This PDF file contains the editorial “Guest Editorial: Imaging Through Scattering Media” for JEI Vol. 12 Issue 04

We demonstrate the effect of representing the solution of a reconstruction as a linear expansion of local basis functions, i.e., functions that have limited support over the domain. Local basis functions are computationally efficient because they lead to linear systems that are sparse. We present two different types of local basis functions: piecewise polynomial regular and irregular functions, and radially symmetric functions on a regular grid (blobs). We demonstrate that the use of higher order polynomial basis functions as well as radially symmetric functions with appropriate choice of shape parameters can reduce the image artifact present in low-order polynomial bases.

We report on the derivation and implementation of the first three-dimensional optical tomographic image reconstruction scheme that is based on the time-independent equation of radiative transfer (ERT) and allows for arbitrarily shaped medium boundaries and arbitrary spatial material distributions. The scheme builds on the concept of model-based iterative image reconstruction, in which a forward model provides prediction of detector readings, and a gradient-based updating scheme minimizes an appropriately defined objective function. The forward model is solved by using an even-parity formulation of the ERT, which lends itself to a finite-element discretization method. The finite-element technique provides the suitable framework for predicting light propagation in arbitrarily shaped three-dimensional media. For an efficient way of calculating the gradient of the objective function we have implemented an adjoint differentiation scheme. Initial reconstruction results using synthetic data from simple media and a three-dimensional mesh of the human forehead illustrate the performance of the code.

The applicability of transform algorithms generally used in projection-computed tomography is substantiated for the case of medical optical diffusion tomography (ODT). To reconstruct tissue optical inhomogeneities, a new method based on a concept of an average statistical trajectory for transfer of light energy [photon average trajectory (PAT)] is proposed. By this method, the inverse problem of ODT is reduced to a solution of an integral equation with integration along a PAT. Within the internal zone of the object, well away from the boundaries, PATs tend to a straight line, and standard integral algorithms based on the inverse Radon transform may be used to restore diffuse optical images. To demonstrate the capabilities of the PAT method, a numerical experiment on cross sectional reconstruction of cylindrical strongly scattering objects with low-contrast absorbing inhomogeneities is conducted. To solve the time-domain ODT inverse problem, two filtered backprojection algorithms (of Radon and Vainberg) are used. The reconstruction results are compared with those obtained by a well-known software package for temporal optical absorption and scattering tomography, based on multiple solutions of a diffusion equation. It is shown that in important cases of low-contrast absorbing inhomogeneities, the PAT method using the Vainberg algorithm allows reconstruction of tissue optical inhomogeneities with a 20% gain in spatial resolution.

Clinical near-infrared (NIR) imaging is a diagnostic tool to quantify hemoglobin concentration and oxygen saturation within tissue. In order to remove system offsets and correct data acquired from the breast during clinical examination, a homogenous tissue-simulating phantom is routinely employed for system calibration. In this study, both hard resin and soft silicon-based materials were used to make calibration phantoms with different physical sizes, shapes, elasticity, and optical properties. Using these calibration phantoms, the imaging performance of two different fiber optic configurations was tested. Images from a patient with a biopsy-confirmed ductal carcinoma tumor were also used to determine the effect of calibration object choice upon real tissue image reconstructions. Softer silicon-based calibration phantoms were found to mimic the elastic properties of human breast tissue quite well with an elastic modulus that could be tailored between 100 and 230 KPa. These values agree with estimates of breast tissue elasticity and we have found that these phantoms provide an optimal model for mimicking breast tissue, while having homogeneous properties, which are ideal for calibration and validation of the system. In this study, the performance of the imaging system with colocalized source and detector optical fibers (transceiver system) yielded better image quality than the system with separated-source detector fibers. In vivo imaging of the ductal carcinoma revealed increased total hemoglobin within the tumor.

We present a color filter array interpolation algorithm to provide the missing colors associated with the commonly used Bayer pattern in digital still camera systems. The developed algorithm utilizes color correlation and directional derivative attributes of neighboring color pixels and is thus named C2D2. The main advantage of this algorithm is that it requires no user-defined parameter, as is the case in many edge-adaptive color filter array interpolation algorithms. Both an objective and subjective comparison are carried out with two other popular edge-adaptive algorithms. The results indicate that this algorithm consistently generates lower mean-squared interpolation errors in the RGB and L^*a^*b^* color spaces.

