In this research the Hurst exponent <i>H</i> is used for quantifying the fractal features of LANDSAT images. The Hurst exponent is estimated by means of the Detrending Moving Average (DMA), an algorithm based on a generalized high-dimensional variance around a moving average low-pass filter. Hence, for a <i>two</i>-dimensional signal, the algorithm first generates an average response for different subarrays by varying the size of the moving low-pass filter. For each subarray the corresponding variance value is calculated by the difference between the original and the averaged signals. The value of the variance obtained at each subarray is then plotted on log-log axes, with the slope of the regression line corresponding to the Hurst exponent. The application of the algorithm to a set of LANDSAT imagery has allowed us to estimate the Hurst exponent of specific areas on Earth surface at subsequent time instances. According to the presented results, the value of the Hurst exponent is directly related to the changes in land use, showing a decreasing value when the area under study has been modified by natural processes or human intervention. Interestingly, natural areas presenting a gradual growth of man made activities or an increasing degree of pollution have a considerable reduction in their corresponding Hurst exponent.
Melanoma is the most deadly form of skin cancer in human in all over the world with an increase number of victims yearly. One traditional form of diagnosis melanoma is by using the so called ABCDE rule which stands for Asymmetry, Border, Color, Diameter and Evolution of the lesion. For melanoma lesions, the color as a descriptor exhibits heterogeneous values, ranging from light brown to dark brown (sometimes blue reddish or even white). Therefore, investigating on color features from digital melanoma images could provide insights for developing automated algorithms for melanoma discrimination from common nevus. In this research work, an algorithm is proposed and tested to characterize the color in a pigmented lesion. The developed algorithm measures the hue of different sites in the same pigmented area from a digital image using the HSI color space. The algorithm was applied to 40 digital images of unequivocal melanomas and 40 images of common nevus, which were taken from several data bases. Preliminary results indicate that visible color changes of melanoma sites are well accounted by the proposed algorithm. Other factors, such as quality of images and the influence of the shiny areas on the results obtained with the proposed algorithm are discussed.
This research introduces an automatic technique designed for the digital restoration of the damaged parts in historical documents. For this purpose an imaging spectrometer is used to acquire a set of images in the wavelength interval from 400 to 1000 nm. Assuming the presence of linearly mixed spectral pixels registered from the multispectral image, our technique uses two lattice autoassociative memories to extract the set of pure pigments conforming a given document. Through an spectral unmixing analysis, our method produces fractional abundance maps indicating the distributions of each pigment in the scene. These maps are then used to locate cracks and holes in the document under study. The restoration process is performed by the application of a region filling algorithm, based on morphological dilation, followed by a color interpolation to restore the original appearance of the filled areas. This procedure has been successfully applied to the analysis and restoration of three multispectral data sets: two corresponding to artificially superimposed scripts and a real data acquired from a Mexican pre-Hispanic codex, whose restoration results are presented.
Autofocus is of fundamental importance for a real time automatic system. In many microscopy applications, a
desired automatic system should provide the best focused image with enough accuracy and the least computation
time. During the last years, several metrics based on images have been proposed for the autofocus process.
Although many of these techniques present good results, their main limitations reside in the high computation
time. Recently, the development of graphics processing units (GPUs) has given place to new scientific applications
oriented to diminish the computational effort of the central processing unit (CPU). This manuscript presents the
parallel implementation of eight different autofocus algorithms using GPUs for microscopy applications. The main
objective of the proposed manuscript is to demonstrate that the use of GPUs can speed up the computational
time required to perform the mentioned techniques. The reduction of computation time achieved with the
proposed implementation suggests that graphics processing units can effectively be used for autofocus in real
Multispectral imaging has motivated new applications related to quality monitoring for industrial applications due to its capability of analysis based on spectral signatures. In practice, however, a multispectral system used for such purposes is limited because of the large amount of data to be analyzed, being necessary to develop fast methods for the unsupervised classification task. This manuscript introduces a fast and efficient algorithm that is used in combination with a multispectral system for the unsupervised classification of food based on quality. In particular, given two types of fruits previously characterized, we first register a multispectral image from them and perform a dimensionality reduction by taking into account the most representative spectral bands that involve their reflection spectra. From the reduced set, the min-W and max-M lattice associative memories are computed and a subset of their columns are used as centroids of specific clusters. Then, the Euclidean distance computed between each centroid and all spectral vectors in the image allows to subdivide the image in clusters. The achieved results state that the technique is fast, reliable, and non-invasive for food classification.
A machine vision system for fault detection in PET bottles is presented. The bottle inspector is divided in three modules for image acquisition of bottle finish, bottle wall and bottle bottom. The captured images are corrected by adaptive gamma correction. An algorithm based in the frequency filtering of <i>n</i> images for defect detection of bottle wall and bottle finish is proposed. We obtain a correct rate classification of 85.5 % in bottle finish, 80.64 % in bottle wall and 95.0 % in bottle bottom.
Multispectral imaging has given place to important applications related to classification and identification of
objects from a scene. Because of multispectral instruments can be used to estimate the reflectance of materials
in the scene, these techniques constitute fundamental tools for materials analysis and quality control. During
the last years, a variety of algorithms has been developed to work with multispectral data, whose main purpose
has been to perform the correct classification of the objects in the scene. The present study introduces a
brief review of some classical as well as a novel technique that have been used for such purposes. The use of
principal component analysis and <i>K</i>-means clustering techniques as important classification algorithms is here
discussed. Moreover, a recent method based on the <i>min-W</i> and <i>max-M</i> lattice auto-associative memories, that
was proposed for endmember determination in hyperspectral imagery, is introduced as a classification method.
