Showing papers by "Alan C. Bovik published in 1989"

Theory of order statistic filters and their relationship to linear FIR filters

Abstract: Necessary and/or sufficient conditions on both the filter coefficients and the signal process are derived in order that nonrecursive order statistic (OS) and linear filtering are equivalent operations. The results indicate that an understanding of OS filters hinges on a better understanding of the properties of signals containing logically monotonic components. The results extend a number of previous theories characterizing the well-known median and ranked-order filters to a broader class of filters and input signals. >

Locally monotonic regression

Abstract: A novel technique for shaping/smoothing discrete signals is introduced. The approach, known as locally monotonic regression, entails finding a locally monotonic signal that best approximates the given signal. The authors present the problem within a theoretical framework, show the existence of a solution, and give an algorithm that computes it. Several examples are used to illustrate the approach. >

Improvement in the resolution of three-dimensional data sets collected using optical serial sectioning

Abstract: SUMMARY In this paper an approach for improving the quality of 3-D microscopic images obtained through optical serial sectioning is described and implemented. A serially sectioned image is composed of a sequence of 2-D images obtained by incrementing the focusing plane of the microscope through the specimen of interest; ideally, the image obtained at each focusing plane should be in focus, and should contain information lying only within that plane. In practice, however, the images obtained contain redundant information from neighbouring focusing planes and are blurred by a three-dimensional low-pass distortion. These degradations are a consequence of the limited aperture of any optical system; using principles of geometric optics and allowing for the passage of light through the specimen, we are able to demonstrate that the microscope distortion can be described as a linear system, if the absorption of the specimen is assumed to be linear and non-diffractive. The transfer function of the microscope is found to zero a biconic region of 3-D spatial frequencies orientated along the optical axis; a closed-form expression is derived for the low-pass transfer function of the microscope outside the region of missing frequencies. The planar resolution of the serial sections can be greatly improved by convolving the image obtained with the inverse of the low-pass distortion function, although the missing cone of frequencies is not recoverable. The reconstruction technique is demonstrated using both simulated images, to demonstrate more clearly the effects of the distortion and the accuracy of the subsequent reconstruction, and actual experiments with a pollen grain and a stained preparation of human cerebellum tissue.

Generalized order statistic filters

Abstract: The authors explore generalizations of order statistic (OS) filters, a class of finite-width discrete windowing filters defined by linearly weighting the samples in the window according to their natural ordering as real numbers. The concept can be extended by defining generalized ordering rules generating different permutations of the sample prior to weighting. Although the resulting class of generalized OS filter is very broad (including, e.g. the linear filters), local signal ordering properties relating to local signal monotonicity unify them. It is envisaged that both the framework for filter/signal description and the class of filters generated will find use in many signal shaping applications. >

Improved initial approximation and intensity-guided discontinuity detection in visible-surface reconstruction

Abstract: Techniques are described for improving the speed and accuracy of iterative visible-surface reconstruction algorithms. In particular, the importance of obtaining accurate early information is emphasized, both in the initial surface approximation and in the early localization of surface discontinuities. The first of these goals is attained using a simple technique known as constraint expansion, which yields a good initial approximation while accounting for detected discontinuities. The second goal is attained by using the locations of the image irradiance edges as a guide in locating potential discontinuities. Discontinuity detection in later stages of computation is augmented by a double-thresholding strategy and discontinuity backtracking.

Computation of shape from stereo images with application to biological shape analysis

Abstract: This dissertation considers the three-dimensional analysis of objects using computational stereo vision techniques, with particular application to the analysis of microscopic-scale biological objects. The principal concern is the derivation of 3-D shape descriptions by integrating binocular and monocular measurements. In binocular processing, we focus the attention on developing a stereo matching algorithm effective for images of biological objects. Many objects of biological interest have ill-defined boundaries in shape and reflectance and often exhibit transparency. In addition, the limited illumination available in the light microscope often makes it difficult to obtain images of sufficiently high contrast. In our approach, a new matching algorithm is introduced using intensity gradients information to effectively solve the problem. The algorithm identifies corresponding points by examining whether two points have similar intensity gradients within a small neighborhood around those two points. Although the algorithm is motivated for biological shape analysis, it has turned out that the algorithm performs well for a wide range of input images. Shape descriptions are computed by exploiting a number of additional processing steps. Two different classes of shape are considered: solid objects and vascular networks. The first class of objects is described using a visible surface representation. An image segmentation approach is combined with the surface reconstruction process to yield a surface representation. Some techniques for computing shape parameters using a dense depth map are also discussed. The second class of objects is expressed in terms of a set of space curves. The 2-D curve representation of vascular networks computed through monocular analysis is integrated with disparity data to yield a space curve representation. Various computational aspects involved in the shape description are discussed in this dissertation. The efficacy of the approach is demonstrated using a number of microscopic-scale biological specimens. We also present an analysis of the imaging geometry in stereoscopic light microscopes in the context of the shape analysis problem.