Digital still color cameras sample the visible spectrum using an array of color filters overlaid on a CCD, such that each pixel samples only one color band. The resulting mosaic of color samples is processed to produce a high-resolution color image, such that a value of a color band not sampled at a certain location is estimated from its neighbors. This is often referred to as "demosaicking." The human retina has a similar structure, although the distribution of cones is not as regular. Motivated by the human visual system, we propose an adaptive demosaicking technique in the framework of bilateral filtering. This approach provides us with a means to denoise, sharpen, and demosaic the image simultaneously. The proposed method, along with a variety of existing demosaicking strategies, are run on synthetic images and real-world images for comparative purposes. A recently proposed image comparison measure geared specifically toward demosaicking has also been applied to these images to provide a performance measure.

Digital interference holography (DIH) is being developed as a novel method of microscopic 3-D imaging. A number of holographic fields are numerically calculated from optically recorded holograms using a range of wavelengths. Numerical superposition of these fields results in a tomographic representation of the object with narrow axial resolution. We demonstrate the practicality of DIH in microscopic imaging with a set of preliminary experiments, yielding approximately 3 μm of lateral resolution and 10 µm of axial resolution, using a simple optical setup and straightforward numerical algorithms.

We propose a fast pairwise nearest neighbor (PNN)-based O(N log N) time algorithm for multilevel nonparametric thresholding, where N denotes the size of the image histogram. The proposed PNN-based multilevel thresholding algorithm is considerably faster than optimal thresholding. On a set of 8 to 16 bits-per-pixel real images, experimental results also reveal that the proposed method provides better quality than the Lloyd-Max quantizer alone. Since the time complexity of the proposed thresholding algorithm is log linear, it is applicable in real-time image processing applications.

We propose a compact description method for image gamut shell shapes. The 3-D image-to-device gamut mapping algorithm (I-D GMA) is an ideal way to map a display image into the inside of a printer gamut, keeping the loss in color information to a minimum. The key point in I-D GMA is to make use of the relation in image and device gamut boundaries along the mapping line. The image gamut surface is shaped into polygon meshes by extracting the most outside points from the random color distributions in the images. A compact gamut boundary descriptor (GBD) attached to the image data is used for executing the I-D GMA flexibly on the user side. In our proposal, the image gamut shell shape is compactly represented by a 2-D monochromatic image, called the r image. Each pixel in the r image denotes the maximum radial vector magnitude extracted from the subdivided segment in discrete polar angle color space. Since the r image is highly correlated spatially when the image has a smooth gamut shell surface, it is easily compressed by applying the conventional transform coding techniques such as the discrete cosine transform (DCT), singular value decomposition, (SVD) or wavelet. The compressed ultra-compact r image is delivered to the users attached to the image data and is used for I-D gamut mapping. We present how the complicated 3-D image gamut shell shape is simply described by the 2-D monochromatic r image and easily reconstructed with its surface colors. In practice, wavelet coding was most efficient in compressing the r image as compared with a DCT-based JPEG. It is shown that the complex shell shapes are well reconstructed from around 400 bytes of compact data compressed by SVD or less by a wavelet.

Moiré phenomena of different types are frequently encountered in electronic imaging. Most common are moiré effects that occur between periodic structures. These effects have been intensively investigated in the past, and their mathematical theory is today fully understood. The same is true for moiré effects between repetitive layers (i.e., between geometric transformations of periodic layers). However, although moiré effects that occur between random layers (Glass patterns) have long been recognized, only little is known today about their mathematical behavior. In this work we study the behavior of such moirés, and compare it with analogous results from the periodic case. We show that all cases, periodic or not, obey the same basic mathematical rules, in spite of their different visual properties. This leads us to a unified approach that explains both the behavior of Glass patterns in the stochastic case, and the well-known behavior of the moiré patterns in periodic or repetitive cases.

The demand for more pixels is beginning to be met as manufacturers increase the native resolution of projector chips. Tiling several projectors still offers a solution to augment the pixel capacity of a display. However, problems of color and illumination uniformity across projectors need to be addressed as well as the computer software required to drive such devices. We present the results obtained on a desktop-size tiled projector array of three D-ILA projectors sharing a common illumination source. A short throw lens (0.8:1) on each projector yields a 21-in. diagonal for each image tile; the composite image on a 3×1 array is 3840×1024 pixels with a resolution of about 80 dpi. The system preserves desktop resolution, is compact, and can fit in a normal room or laboratory. The projectors are mounted on precision six-axis positioners, which allow pixel level alignment. A fiber optic beamsplitting system and a single set of red, green, and blue dichroic filters are the key to color and illumination uniformity. The D-ILA chips inside each projector can be adjusted separately to set or change characteristics such as contrast, brightness, or gamma curves. The projectors were then matched carefully: photometric variations were corrected, leading to a seamless image. Photometric measurements were performed to characterize the display and are reported here. This system is driven by a small PC cluster fitted with graphics cards and running Linux. It can be scaled to accommodate an array of 2×3 or 3×3 projectors, thus increasing the number of pixels of the final image. Finally, we present current uses of the display in fields such as astrophysics and archaeology (remote sensing).

