Shapes, shocks, and deformations I: The components of two-dimensional shape and the reaction-diffusion space

Edge-Supervised Linear Object Skeletonization for High-Speed Camera

This paper presents a high-speed skeletonization algorithm for detecting the skeletons of linear objects from their binary images. The primary objective of our research is to achieve rapid extraction of the skeletons from binary images while maintaining accuracy for high-speed cameras. The proposed algorithm uses edge supervision and a branch detector to efficiently search inside the object, avoiding unnecessary computation on irrelevant pixels outside the object. Additionally, our algorithm addresses the challenge of self-intersections in linear objects with a branch detection module, which detects existing intersections and initializes new searches on emerging branches when necessary. Experiments on various binary images, such as numbers, ropes, and iron wires, demonstrated the reliability, accuracy, and efficiency of our approach. We compared the performance of our method with existing skeletonization techniques, showing its superiority in terms of speed, especially for larger image sizes.

The many facets of shape

Shape is an interesting property of objects because it is used in ordinary discourse in ways that seem to have little connection to how it is typically defined in mathematics. The present article describes how the concept of shape can be grounded within Euclidean and non-Euclidean geometry and also to human perception. It considers the formal methods that have been proposed for measuring the differences among shapes and how the performance of those methods compares with shape difference thresholds of human observers. It discusses how different types of shape change can be perceptually categorized. It also evaluates the specific data structures that have been used to represent shape in models of both human and machine vision, and it reviews the psychophysical evidence about the extent to which those models are consistent with human perception. Based on this review of the literature, we argue that shape is not one thing but rather a collection of many object attributes, some of which are more perceptually salient than others. Because the relative importance of these attributes can be context dependent, there is no obvious single definition of shape that is universally applicable in all situations.

Constant curvature modeling of abstract shape representation

How abstract shape is perceived and represented poses crucial unsolved problems in human perception and cognition. Recent findings suggest that the visual system may encode contours as sets of connected constant curvature segments. Here we describe a model for how the visual system might recode a set of boundary points into a constant curvature representation. The model includes two free parameters that relate to the degree to which the visual system encodes shapes with high fidelity vs. the importance of simplicity in shape representations. We conducted two experiments to estimate these parameters empirically. Experiment 1 tested the limits of observers’ ability to discriminate a contour made up of two constant curvature segments from one made up of a single constant curvature segment. Experiment 2 tested observers’ ability to discriminate contours generated from cubic splines (which, mathematically, have no constant curvature segments) from constant curvature approximations of the contours, generated at various levels of precision. Results indicated a clear transition point at which discrimination becomes possible. The results were used to fix the two parameters in our model. In Experiment 3, we tested whether outputs from our parameterized model were predictive of perceptual performance in a shape recognition task. We generated shape pairs that had matched physical similarity but differed in representational similarity (i.e., the number of segments needed to describe the shapes) as assessed by our model. We found that pairs of shapes that were more representationally dissimilar were also easier to discriminate in a forced choice, same/different task. The results of these studies provide evidence for constant curvature shape representation in human visual perception and provide a testable model for how abstract shape descriptions might be encoded.

Development of a transperineal prostate biopsy robot guided by MRI-TRUS image

BACKGROUND

In the transrectal ultrasound (TRUS)-guided transperineal prostate biopsy, doctors determine the biopsy target by observing the prostate region in TRUS images. However, ultrasound images with low imaging quality make doctors easy to be interfered when determining the biopsy route, which reduces the biopsy success rate.

METHODS

This paper introduces the guidance method of magnetic resonance image (MRI) registration to ultrasound image and develops a 5-degrees of freedom robot for prostate biopsy guided by MRI-TRUS image. The robot uses a structure attached to the ultrasound probe to reduce the space occupied. By registering the posture relationship between MRI, TRUS image, ultrasonic probe and the robot base, the accurate localization of the suspected lesion area can be achieved with the preoperative MRIs.

RESULTS

The prostate phantom biopsy based on the robotic biopsy system in this paper, the average biopsy error is 1.44 mm, and the maximum biopsy error is 2.23 mm.

CONCLUSIONS

We build a robotic biopsy platform with prostate phantom, and evaluate the biopsy accuracy of MRI-TRUS guided prostate biopsy robot, the results meet clinical prostate biopsy requirements.

