approach are its direct geometric interpretations, simplicity and efficiency in implementation, some image examples are given to show the effectiveness of this approach.

In this paper a multiprocessor architecture is proposed which is capable of handling real-time parameter estimation algorithms for estimating 3D body parameters from 2D image sequences. The implicit parallelism of the algorithm is used to obtain a highly efficient architecture while retaining modularity and flexibility.

Many applications in image processing, such as digitized angiography and scan conversion in medical imaging, sensor distorsion correction or image registration, require real time geometric transformations. Therefore, the Laboratoires d’Electronique Philips (LEP) and TELECOM Paris University are currently developing a chip performing in real-time a large class of geometric image transformations with third degree polynomials. We present here the VLSI architecture of this chip. The different problems associated with real-time image processing are discussed and some new architectural concepts, local memories combined with incremental calculation on a block and processing by patches, are used to overcome these problems. The chip operates on frame sizes of up to 1024x1024 pixels with a spatial resolution of 1/16 pixel at a maximum rate of 30 images per second.

A focal-plane-array chip designed for real-time, general-purpose, image preprocessing is reported. A 48 X 48 pixel detector array and a 24 X 24 processing element processor array are monolithically integrated on the chip. The analog, charge-coupled device-based VLSI chip operates in the charge domain and has sensing, storing, and computing capabilities. The chip was fabricated with a double-poly, double-metal process in a commercial CCD foundry. The simulation of an edge detection algorithm implemented by the chip is presented. An overview of the chip performance is described as well.

This paper describes a mapping technique for transforming a linear systolic array into multidimensional systolic arrays in order to achieve high-speed with less overhead. This technique is systematic, therefore, it would be useful for logic synthesis. The application of this technique in DSP and numerical computations reduces the design time which results in low design cost. This technique produces various structures (semi-systolic, quasi-systolic and pure systolic arrays) which could be considered as application specific array processors.

This paper presents the design of a mixed digital/analog array to implement several signal processing algorithms used in coordinate rotation for image processing. The advantages of hybrid arrays in which the processor element can be either analog or digital depending on a specific computing requirement are discussed. The interfaces between processor elements of different types are considered and several circuits are designed for this task. The proposed mixed array architecture is shown to possess strong potential in other high-performance computing applications.

With the breakthrough achieved in both memory capacities and very large scale integration, a large field of sophisticated algorithms can now be implemented in real time or video rate. This is especially true for low level operations which are taking into account the video image itself. At this level, most of the operations can be carried out using a restricted group of basic functions. This has led to the realisation of a coherent VLSI chip set named MIP (Modular Image Processor) carried out in the framework of a EUREKA project. The methodology which has ruled the design, the resulting chip set description as well as one of its applications are presented.

We report on a VLSI-based analog processor for fully parallel, associative, high-speed pattern matching. The processor consists of two main components: one, an analog memory matrix for storage of a library of patterns, and the other, a winner- take-all (WTA) circuit for selection of the stored pattern that best matches an input pattern. An inner product is generated between the input vector and each of the stored memories. The resulting values are applied in parallel to a WTA network for determination of the closest match. Patterns with up to 22% overlap are successfully classified with a WTA settling time of less than 10|is. Applications such as star pattern recognition and mineral classification with bounded overlap patterns have been successfully demonstrated. This architecture has a potential for an overall pattern matching speed in excess of 109 bits per second for a large (32-bit x 1000-pattern) memory.

Both biological and man-made (usually computer-based) vision systems have to acquire visual data and process it in real time at a formidable bit rate. To cope with this fundamental problem, biological systems of higher species employ mechanisms of data reduction already at the level of visual data acquisition.

A video codec based on several parallel digital signal processors is described. The digital signal processors (DSPs) can be easily programmed to implement the H.261 algorithm and are organized as a single instruction multiple data (SIMD) computing architecture. Both the encoder and the decoder divide a picture in regions of horizontal strips and use one local processor per region. These local processors code (decode) one horizontal strip of data which, using the terminology of the H.261 standard, corresponds to two group of blocks (GOBs). They also communicate to a central processor which multiplexes (demultiplexes) the coded data from (for) the processors in the encoder (decoder). In the case of the encoder the central processor also controls a data buffer for bit-rate adaptation. Lateral communication between adjacent processors is implemented to allow comparisons between blocks situated in neighbouring regions, as required by most motion estimation algorithms.

The hardware implementation of a DPCM coding algorithm with 2D prediction, noise shaping and fixed codeword length for the transmission of HDTV signals with 560 Mbit/s bit rate has been investigated. In order to reduce timing requirements an architecture with parallel processing elements and with modified DPCM-structure is proposed. DPCM and FIFO circuits as major components for such a codec have been designed for a VLSI-realization using 1.2|im CMOS technology.