Image cross talk is a problem specific to stereoscopic display, which influences the conspicuity of "ghost images" and the development of asthenopia. The higher the image cross talk, the lower the visual comfort for the observer, who may suffer from eye strain and headaches. The stereoscopic laser-based display system presented uses processing to provide command variables for the optical modulation device from the pixel intensities of both views of the stereo pairs. Two processing solutions, one minimizing the quadratic error and the other one canceling the image cross talk, are developed and compared using original evaluation tools. Finally, by comparing numerical results and the visual effects obtained with tests on stereo pairs, the presented results show objectively that the second processing solution is preferable.

The interrelationships among spatial distribution in the red, green, and blue channels of texture images of differently woven textile fabrics are investigated. A computational model for color mapping is developed based on the channel proportionality found in the investigation. The computational model developed has two modes: gray-to-color mapping (GCM) and color-to-color mapping (CCM) that deal with different images. For the GCM mode, the spatial distribution of luminance is known. The algorithm needs to deduce data in three channels for a color image from 1-D spatial distribution of luminance. Whereas in the CCM mode, the information for each of the three channels is known. Numerical and psychophysical experiments are carried out to evaluate the accuracy of the color mapping algorithm quantitatively. Satisfactory color accuracy of the mapped images was obtained according to the results of both numerical calculation and visual experiment.

We present an approach of color image interpretation and a recall scheme. The components of the system include image feature extraction, indexing process, and linguistic inference rules constructed for image interpretation. Based on these processes, each one of the segmented regions in an image can be described in terms of global linguistic meaning. We use the properties of color, texture, and spatial relationships to represent image features of an object. Each object can be first classified into a cluster by means of human experiences and knowledge, and can obtain the corresponding features of an object by using our proposed method. According to human experiences and cognition ability, linguistic inference rules can be further constructed. On the other hand, it can explain the interesting regions in an image. One of the distinguishing aspects of this system is the automatic recall process that uses both the localized region information and indexing process. The main procedure has two parts, which consist of the forward and recall processes. The forward process mainly achieves the linguistic meaning description of objects for an image. The recall process reconstructs the image region, which presents the rough mental image of human memory by means of the former result. Experiments show that this approach is reasonable and feasible.

Conventional quantitative coronary arteriography techniques are limited for the case of small vessel diameters (diam<1.5 mm). A watergauge algorithm is proposed for accurate estimation of small vessel diameters. The algorithm consists of setting up watergauges and waterlines on intensity profiles, followed by searching for the intersections of the waterlines with the profile. The vessel paths are naturally represented by valley courses, thereby avoiding the unnecessary image inversion. The scan direction of the intensity profiles is perpendicular to the vessel direction, which is determined from the valley course. The edge points on both sides of a valley on the scanline profile are then identified using a watergauge algorithm. The term "watergauge" reflects the fact that this algorithm is independent of the ramp shape of the scanline profile. It is only dependent on the valley/peak (minima/maxima) features of the profile. Therefore, this watergauge algorithm exhibits high stability to image noise and cluttered background. The proposal of this algorithm is motivated by observing the intensity drop caused by the convolution blurring of an imaging system, under the influences of various factors including image blurring, vessel diameter, spatial orientation, and injected contrast materials. The technique is experimentally verified using physical phantoms, and the results are compared with the edge detection technique using a derivative-based method. In conclusion, the watergauge algorithm offers an effective method for diameter measurement by exploiting the local minima/maxima features of a profile, as compared with the derivative-based edge detection, which exploits the ramp behavior of the profile. Experiments show that, for lumen measurement of large vessels (diam>1.5 mm), both the watergauge algorithm and the derivative-based method produce similar results; however, for the small vessel (diam<1.5 mm), the watergauge algorithm yields better results. The success rate of the watergauge algorithm was substantially better than the derivative-based method for small vessel diameters with nonuniform or cluttered background.

This PDF file contains the editorial “Book Rvw, Handbook of Image Quality: Characterization and Prediction," by Brian W. Keelan for JEI Vol. 12 Issue 04