Fitting unbranching skeletal structures to objects

Representing an object by a skeletal structure can be powerful for statistical shape analysis if there is good correspondence of the representations within a population. Many anatomic objects have a genus-zero boundary and can be represented by a smooth unbranching skeletal structure that can be discretely approximated. We describe how to compute such a discrete skeletal structure ("d-s-rep") for an individual 3D shape with the desired correspondence across cases. The method involves fitting a d-s-rep to an input representation of an object's boundary. A good fit is taken to be one whose skeletally implied boundary well approximates the target surface in terms of low order geometric boundary properties: (1) positions, (2) tangent fields, (3) various curvatures. Our method involves a two-stage framework that first, roughly yet consistently fits a skeletal structure to each object and second, refines the skeletal structure such that the shape of the implied boundary well approximates that of the object. The first stage uses a stratified diffeomorphism to produce topologically non-self-overlapping, smooth and unbranching skeletal structures for each object of a population. The second stage uses loss terms that measure geometric disagreement between the skeletally implied boundary and the target boundary and avoid self-overlaps in the boundary. By minimizing the total loss, we end up with a good d-s-rep for each individual shape. We demonstrate such d-s-reps for various human brain structures. The framework is accessible and extensible by clinical users, researchers and developers as an extension of SlicerSALT, which is based on 3D Slicer.

Skeletonizing the Dynamics of Soft Continuum Body from Video

Soft continuum bodies have demonstrated their effectiveness in generating flexible and adaptive functionalities by capitalizing on the rich deformability of soft material. Compared with a rigid-body robot, it is in general difficult to model and emulate the morphology dynamics of a soft continuum body. In addition, a soft continuum body potentially has an infinite degree of freedom, requiring considerable labor to manually annotate its dynamics from external sensory data such as video. In this study, we propose a novel noninvasive framework for automatically extracting the skeletal dynamics from video of a soft continuum body and show the applications and effectiveness of our framework. First, we demonstrate that our framework can extract skeletal dynamics from animal videos, which can be effectively utilized for the analysis of soft continuum body including animal motion. Next, we focus on a soft continuum arm, a commonly used platform in soft robotics, and evaluate the potential information-processing capability. Normally, to control such a high-dimensional system, it is necessary to introduce many sensors to completely capture the motion dynamics, causing the deterioration of the material's softness. We illustrate that the evaluation of the memory capacity and sensory reconstruction error enables us to verify the minimum number of sensors sufficient for fully grasping the state dynamics, which is highly useful in designing a sensor arrangement for a soft robot. Also, we release the software developed in this study as open source for biology and soft robotics communities, which contributes to automating the annotation process required for the motion analysis of soft continuum bodies.

The role of semantics in the perceptual organization of shape

Establishing correspondence between objects is fundamental for object constancy, similarity perception and identifying transformations. Previous studies measured point-to-point correspondence between objects before and after rigid and non-rigid shape transformations. However, we can also identify 'similar parts' on extremely different objects, such as butterflies and owls or lizards and whales. We measured point-to-point correspondence between such object pairs. In each trial, a dot was placed on the contour of one object, and participants had to place a dot on 'the corresponding location' of the other object. Responses show correspondence is established based on similarities between semantic parts (such as head, wings, or legs). We then measured correspondence between ambiguous objects with different labels (e.g., between 'duck' and 'rabbit' interpretations of the classic ambiguous figure). Despite identical geometries, correspondences were different across the interpretations, based on semantics (e.g., matching 'Head' to 'Head', 'Tail' to 'Tail'). We present a zero-parameter model based on labeled semantic part data (obtained from a different group of participants) that well explains our data and outperforms an alternative model based on contour curvature. This demonstrates how we establish correspondence between very different objects by evaluating similarity between semantic parts, combining perceptual organization and cognitive processes.