Numerical Analysis of Image Patterns

Abstract: We find similarities between spatial pattern analysis and other low-level cooperative visual processes. Numerical algorithms for computing intrinsic scene attributes, e.g. shape-from-X (shading, texture, etc.) and optical flow typically involve estimating generalized orientation components via iterative constraint propagation. Smoothing or regularizing terms imposed on the constraint equations often enhance the uniqueness / stability (well-posedness) of the solutions. The numerical approach to visual pattern analysis developed here proceeds analogously via estimation of emergent 2-D image frequencies. Unlike shape-from-X or optical flow paradigms, constraints are derived from the responses of multiple oriented spatial frequency channels rather than directly from the image irradiance measurements. By using channel filters that are sufficiently concentrated in both space and frequency, highly accurate spatial frequency estimates are computed on a local basis. Two methods are proposed. In the first, constrained estimates of the emergent image frequencies are obtained by resolving the responses of multiple channel filters in a process similar to photometric stereo. The second approach formulates the estimation of frequencies as an extremum problem regularized by a smoothing term. An iterative constraint propagation algorithm is developed analogous to those used in variational / relaxational approaches to shape-from-X (shading, texture) and optical flow. Examples illustrate each approach using synthetic and natural images.

Channel interactions in visible pattern analysis

Abstract: The efficacy of the 2-D Gabor channel filters for segmenting images based on the division of the image into textures was established previously. In the present work, the authors extend the model for the direct estimation of the emergent spatially localized orientation/frequencies of visible patterns using a variational scheme. The most significant result of this extension is that patterns with space-varying frequency characteristics, arising from, e.g. surface deformation, can still be analyzed and segregated. Moreover, the information extracted can provide a means for developing shape-from-texture algorithms that are optimally localized. The implementation of the filtering scheme is described. >

Fast Image Coding Using Simple Image Patterns

Abstract: We present a very fast image coding algorithm that employs the recently-developed visual pattern image coding (VPIC) algorithm embedded in a multi-resolution (pyramid) structure. At each level in the hierarchy, the image is coded by the VPIC algorithm [1]. The low-resolution images coded at the upper levels of the pyramid are used to augment coding of the higher-resolution images. The interaction between the different resolution levels is both simple and computationally efficient, and yields a significant increase in compression ratio relative to simple VPIC with improved image quality and with little increase in complexity. The resulting hierarchical VPIC (HVPIC) algorithm achieves compression ratios of about 24:1 and in the implementation demonstrated here, requires only 22.8 additions and 3.84 multiplications per image pixel.

Chromatic stereopsis

Abstract: One approach to developing faster, more robust stereo algorithms is to seek a more complete and efficient use of information available in stereo images. The use of chromatic (color) information has been largely neglected in this regard. Motivations for using chromatic information are discussed, including strong evidence for the use of chromatic information in the human stereo correspondence process in the form of a novel psychophysical experiment which we have performed. Specifically, we measured the minimum disparity needed to produce a reversal in apparent depth in ambiguous chromatic "wallpaper" stereograms. Our results indicate that chromatic information plays an important role in the stereo correspondence process when luminances variations are present. To investigate the potential role of chromatic information in computational stereo algorithms, a novel chromatic matching constraint -- the chromatic gradient matching constraint -- is presented. Then, a thorough analysis of the utility of this constraint in the PMF Algorithm is performed for a large range of sizes of the matching strength support neighborhood, and the performances of the algorithm with and without these constraints are directly compared in terms of disambiguation ability, matching accuracy and algorithm speed. The results demonstrate that chromatic information can gready reduce the matching ambiguity, while significantly increasing both matching accuracy and algorithm speed.

Numerical analysis of visual patterns

Abstract: Summary form only given, as follows. Similarities are found between spatial pattern analysis and other low-level cooperative image analysis tasks. Visual pattern analysis proceeds analogously via estimation of emergent 2D image frequencies. Unlike shape-from-X or optical flow paradigms, constraints are derived from the responses of multiple oriented spatial frequency channels rather than directly from the image irradiance measurements. By selecting channel filters that are sufficiently concentrated in both space and frequency, highly accurate spatial frequency estimates are computed on a local basis. Two related methods are proposed. In the first, a constrained estimate of the emergent image frequencies is obtained by resolving the responses of multiple channel filters in a process similar to photometric stereo. The second approach formulates the estimation of frequencies as an extremum problem regularized by a smoothing term. An iterative constraint propagation algorithm is developed analogous to those used in variational/relaxational approaches to shape-from-X (shading, texture) and optical flow. Examples illustrate both approaches using synthetic and natural images. >

Computing 3-D symbolic representation of blood vessels from stereo-microscopic images

Abstract: The authors consider the three-dimensional analysis of vacular networks from stereo-microscopic images. The principal concern is to describe their 3-D structure using a set of parametric space curves. This representation is computed by integrating monocular and binocular processing: the 2-D curve representation of blood vessels computed by monocular analysis is integrated with disparity data to yield a space curve representation. A connection graph is computed to indicate the connection among space curves. The efficacy of the approach was demonstrated using vascular cast images. >

From stereo-microscopic images

Abstract: This paper considers the three-dimensional anal- ysis of vascular networks from stereo-microscopic images. The principal concern is to describe the 3-D structure of vascular networks using a set of parametric space curves. This repre- sentation is computed by integrating monocular and binocu- lar processing; the 2-D curve representation of blood vessels computed through monocular analysis is integrated with dis- parity data to yield a space curve representation. A connec- tion graph is also computed to indicate the connections among space curves.