This paper describes VLSI-architectures for HDTV-suitable implementations of two well-known hierarchical block-matching algorithms: the three-step search algorithm and the one-at-a-time search algorithm. The architectures exploit the regularity and design efficiency of systolic arrays, combined with a decision-driven on-chip data handling. They are capable of treating (16*16)-blocks, with a maximum displacement of +/-14 pixels, at 50MHz pixel rate. Another important feature is the small input-data bandwidth, which keeps to a minimum the requirements to external memory units. Transistor count and chip area estimations show that the architectures can be realized with today's CMOS technologies.

The Discrete Cosine Transform (DCT) is considered to be the most effective transform coding technique for image and video compression. In this paper, a new implementation of an experimental prototype multi-function DCT/IDCT (Inverse DCT) chip is reported. The chip is based on a distributed arithmetic architecture. The main features of the chip include: 1) The DCT and the IDCT are integrated in the same chip, 2) the chip achieves high accuracy, exceeding the stringent requirements of a proposed CCITF standard, 3) it achieves a high operating speed of 27 MHz, and is thus applicable to a wide-range of real-time image and video applications, 4) the internal clock frequency is the same as the pixel rate, and 5) with an on-chip zigzag scan converter and an adder/subtractor, it is multifunctional and useful in a DPCM configuration. The chip is implemented with standard cells and contains about 156k transistors.

We propose a method to locate three vanishing points on an image corresponding to three orthogonal directions of the scene. This method is based upon the Hough Transform. With the help of a correction of errors due to the limitation of the retina, and errors due to the detection inaccuracy of the image segments, this method was improved to work on noisy images of real complex scenes.

We describe a possibility to reconstruct 3-D information from a single view of an 3-D bilateral symmetric object. The symmetry assumption allows us to obtain a “second view” from a different viewpoint by a simple reflection of the monocular image. Therefore, we have to solve the correspondence problem in a special case, where known feature-based or area-based binocular approaches fail. In principle, our approach is based on a frequency domain template matching of the features on the epipolar lines. During a training period, our system “learns” the assignment of correspondence models to image features. The object shape is interpolated, when no template matches to the image features. This fact is an important advantage of this methodology, because no “real world” image holds the symmetry assumption perfectly. To simplify the training process, we used single views on human faces (e.g. passport photos), but our system is trainable on any other kind of objects.

We present a new iterative algorithm for 3D reconstruction under constraints from a limited number of radiographic projections, with adjustment of the constraints during the iterations. The first step of the algorithm is a classical iterative reconstruction ART type method (Algebraic Reconstruction Technique) which provides a rough volumic reconstructed 3D zone containing a flaw. Then, this reconstructed zone is modelled by a Markov Random Field (MRF) which allows us to estimate some 3D support and orientation constraints using a Bayesian restoration method. This fundamental step is an important one in the sense that it allows the introduction of local geometric a priori knowledge concerning the faults. The next step consists in reintroducing these strong constraints in the reconstruction algorithm. Few iterations of the algorithm are necessary to improve quality of the reconstructed 3D zone. Simulated radiographic projections allow the performance of the algorithm to be evaluated.

We propose here a pre-processing of 3D shapes which allows to give greater importance to the match between some parts of the surface of one object and some parts of the surface of the other object during the matching of the two objects. The method is working with objects defined on a digital grid and consists in a segmentation step to separate the main components of the shapes, and in a distance computation step to determine matching weights to be assigned to the surface points. Several new algorithms are developed: a 3D segmentation algorithm based on mathematical morphology, a fast method to compute geodesic distances on a 3D surface, a simple sphere creation algorithm on a digital grid. The method has been applied to chemical molecules.

A new approach to motion-estimation for hybrid image sequence coding is presented. Instead of minimizing the displaced frame difference (DFD), the estimator introduced in this paper maximizes the probability to determine the ’true’ physical motion of the scene. The probability expression is derived from two models, one for the statistics of the prediction error image and one for the interdependency of vectors in a vectorfield. The physical vectorfield is smoother than the vectorfield of a DFD-estimator and stronger statistical bindings between vectors exist. Therefore a coding algorithm for the vectorfield combining contour coding of regions of similar displacement with predictive coding of the vectors inside each region proves efficient. This allows the estimator to work with decreased blocksize and (even in DFD sense) to supply a distinctly improved displacement-compensation without spending more datarate for displacement-compensation than the DFD- estimator.

The work herein, applying the concept of irreversible coding via copying to low-rate video compression, has devised some new variants of universal pattern-matching interframe coding (PMIC), which produces the extra effect of generalizing the definition of a search area used in the conventional block-matching motion compensation. We have experimentally shown the performance gain provided by the generalization within the framework of irreversible coding via copying, and demonstrated that PMIC is useful and potential as a basic means for low-rate video compression.