Skeletal representations of shape in human vision: Evidence for a pruned medial axis model

A representation of shape that is low dimensional and stable across minor disruptions is critical for object recognition. Computer vision research suggests that such a representation can be supported by the medial axis-a computational model for extracting a shape's internal skeleton. However, few studies have shown evidence of medial axis processing in humans, and even fewer have examined how the medial axis is extracted in the presence of disruptive contours. Here, we tested whether human skeletal representations of shape reflect the medial axis transform (MAT), a computation sensitive to all available contours, or a pruned medial axis, which ignores contours that may be considered "noise." Across three experiments, participants (N = 2062) were shown complete, perturbed, or illusory two-dimensional shapes on a tablet computer and were asked to tap the shapes anywhere once. When directly compared with another viable model of shape perception (based on principal axes), participants' collective responses were better fit by the medial axis, and a direct test of boundary avoidance suggested that this result was not likely because of a task-specific cognitive strategy (Experiment 1). Moreover, participants' responses reflected a pruned computation in shapes with small or large internal or external perturbations (Experiment 2) and under conditions of illusory contours (Experiment 3). These findings extend previous work by suggesting that humans extract a relatively stable medial axis of shapes. A relatively stable skeletal representation, reflected by a pruned model, may be well equipped to support real-world shape perception and object recognition.

Frequency tuning of shape perception revealed by classification image analysis

Classification image analysis is a powerful technique for elucidating linear detection and discrimination mechanisms, but it has primarily been applied to contrast detection. Here we report a novel classification image methodology for identifying linear mechanisms underlying shape discrimination. Although prior attempts to apply classification image methods to shape perception have been confined to simple radial shapes, the method proposed here can be applied to general 2-D (planar) shapes of arbitrary complexity, including natural shapes. Critical to the method is the projection of each target shape onto a Fourier descriptor (FD) basis set, which allows the essential perceptual features of each shape to be represented by a relatively small number of coefficients. We demonstrate that under this projection natural shapes are low pass, following a relatively steep power law. To efficiently identify the observer's classification template, we employ a yes/no paradigm and match the spectral density of the stimulus noise in FD space to the power law density of the target shape. The proposed method generates linear template models for animal shape detection that are predictive of human judgments. These templates are found to be biased away from the ideal, overly weighting lower frequencies. This low-pass bias suggests that higher frequency shape processing relies on nonlinear mechanisms.

Fuzzy Object Skeletonization: Theory, Algorithms, and Applications

Skeletonization offers a compact representation of an object while preserving important topological and geometrical features. Literature on skeletonization of binary objects is quite mature. However, challenges involved with skeletonization of fuzzy objects are mostly unanswered. This paper presents a new theory and algorithm of skeletonization for fuzzy objects, evaluates its performance, and demonstrates its applications. A formulation of fuzzy grassfire propagation is introduced; its relationships with fuzzy distance functions, level sets, and geodesics are discussed; and several new theoretical results are presented in the continuous space. A notion of collision-impact of fire-fronts at skeletal points is introduced, and its role in filtering noisy skeletal points is demonstrated. A fuzzy object skeletonization algorithm is developed using new notions of surface- and curve-skeletal voxels, digital collision-impact, filtering of noisy skeletal voxels, and continuity of skeletal surfaces. A skeletal noise pruning algorithm is presented using branch-level significance. Accuracy and robustness of the new algorithm are examined on computer-generated phantoms and micro- and conventional CT imaging of trabecular bone specimens. An application of fuzzy object skeletonization to compute structure-width at a low image resolution is demonstrated, and its ability to predict bone strength is examined. Finally, the performance of the new fuzzy object skeletonization algorithm is compared with two binary object skeletonization methods.

Colour, contours, shading and shape: flow interactions reveal anchor neighbourhoods

Two dilemmas arise in inferring shape information from shading. First, depending on the rendering physics, images can change significantly with (even) small changes in lighting or viewpoint, while the percept frequently does not. Second, brightness variations can be induced by material effects-such as pigmentation-as well as by shading effects. Improperly interpreted, material effects would confound shading effects. We show how these dilemmas are coupled by reviewing recent developments in shape inference together with a role for colour in separating material from shading effects. Aspects of both are represented in a common geometric (flow) framework, and novel displays of hue/shape interaction demonstrate a global effect with interactions limited to localized regions. Not all parts of an image are perceptually equal; shape percepts appear to be constructed from image anchor regions.

