The local structure of image discontinuities in one dimension

Trajectory Fusion for Three-dimensional Volume Reconstruction

We address the 3D volume reconstruction problem from depth adjacent sub-volumes acquired by a confocal laser scanning microscope (CLSM). Our goal is to align the sub-volumes by estimating a set of optimal global transformations that preserve morphological continuity of medical structures, e.g., blood vessels, in the reconstructed 3D volume. We approach the problem by learning morphological characteristics of structures of interest in each sub-volume to understand global alignment transformations. Based on the observations of morphology, sub-volumes are aligned by connecting the morphological features at the sub-volume boundaries by minimizing morphological discontinuity. To minimize the discontinuity, we introduce three morphological discontinuity metrics: discontinuity magnitude at sub-volume boundary points, and overall and junction discontinuity residuals after polynomial curve fitting to multiple aligned sub-volumes. The proposed techniques have been applied to the problem of aligning CLSM sub-volumes acquired from four consecutive physical cross sections. Our experimental results demonstrated significant improvements of morphological smoothness of medical structures in comparison with the results obtained by feature matching at the sub-volume boundaries. The experimental results were evaluated by visual inspection and by quantifying morphological discontinuity metrics.

Intravital leukocyte detection using the gradient inverse coefficient of variation

The problem of identifying and counting rolling leukocytes within intravital microscopy is of both theoretical and practical interest. Currently, methods exist for tracking rolling leukocytes in vivo, but these methods rely on manual detection of the cells. In this paper we propose a technique for accurately detecting rolling leukocytes based on Bayesian classification. The classification depends on a feature score, the gradient inverse coefficient of variation (GICOV), which serves to discriminate rolling leukocytes from a cluttered environment. The leukocyte detection process consists of three sequential steps: the first step utilizes an ellipse matching algorithm to coarsely identify the leukocytes by finding the ellipses with a locally maximal GICOV. In the second step, starting from each of the ellipses found in the first step, a B-spline snake is evolved to refine the leukocytes boundaries by maximizing the associated GICOV score. The third and final step retains only the extracted contours that have a GICOV score above the analytically determined threshold. Experimental results using 327 rolling leukocytes were compared to those of human experts and currently used methods. The proposed GICOV method achieves 78.6% leukocyte detection accuracy with 13.1% false alarm rate.

A structural-description-based vision system for automatic object recognition

This paper presents the results of the integration of a proposed part-segmentation-based vision system. The first stage of this system extracts the contour of the object using a hybrid first- and second-order differential edge detector. The object defined by its contour is then decomposed into its constituent parts using the part segmentation algorithm given by Bennamoun (1994). These parts are then isolated and modeled with 2D superquadrics. The parameters of the models are obtained by the minimization of a best-fit cost function. The object is then represented by its structural description which is a set of data structures whose predicates represent the constituent parts of the object and whose arguments represent the spatial relationship between these parts. This representation allows the recognition of objects independently of their positions, orientations, or sizes. It is also insensitive to objects with partially missing parts. In this paper, examples illustrating the acquired images of objects, the extraction of their contours, the isolation of the parts, and their fitting with 2D superquadrics are reported. The reconstruction of objects from their structural description is illustrated and improvements are suggested.

Nonlinear filtering approach to 3-D gray-scale image interpolation

Three-dimensional (3-D) images are now common in radiology. A 3-D image is formed by stacking a contiguous sequence of two-dimensional cross-sectional images, or slices. Typically, the spacing between known slices is greater than the spacing between known points on a slice. Many visualization and image-analysis tasks, however, require the 3-D image to have equal sample spacing in all directions. To meet this requirement, one applies an interpolation technique to the known 3-D image to generate a new uniformly sampled 3-D image. The authors propose a nonlinear-filter-based approach to gray-scale interpolation of 3-D images. The method, referred to as column-fitting interpolation, is reminiscent of the maximum-homogeneity filter used for image enhancement. The authors also draw upon the paradigm of relaxation labeling to devise an improved column-fitting interpolator. Both methods are typically more effective than traditional gray-scale interpolation techniques.

On the problem of correspondence in range data and some inelastic uses for elastic nets

In this work, the authors propose a novel method to obtain correspondence between range data across image frames using neural like mechanisms. The method is computationally efficient and tolerant of noise and missing points. Elastic nets, which evolved out of research into mechanisms to establish ordered neural projections between structures of similar geometry, are used to cast correspondence as an optimization problem. This formulation is then used to obtain approximations to the motion parameters under the assumption of rigidity (inelasticity). These parameter scan be used to recover correspondence. Experimental results are presented to establish the veracity of the scheme and the method is compared to earlier attempts in this direction.

A theory of visual interpolation in object perception

We describe a new theory explaining the perception of partly occluded objects and illusory figures, from both static and kinematic information, in a unified framework. Three ideas guide our approach. First, perception of partly occluded objects, perception of illusory figures, and some other object perception phenomena derive from a single boundary interpolation process. These phenomena differ only in respects that are not part of the unit formation process, such as the depth placement of units formed. Second, unit formation from static and kinematic information can be treated in the same general framework. Third, spatial and spatiotemporal discontinuities in the boundaries of optically projected areas are fundamental to the unit formation process. Consistent with these ideas, we develop a detailed theory of unit formation that accounts for most cases of boundary perception in the absence of local physical specification. According to this theory, discontinuities in the first derivative of projected edges are initiating conditions for unit formation. A formal notion of relatability is defined, specifying which physically given edges leading into discontinuities can be connected to others by interpolated edges. Intuitively, relatability requires that two edges be connectable by a smooth, monotonic curve. The roots of the discontinuity and relatability notions in ecological constraints on object perception are discussed. Finally, we elaborate our approach by discussing related issues, some new phenomena, connections to other approaches, and issues for future research.

Points and endpoints: a size/spacing constraint for dot grouping

One-dimensional arrangements of dots immediately group into contours. It is reported that, when these contours participate in certain larger arrangements, there is an abrupt point at which the percept changes as a function of dot spacing (or density along the contour). Closely spaced arrangements give rise to subjective effects involving apparent brightness and depth, whereas sparsely spaced ones do not. The effects are most clear in configurations that involve endpoints and possible occlusions. For these configurations, densely dotted contours are perceptually equivalent to solid ones, but sparse ones are not. This change in percept occurs abruptly and consistently at a dot to space ratio of 1:5, when the dot density is normalized by dot size, and this point is called the size/spacing constraint. It holds only for dots of the order of 1 min visual angle in diameter when small to modest contrast values are used. The subjective effects are not present for dotted contours (or even for solid ones) that are smaller (less than 0.5 min), and differ for contours that are larger (greater than 10 min). To demonstrate the significance of size/spacing constraints for early vision, a framework for grouping consisting of processes at many different levels is outlined, and the requirements for the earliest one (orientation selection) are sketched in greater detail. The size/spacing constraint follows directly from one of these requirements--receptive field structure--and seems to indicate a switch from early orientation-selection processes to later ones.

Author's Reply

We present evidence that the Laplacian zero-crossing operator does not use neighborhood information as effectively as the second directional derivative edge operator. We show that the use of a Gaussian smoother with standard deviation 5.0 for the Laplacian of a Gaussian edge operator with a neighborhood size of 50 × 50 both misses and misplaces edges on an aerial image of a mobile home park. Contrary to Grimson and Hildreth's results, our results of the Laplacian edge detector on a noisy test checkerboard image are also not as good as the second directional derivative edge operator. We conclude by discussing a number of open issues on edge operator evaluation.