A compression technique based on an expansion is presented. The elementary functions of the expansion form a class of pyramidal Gabor functions covering the frequency domain in octave bands. The image sequence is coded by differentially coding selected coefficients of this expansion. Simulation results show sequences reconstructed with good quality for a bit rate less than 64 Kbit/s.

We have modified the interpolation and quad-tree based still picture Recursive Binary Nesting algorithm to code moving sequences. Central to the efficiency of this is the mechanism by which the extent of the quad-tree decomposition is controlled. Termed block testing, this forms the subject of this paper.

A lot of different algorithms for background prediction and memory control have been investigated mainly in the field of low bit-rate coding. Two problems arise with background prediction: 1. How to tell the receiver which parts of the prediction image may be taken from the background memory? 2. How to distinguish at the receiver’s side between object, stationary, covered and uncovered background? This paper presents a method for pel-accurate distinction between moving object and background without transmitting a single bit. In addition an object-oriented motion estimation and compensation is introduced.

A new 3-D segmentation-based coding technique is proposed for transmitting the motion video with reasonablly acceptable quality even at a very low bit rate. Only meaningful motion areas are extracted by using two change detection masks and a current frame is directly segmented rather than a difference frame itself so that a good image quality can be obtained at high compression ratios. Through the experiments, the sequence of Miss America is reconstructed with visually acceptable quality at the very high compression ratio of 360 : 1.

Visual pattern image coding, or VPIC1-5, is an important new digital image coding process that possesses significant advantages relative to all other existing technologies: VPIC is capable of coding (i) with visual fidelity comparable to the best available techniques; (ii) at very high compressions exceeding the best available technologies: compressions in the range 30:1—40:1 are obtained routinely; (iii) with absolutely unprecedented coding efficiency - coding/decoding via VPIC is completely linear with respect to image size and entails a complexity 1-2 orders of magnitude faster than any prior high compression strategy; (iv) configurability. In the current work, the VPIC coding framework developed initially for single images is extended to image sequences. The algorithm for image sequence coding presented here, termed Visual Pattern Image Sequence Coding (or VPISC) exploits all of the advantages of "static" VPIC in the reduction of information from an additional (temporal) dimension to achieve unprecedented image sequence coding performance stated in terms of coding complexity, compression, and visual fidelity.

Filter banks based on recursive filters have recently been applied with success in subband coding of still images [1, 2]. Their main feature, low computational complexity, make these filter banks extremely attractive for video coding applications. In. this paper we demonstrate the suitability of these filter banks in low bit rate image sequence coders operating in the 64 —200 Kbps range. In particular we compare the performance of two types of recursive filter banks with that of a more traditional one based on quadrature mirror FIR filters (QMF). It is shown that the performance of our hR based systems is comparable to that of the more complex FIR based systems. Also, we show that the encoding strategy of CCITT's reference model no. 7 can be adapted successfully to fit into our subband coding scheme. Finally we discuss alternative approaches to motion estimation in hybrid image sequence coders and show preliminary results in the context our video subband coder.

A new interframe coding technique is presented in this paper called Interframe Hierarchical Address- Vector Quantization (IHA-VQ). It exploits the local characteristics of a moving image's motion compensated (via block matching) difference signals by using quadtree segmentation to divide each signal into large, uniform regions and smaller, highly detailed regions. The detailed regions are encoded by Vector Quantization (VQ), and the larger, low detail regions are replenished from the previous image. IHA-VQ also exploits the correlation between the small blocks by encoding the addresses of neighboring vectors using several codebooks of address-codevectors. The IHA-VQ technique is applied to a test sequence of images in a computer simulation. The sequence was encoded at an average bit rate of 0.607 bits per pixel (bpp). The Signal-to- Noise Ratio (SNR) averaged 39.5 dB. By changing the quadtree segmentation parameter a much lower bit rate, 0.237 bpp, is achieved for a lower SNR, 37.73 dB.

The Broadband Integrated Services Digital Network (BISDN) based on lightwave technology is supposed to become the all-purpose exchange area communications network of the future. All digital video services are integrated with applications ranging from videophone, teleconferencing to digital TV (signals according to the CCIR rec. 601) and High Definition TV (HDTV) distribution. A desirable feature of the various video services is the upward and downward compatibility in resolution in order to guarantee a free exchange of services, transmitters and receivers. This paper proposes an n-level progressive hierachical intraframe coding scheme based on subband coding. In this scheme several spatial low-resolution services are available as subsets of the coded HDTV data which can directly be received at lower bit rates. Progressive coding of the HDTV signal is employed in order to prevent quantization errors from propagating to higher resolution signals. Special attention is given to the design of the quantizers required for the progressive coding, and to the incorporation of the side panels coding.