Besides a discussion of their mathematical foundation, we emphasize their main characteristics and the results
achieved for two exemplar images conformed by objects similar in appearance, but spectrally different. The
classification results state that the first components computed from principal component analysis can be used to
highlight areas with different spectral characteristics. In addition, the use of lattice auto-associative memories
provides good results for materials classification even in the cases where some spectral similarities appears in
their spectral responses.
In this work, the analysis of an optical - digital system based on the Fourier transform hologram architecture is presented. We are interested in the diffractive effects in the Spatial Light Modulators as the sampling in the Fourier plane and the diffraction produced by squircle-geometry apertures of pixels. Also, a mathematical analysis is done in terms of the fringes visibility of the filters. Simulations and experimental results of the method are shown.
An essential and indispensable component of automated microscopy framework is the automatic focusing system, which determines the in-focus position of a given field of view by searching the maximum value of a focusing function over a range of z-axis positions. The focus function and its computation time are crucial to the accuracy and efficiency of the system. Sixteen focusing algorithms were analyzed for histological and histopathological images. In terms of accuracy, results have shown an overall high performance by most of the methods. However, we included in the evaluation study other criteria such as computational cost and focusing curve shape which are crucial for real-time applications and were used to highlight the best practices.
An essential and indispensable component of automated microscopy is the automatic focusing system, which
determines the in-focus position of a given field of view by searching for the maximal of an autofocus function
over a range of z-axis positions. The autofocus function and its computation time are crucial to the accuracy
and efficiency of the system. In this paper, we analyze and evaluate fifteen autofocus algorithms for biopsy and
cytology microscopy images, ranging from the already well known methods to those proposed recently. Results
have shown that there is a trade-off between computational cost and accuracy. Finally, the error committed by
each of the algorithms is presented.
Recent developments, based on lattice auto-associative memories, have been proposed as novel and alternative
techniques for endmember determination in hyperspectral imagery. The present paper discusses and compares
three such methods using, as a case study, the generation of vegetation abundance maps by constrained linear
unmixing. The first method uses the canonical min and max autoassociative memories as detectors for lattice
independence between pixel spectra; the second technique scans the image by blocks and selects candidate
spectra that satisfies the strong lattice independence criteria within each block. Both methods give endmembers
which correspond to pixel spectra, are computationally intensive, and the number of final endmembers are
parameter dependent. The third method, based on the columns of the matrices that define the scaled min and
max autoassociative memories, gives an approximation to endmembers that do not always correspond to pixel
spectra; however, these endmembers form a high-dimensional simplex that encloses all pixel spectra. It requires
less computations and always gives a fixed number of endmembers, from which final endmembers can be selected.
Besides a quantification of computational performance, each method is applied to discriminate vegetation in the
Jasper Ridge Biological Preserve geographical area.
Lattice associative memories also known as morphological associative memories are fully connected feedforward
neural networks with no hidden layers, whose computation at each node is carried out with lattice algebra
operations. These networks are a relatively recent development in the field of associative memories that has
proven to be an alternative way to work with sets of pattern pairs for which the storage and retrieval stages use
minimax algebra. Different associative memory models have been proposed to cope with the problem of pattern
recall under input degradations, such as occlusions or random noise, where input patterns can be composed
of binary or real valued entries. In comparison to these and other artificial neural network memories, lattice
algebra based memories display better performance for storage and recall capability; however, the computational
techniques devised to achieve that purpose require additional processing or provide partial success when inputs
are presented with undetermined noise levels. Robust retrieval capability of an associative memory model is
usually expressed by a high percentage of perfect recalls from non-perfect input. The procedure described here
uses noise masking defined by simple lattice operations together with appropriate metrics, such as the normalized
mean squared error or signal to noise ratio, to boost the recall performance of either the min or max lattice auto-associative
memories. Using a single lattice associative memory, illustrative examples are given that demonstrate
the enhanced retrieval of correct gray-scale image associations from inputs corrupted with random noise.
The advances in image spectroscopy have been applied for Earth observation at different wavelengths of the
electromagnetic spectrum using aircrafts or satellite systems. This new technology, known as hyperspectral
remote sensing, has found many applications in agriculture, mineral exploration and environmental monitoring
since images acquired by these devices register the constituent materials in hundred of spectral bands. Each pixel
in the image contains the spectral information of the zone. However, processing these images can be a difficult
task because the spatial resolution of each pixel is in the order of meters, an area of such size that can be composed
of different materials. The following research presents an alternative methodology to detect pixels in the image
that best represent the spectrum of one material with as little contamination of any other as possible. The
detection of these pixels, also called endmembers, represents the first step for image segmentation and is based
on morphological autoassociative memories and the property of strong lattice independence between patterns.
Morphological associative memories and strong lattice independence are concepts based on lattice algebra. Our
procedure subdivides a hyperspectral image into regions looking for sets of strong lattice independent pixels.
These patterns will be identified as endmembers and will be used for the construction of abundance maps.
Lattice independence and strong lattice independence of a set of pattern vectors are fundamental mathematical
properties that lie at the core of pattern recognition applications based on lattice theory. Specifically, the development
of morphological associative memories robust to inputs corrupted by random noise are based on strong
lattice independent sets, and real world problems, such as, autonomous endmember detection in hyperspectral
imagery, use auto-associative morphological memories as detectors of lattice independence. In this paper, we
present a unified mathematical framework that develops the relationship between different notions of lattice
independence currently used in the literature. Computational procedures are provided to test if a given set of
pattern vectors is lattice independent or strongly lattice independent; in addition, different techniques are fully
described that can be used to generate sets of vectors with the aforementioned lattice properties.