A coding technique for the transmission of HDTV signals at a bit rate of 140 Mbit/s is presented. Since the capability of downward compatibility to standard TV is desired a four band subband approach has been taken. Because of the intended realization of the codec using CMOS-VLSI technology, the subband filter bank and the coding algorithm are designed considering hardware constraints and system restrictions of the subband filterbank. The design results in Quadrature Mirror Filters realizable with simple integer arithmetic. An adaptive intrafield coding algorithm is used for coding the four subbands. Separable QMFs with 10 coefficients in vertical and 14 coefficients in horizontal filtering are preferred to QMFs with less coefficients because of the coding gain.

The principle of subband coding has recently been applied for the purpose of image data compression. In this paper we present new results pertaining to our subband coder for images featuring an exact reconstruction parallel complex filter bank based on HR filters. This filter bank is characterized by its low complexity. The main advantage of subband coding is the possibility of separate coding of each subband such that the perceptually important coding noise is minimized. In this paper we exploit the nature of the complex valued subband signals of this particular coder by coding the module and phase rather than the real and imaginary parts. We determine the tolerable quantization noise levels for the module and phase signals in all subbands. These empiricaly derived data are employed in the coding simulations presented. Finally we present coding results for bit rates between 0.25 and 1.0 bits/pel.

This paper describes a class of orthogonal binomial filters which provide a set of basis functions for a bank of perfect reconstruction Finite Impulse Response Quadrature Mirror Filters (FIR-QMF). These Binomial QMFs are shown to be the same filters as those derived from a discrete orthonormal wavelet approach by Daubechies [13]. The proposed filters can be implemented very efficiently with output scaling, but otherwise no multiply operations. The compaction performance of the proposed signal decomposition technique is computed and shown to be better than that of the DCT for the AR(1) signal models, and also for standard test images.

This paper is an attempt to bring together a number of current ideas in multiresolution image processing into a single framework. The unification is achieved by introducing a two-level image model, comprising a quadtree containing parameters which control the evolution of the image as a sequence of successive refinements through scale-space. Examples of the method's application to image coding and analysis are used to illustrate the principles and show its usefulness.

This paper describes the Three Dimensional Laplacian Pyramid Coding as an extension of previously reported work on static images. The algorithms that we present when applied to image sequences gives high compression rates being very useful for videotelephone or videoconference applications. The image sequence is splitted into subsequences which are composed of a small number of images, then the three dimensional algorithms are applied. The coding scheme is based on the construction of spatial/temporal pyramid structures defined on arbitrary sampling lattices. A three dimensional treatment study of sampling rate conversion using matrix notation is also presented.

The three-dimensional properties of an optical microscope are analyzed and a defocusing technique is proposed to recover the spatial distribution of the specimens under investigation. Limitations and real capabilities of the 3D reconstruction are pointed out. As a result, lateral views are obtained by means of operations in the spatial frequency domain. In such a way, it is possible to represent side views of an object within the angular aperture range of the microscope. A theory concerning image formation is discussed and simulations of side view reconstructions are reported.

Many applications require the acquisition of 3D CT images made of a stack of 2D X- ray slices. The different slices are obtained by the displacement of the patient table, which sets the resolution in the z direction perpendicularly to the slice plane. This resolution is physically limited by the detector width, on which the X-ray radiation is integrated. Those detectors inherently carry out a low pass filtering process and aliasing effects. As a consequence the reconstruction of a slice in any direction can present artefacts. Then we propose to apply a superresolution technique based on a deconvolution method associated to oversampling using subpixel motion in order to improve the resolution in the z-direction. This method requires the acquisition of overlapping slices which are later processed directly in the spatial domain, what is particularly interesting for computer time. Its application provides thinner and accurate new slices. After the presentation of the method, the results obtained on experimental images coming from a conventional CT scanner are presented.

Hierarchical image segmentation techniques have been applied to spin-echo magnetic resonance images of the brain. From T1- and T2-weighted clinical images, areas representing gray matter, white matter and cerebrospinal fluid were segmented. In the segmentations à priori anatomic information was used and the procedures were performed in an ordered sequence of anatomy.

This paper describes the application of digital image processing to the morphological evaluation of human corneal endothelial cell patterns. This morphological evaluation is used in both basic and clinical ophthalmology. There is interest in investigating the fundamental processes involved in the pattern formation and the variation in the pattern over time. Digital image processing and analysis of the binary segmented images of cell boundaries can be used to determine for each cell border the following features as: area, perimeter, aspect ratio, roundness, form factor, fractal dimension, length, breadth, width, equivalent diameter, x and y center of gravity, orientation angle, and moment angle. The question of the nature of the physical processes which result in the dynamic polygonal cell patterns is presented.

We present a three-stage method for segmenting NMR-datasets of the head into 3D-regions corresponding to different brain matter classes, liquid containing structures, cranium, and background. Our technique works from the beginning with 3D-regions, whose internal ’grey’ values as well as shapes are described by stochastic models. The first phase starts by assuming the entire dataset as consisting of only one region, and then recursively extracts those areas which are not compatible with this hypothesis. During this step, special emphasis is given to the problem of accurately locating the region surfaces. In the second stage, a Bayes classifier groups the regions into different categories, like brain matter, liquid, cranium, and background. Classification errors are corrected largely automatically during the third stage by applying simple knowledge about the topological relationships between the classes.

The widespread prevalence of atherosclerotic vascular disease has given rise to the need for a simple, noninvasive imaging examination of the cardiovascular performance of patients. The potential of using Magnetic Resonance (MR) Imaging to quantify flow in vivo has for reaching possibilities for the future of preventive medicine. In this paper we address the problem of using MR velocity imaging to analyse the flow boundaries in human arteries which are of great importance to the early diagnosis of occlusive diseases. A flow related enhancement process is introduced in this paper. It is designed to suppress the residuals and the noisy background of the MR velocity images caused by misregistration, tissue movement and uneven magnetic field and provide great improvement in signal to noise ratio. From the enhanced image, the main flow areas can be delineated by a thresholding process which defines the kernel of the flow. The boundaries of the kernel region are then dynamically guided by a defined flow boundary localization process to their final positions. The results of the application of this coarse to fine process show its robustness and effectiveness for the determination of the blood blow boundaries form very low quality MR velocity images.

The diagnostic quality of radiographic images can be improved with some basic image processing algorithms. This is shown by a two step procedure on X-ray chest images in this paper. First, a revised adaptive unsharp masking method was applied which sharpens some boundary features and in the meantime smooths some others. After this, an extended Sobel edge detection and region growing process followed which further delineates the suspected lung nodules. The final results give a clearer show of wanted features.

In this paper we describe a model-based system for the assessment of skeletal maturity on hand radiographs by the TW2 method. The problem consists in classifiying a set of bones appearing in an image, in one of several stages described in an atlas. A first approach consisting in pre-processing, segmentation and classification independent phases is also presented. However, it is only well suited for well contrasted, low noise images, without superimposed bones, were the edge detection by zero crossing of second directional derivatives is able to extract all bone contours, maybe with little gaps, and few false edges on the background. Hence, the use of all available knowledge about the problem domain is needed to build a rather general system. We have designed a rule-based system for narrow down the rank of possible stages for each bone, and guide the analysis process. It calls procedures written in conventional languages for matching stage models against the image, and getting features needed in the classification process.

In the design and implementation of Picture Archiving and Communication Systems (PACS), two types of problems have to be solved. The first is in the aspect of image data formatting and the second is in the image transmission. Radiography, X-ray Computed Tomography (CT), radionuclide emission tomography, magnetic resonance imaging (MRI), and ultrasonic imaging are the widely used medical imaging. Microscopic images are the examples of bioimaging. Some of these biomedical imaging modalities, such as X-ray CT, MRI, etc, directly create digitized images, which are stored in computer disks. Some of them produce non-digitized images, which are recorded on films or video-tapes. Using scanners (flatbed, overhead, slide) or video camera, the non-digitized images can be digitized. Due to the diversity of physical principles and image reconstruction procedures of these imaging modalities, the image data formats of the digitized biomedical images are extremely different. In addition, the data size of the digitized images are usually very large, especially when the higher resolution is required. For instance, a transaxial thoracic image, created by the 3-rd generation of X-ray scanner, has about 150 X 103 bytes, a digitized radiographic film (14” X 17”), in the moderate resolution (300 pixel-per-inch), occupies about 20 X 106 bytes. Therefore, seeking an unified image data format and compressing the image data for digitized biomedical images are the first issue in developing PACS . Computer networks provide the effective means for exchanging images. Currently, mainframe computers are linked by networks such as Bitnet, ARPAnet, etc. Personal (micro) computers (including workstations) are linked by LAN etc. Micro-mainframe connectivity is also available. In order to establish the communications among these computers, the same protocol is required. Once the compressed images are captured, opening, z.e., redisplaying the captured images requires the same or compatible applications (softwares). For the further processing and analysis, these compressed images may be required to change to the standard text data format (e.g. ASC) to meet a variety of needs of different computer systems and processing techniques. It is evident that speed in image transmission is another key factor, especially when image data size is very large. Thus, speeding up image transmission, decoding the compressed images, and selecting protocol and application are the second issue in developing a PACS . The problems addressed above have been considered and solved. An Image Transfer System, ITS, has been developed in the University of Maryland School of Medicine (Baltimore) and tested between micro- to micro-computers, micro- to mainframe computers, and mainframe to mainframe computers. 1. The Tag Image File Format, TIFF, is utilized as an unified data format for image data compression and transmission. TIFF was originated in 1986 and some ideas behind it came from the ACR/NEMA communication protocol for radiological images. We extend it to more general medical images . Comparing with traditional data file formats which use a fixed-position organization, TIFF employs a different structure based on tagged information. This structure is commonly used in data base design. Each tag of TIFF consists of several fields and a pointer. It describes not only the height and width of image, but also contain resolution information, support grayscale a d color data, and allow for private and public data compression schemes. Although the tag structure of TIFF may seem to add an unnecessary layer of overhead, it provides a key advantage over a fixed- position format. It is very easy to add new tags to the format without requiring all supporting software to be rewritten . Standard data compression schemes are defined within TIFF. For bilevel image, a simple run- length encoding is used. For grayscale and color images, a form of LZW (Lempel-Ziv and Welch) encoding is used. According to our results, compression ratio is up to 3.65 . 2. A special firmware and a selected protocol (University of Maryland School of Medicine is going to file patent protection) are utilized to transfer images (in TIFF format) between micro- to micro-computers, and micro- to mainframe computers. This firmware provides a speed (in image transfer) which is four (4) times faster than that in normal data transfer . Once the transferred images are captured, they can be directly displayed and printed. Using phototypesetter printer such as Linotronic, a photo-quality prints can be produced. Using several public softwares, these captured images can be directly manipulated. A decoding technique which can translate the coded, compressed TIFF image data into standard text image data is also developed. Thus, almost every image processing and analysis approach, e.g. edge-detection and region-segmentation in the lower-level analysis and object recognition and labeling in the higher- level analysis, either in mainframe or in micro-computer, can use these image data for further processing . Our research and development showed that ITS has the following advantages: A. it can accept both digitized and non-digitized images, as inputs, from different biomedicalimaging modalities; B. various image data formats can be converted to an unified format, TIFF, which is extensible,portable, and revisable; C. it can achieve pretty high data compression ratio, up to 3.65; D. it can achieve quite fast transmission speed, 4 times faster than normal data transfer; E. its communication protocol and applications are simple and public; F. its decompression (i.e. decoding) procedure makes the captured image be processed in almostevery computer system and by existing processing/analysis techniques; G. it is very user-friendly: it does not require special computer training; H. it is also extremely cost-effective; ITS demonstrates the great promise and is a practical Picture Archiving and Communication System.

Discussed are the most relevant architectural aspects of the the so-called Image Reference Data Base (IRDB), that is the distributed Information System which is under development within the framework of TELEMED Project of the program RACE, project no.R1086, of the Commission of the European Community. The TELEMED Project has the objective of developing a pilot application for experimenting Integrated Broadband Communication of medical, anatomical and radiological information. A major design objective has been the definition of an open system architecture permitting a multisite implememtation of IRDB. To this end, the proposed architecture builds a federation of IRDB and provides a logical view of each individual IRDB as if it were a partition of single database.

Field rate upconversion is used in many modem television systems in order to improve the picture quality. Motion estimation by motion vector computation is used to improve motion portrayal. Usually, motion compensated upconversion requires some further processing of the standard 50 Hz motion vectors. In this paper, a nonlinear algorithm, called vector median, is introduced for this purpose. The suggested postprocessing was applied to the High Definition Multiplexed Analogue Components (HD-MAC) system introduced by the Eureka 95 project.

A new subband technique for coding high-definition television (HDTV) signals is presented. Intrafield processing is sufficient because of motion adaptive subband suppression. The scheme can be implemented in hardware very similar to two-dimensional subband coding schemes.

In this paper results of investigations about the effects of channel errors in the transmission of images compressed by means of techniques based on Discrete Cosine Transform (DCT) and Vector Quantization (VQ) are presented. Since compressed images are heavily degraded by noise in the transmission channel, more seriously for what concern VQ-coded images, theoretical studies and simulations are presented in order to define and evaluate this degradation. Some channel coding schemes are proposed in order to protect information during transmission. Hamming codes (7,4), (15,11) and (31,26) have been used for DCT-compressed images; more powerful codes, such as Golay (23,12), for VQ-compressed images. Performances attainable with soft- decoding techniques are also evaluated; better quality images have been obtained than using classical hard decoding techniques. All tests have been carried out to simulate the transmission of a digital image from HDTV signal over an AWGN channel with PSK modulation.

Gradual introduction of HDTV is considered to be important. In this paper, a bit-rate reduction system is introduced, which decreases the bit rate of digital HDTV from 664 Mbit/s to about 80 Mbit/s, while ensuring compatibility with TV. The system is based on first subband splitting the interlaced HDTV signal into an interlaced compatible TV signal and three surplus signals. Then, the compatible TV signal is coded with intraframe DCT coding, whereas the surplus signals are coded with quantization, variable-length coding and runlength coding.

For a number of real-time applications extremely high throughput (up to several kiloMIPS) is needed at very low hardware cost. For at least another decade this mostly will be possible only with dedicated hardware, but not with programmable von-Neumann-type universal hardware.

In this paper we have studied what performances can be obtained by mapping processing image algorithms on parallel architectures. For this reason we have focused our attention on a particular problems we have studied a processing chain to detect ship wakes in SAR images. It allowed us to test low and medium level algorithms. Because of the noisy nature of SAR images great attention has been put on the choice of the most appropriate filtering technique. It has been done both through theoretical considerations on the nature of noise and experimental results on filtered images. The chain has been implemented on a sequential machine like MicroVAX II and on some parallel architectures based on eight transputers IMS T800. The performances obtained in this way have been discussed and some general considerations have been deduced from them.

The National Aerospace Laboratory of the Netherlands NLR realized under contract with the European Space Operation Center (ESOC) a system to demonstrate the feasibility of using data compression for the European METEOrological SATellite (METEOSAT) dissemination link. The used compression method doubles the amount of image data that can be disseminated to the users via the existing channel without introducing any errors in the reconstructed image after decompression. The compression and decompression functions are performed in real-time during the METEOSAT dissemination (166 Kbit/sec). For this project a multi processor system based on the INMOS Transputer has been selected to provide the required processing power.

This paper discusses the bit-rate compression of super high definition images with Discrete Cosine Transform (DCT). Super high definition images with more than 2048x2048 pixels of resolution are introduced as the next generation image category beyond HDTV. In order to develop bit-rate reduction algorithms, an image I/O system for super high definition still images is assembled. A traditional DCT based coding algorithm called Scene Adaptive Coder (SAC) is applied to super high definition images and related problems are clarified. A new coding algorithm is proposed, which takes human visual perception characteristics into consideration, and its coding performance is examined for super high definition images.

In this paper, a new approach of a variable block size VQ coding scheme is proposed. Most natural image can be divided into regions of high and low detail. Traditional coding schemes do not adapt the blocksize on the space-varying characteristics of natural images, but break the image into blocks of a fixed size prior to processing. The blocksize in transform coding is usually too large to handle partial high-detail region satisfactorily. On the other hand, the block size in conventional vector quantizer is too small to take advantage of large homogeneous regions in an image. For this reason, it can be very attractive to implement a variable block size image coding scheme which allow a greater variation of the number of bits spent per unit area according to the local detail.

A clustering algorithm for the design of efficient vector quantizers to be followed by entropy coding is proposed. The algorithm generates a sequence of quantizers whith rates close to theoretical rate- distortion bound. A fast version of this algorithm can be used as an alternative to the entropy-constrained vector quantizer technique proposed by Chou, Lookabaugh and Gray.

This paper discusses the design and performance evaluation of a variable block-sized vector (plantizer with unconstrained tiling (ETYQ). a novel block coder that segments the input image into an unconstrained tiling of various-sized, nou-overlapping rectangular regions, each of which is then coded with a vector cpiantizer. ETYQ is compared with the more constrained quadtree vector cpiantizer (QTYQ) approach. A transmission .scheme is described which reduces the overhead required to convey ETYQ segmentation geometry. Several l:TYQ segmentation strategies are presented, and mean-residual codebook generation methods with appropriate side stream compression techniques are discussed. ETYQ outperforms QTYQ in a projected rate sense, since it can segment an image into fewer blocks, each of which satisfies a specified homogeneity constraint. Furthermore, lTTYQ outperforms QTYQ in a rate-distortion sense for certain applications. The maximum separation which we have observed between our experimental ETYQ rate-distortion curves and those for the QTYQ system is 0.4 dB.

In this paper, a new technique for designing linear phase QMF filters is proposed. These filters have the frequency responses of sharp and symmetrical transition charcteristics, and the capabilities of perfect reconstruction and simple implementation. By applying video signals into basic sub-band systems, the performances between designed QMF pair and other QMF pairs1,2 are compared in alias-cancellation!reconstruction errors and Peek Signal- to-Noise Ratios(PSNRs). It is shown that the proposed QMF pair has better performance than the short kernel filter pair1, and similar performance as the long kernel filter pair2.

There exists a transform trellis code that is optimal for stationary Gaussian sources and the squared- error distortion measure at all rates. In this paper, we train an asymptotically optimal version of such a code to obtain one which is matched better to the statistics of real world data. The training algorithm uses the M-algorithm to search the trellis codebook and the LBG-algorithm to update the trellis codebook. To adapt the codebook for the varying input data, we use two gain-adaptive methods. The gain-adaptive sheme 1, which normalizes input block data by its gain factor, is applied to images at rate 0.5 bits/pixel. When each block is encoded at the same rate, the nonstationarity among the block variances leads to a variation in the resulting distortion from one block to another. To alleviate the non-uniformity among the encoded image, we design four clusters from the block power, in which each cluster has its own trellis codebook and different rates. The rate of each cluster is assigned through requiring a constant distortion per-letter. This gain-adaptive scheme 2 produces good visual and measurable quality at low rates.

Traditional block transform coding scheme would generate the artifact called blocking effects near block boundaries which degrate the low bit rate coded images. In this paper; the Double Shift DCT ( DS-DCT ) image coding scheme is to be presented. The pixels in spatial and coefficients domain has been shifted according to the equal-pitch principle before DCT transformation. Finally; the blocking effects will be reduced to a very low level. At the mean time; the energy with in subblocks will be more compacted. Therefore; the benefits of more data compression will be accompanied with the reducing blocking effects. The DS-DCT results in smaller image reconstruction errors; better signal to noise ratio and more data compression than the adaptive DCT image coding scheme from Chen1 .

In many source and data compression schemes, information relating to positions of high energy samples or areas of importance often needs to be relayed to the decoder. The error resilient positional code (ERPC) is an efficient fixed rate coding scheme for encoding such positional information, or equivalently, sparse binary data patterns. It has also been designed with good channel error robustness properties, whose performance degrades gracefully with worsening channel conditions, without the possibility of breakdown or loss of sync. In this paper, the coding efficiency of the ERPC is compared to a few other standard schemes, and as well as being efficient, its error extension is shown to be low and non-catastrophic. The ERPC is then applied to an efficient error robust adaptive image coding example based on a SBC/VQ codec capable of operating in harsh channel conditions without the aid of channel coding.

Subband Coding of images, which can be seen as an extension of orthogonal transformations, has been introduced by Woods and O’Neil [8]. In [8], the subbands are further encoded by DPCM. In this study, it is proposed to use subband coding as a stand alone coding technique. The emphasis is put on the question of subband quantization. A methology is proposed where the quantization step of the subbands is taken so as to minimize a quantization noise power weighted by a sensitivity function of the eye.

We present an image coding scheme based on the properties of the early stages of the human visual system. The image signal is decomposed via even and odd symmetric, frequency and orientation selective band-pass filters in analogy to the quadrature phase simple cell pairs in the visual cortex. The resulting analytic signal is transformed into a local amplitude and local phase representation in order to achieve a better match to its signal statistics. Both intra filter dependencies of the analytic signal and inter filter dependencies between different orientation filters are exploited by a suitable vector quantization scheme. Inter orientation filter dependencies are demonstrated by means of a statistical evaluation of the multidimensional probability density function. The results can be seen as an empirical confirmation of the suitability of vector quantization in subband coding. Instead of generating a code book by use of an conventional design-algorithm, we suggest a feature specific partitioning of the multidimensional signal space matched to the properties of human vision. Using this coding scheme satisfactory image quality can be obtained with about 0.78 bit/pixel.

In this paper, we show two basic results to pyramid coding for a progressive image transmission. We first show that in a hierarchical pyramid structure, the transform coding can provide a gain over a simple scalar quantizer. The optimum bit allocation strategy among the Laplacian pyramid for transform coding is also described. Secondly, based on th.e use of transform coding, we show that especially at low bit rates a hierarchical pyramid structure provides a significant gain over encoding of an input image directly. This is particularly attractive to the progressive transmission using a hierarchical pyramid structure.

Vector Quantization (VQ) is a well-known technique for reducing the transmission bit rates or the storage in image coding. It exploits the high correlation and spatial redundancy between neighboring pixels to minimize the mean square error distortion. In this paper, we present a simple and efficient image coding method called hybrid predictive ordering linear approximation and VQ (POLA-VQ). By taking as reference the previous received scan line, the pixels of the present scan line are placed in a decreasing order of amplitudes. The regression line of the ordered pixels is estimated. The linear approximation is refined by computing the one-bit error pattern of the scan line and by selecting an optimal codevector from the codebook. We found that an acceptable quality of coded image at low bit rates can be achieved with our approach.

This paper illustrates the practical use of deformable contour models in the context of multi-spectral image segmentation. A discussion of color boundary energies is made, and an algorithm (Boundary Search) is presented that adaptively fits a contour line through locally optimized boundary points.

Shape of medical objects, such as the human bones or skeletons, conveys information about the object’s anatomic structures and their pathological states. The sectional contours of the objects, which are observable through computer tomograms, carry descriptive clues for analyzing shapes. To build and represent the descriptions of contours, one should derive stable structural elements and their sensitive attributes from the contours. Sectional contours of the medical objects are highly curved and complex, therefore, they should be described in a higher order parameter space than just in a linear one. These considerations have guided us to examine the scale-space transformation, and to develop methods for expressing, describing, and extracting structures in the scale-space images of the contours. In this paper we introduce a tree-based data structure for representing descriptions of structures in the scale-space, and further demonstrate its applications to shape analysis.

One of the most popular technique for edge detection is based on the convolution of the image with a LoG operator, namely the Laplacian of Gaussian, characterized by a space constant