An Improved Adaptive Level Set Method for Image Segmentation

In order to improve the accuracy of image segmentation, an improved adaptive level set method is proposed based on level set evolution without re-initialization method and adaptive distance preserving level set evolution method. A new definition of weight coefficient in evolution equations is the main innovation of this paper. The improved method can detect certain object boundaries, interior and exterior contours of an object, edges of multi-objects and weak boundaries of an object by synthetic and real images numerical experiments. Numerical results show that the improved adaptive level set method has faster segmentation speed and higher segmentation accuracy compared with the previous two methods, especially in weak boundaries and edges of multi-objects segmentation problems.

Robust Active Contour Model Guided by Local Binary Pattern Stopping Function

Edge based active contour models are adequate to some extent in segmenting images with intensity inhomogeneity but often fail when applied to images with poorly defined or noisy boundaries. Instead of the classical and widely used gradient or edge stopping function which fails to stop contour evolution at such boundaries, we use local binary pattern stopping function to construct a robust and effective active contour model for image segmentation. In fact, comparing to edge stopping function, local binary pattern stopping function accurately distinguishes object’s boundaries and determines the local intensity variation dint to the local binary pattern textons used to classify the image regions. Moreover, the local binary pattern stopping function is applied using a variational level set formulation that forces the level set function to be close to a signed distance function to eliminate costly re-initialization and speed up the motion of the curve. Experiments on several gray level images confirm the advantages and the effectiveness the proposed model.

Visual perception of complex shape-transforming processes

Morphogenesis-or the origin of complex natural form-has long fascinated researchers from practically every branch of science. However, we know practically nothing about how we perceive and understand such processes. Here, we measured how observers visually infer shape-transforming processes. Participants viewed pairs of objects ('before' and 'after' a transformation) and identified points that corresponded across the transformation. This allowed us to map out in spatial detail how perceived shape and space were affected by the transformations. Participants' responses were strikingly accurate and mutually consistent for a wide range of non-rigid transformations including complex growth-like processes. A zero-free-parameter model based on matching and interpolating/extrapolating the positions of high-salience contour features predicts the data surprisingly well, suggesting observers infer spatial correspondences relative to key landmarks. Together, our findings reveal the operation of specific perceptual organization processes that make us remarkably adept at identifying correspondences across complex shape-transforming processes by using salient object features. We suggest that these abilities, which allow us to parse and interpret the causally significant features of shapes, are invaluable for many tasks that involve 'making sense' of shape.

The Role of Part Structure in the Perceptual Localization of a Shape

The process of object localization may be accomplished with respect to a particular reference location, such as the center of gravity, COG (eg Vishwanath and Kowler, 2003 Vision Research43 1637 – 1653). Here, we investigated how part structure affects an object's reference location. The reference location was evaluated with a measure of the illusory displacement of an internal target element embedded within a larger object (Morgan et al, 1990 Vision Research30 1793 – 1810). To examine whether the reference location is different for shapes with part structure, two shapes were tested: circle (small and large; no part structure) and bell (shape with two parts, one larger than the other). Results were examined with respect to two predictions: either the location of an object is based on its shape as a whole, disregarding part structure (ie a single, overall COG), or the parts are processed separately (different COGs).

With the circles, the results showed a systematic illusory displacement of the internal target toward the COG. With the bell, the illusion was significantly weaker than with both circles—even though the main part of the bell had the same size as the small circle, and its horizontal axis had the same extent as the large circle. Moreover, the distance judgments for the bell were consistent with a (weaker) reference point being located at the COG of the larger part, rather than at the COG of the entire bell. These results show that the part structure of a shape plays a role in the representation of its location, and that for complex shapes the perceived location of an embedded element depends more on the parts within which it is embedded, rather than on the whole shape.

Three-Dimensional Bilateral Symmetry Bias in Judgments of Figural Identity and Orientation

The two experiments reported explored a bias toward symmetry in judging identity and orientation of indeterminate two-dimensional shapes Subjects viewed symmetric and asymmetric filled, random polygons and described “what each figure looks like” and its orientation Viewers almost universally interpreted the shapes as silhouettes of bilaterally symmetric three-dimensional (3-D) objects This assumption of 3-D symmetry tended to constrain perceived vantage of the identified objects such that symmetric shapes were interpreted as straight-on views, and asymmetric shapes as profile or oblique views Because most salient objects in the world are bilaterally symmetric, these findings are consistent with the view that assuming 3-D symmetry can be a robust heuristic for constraining orientation when identifying objects from indeterminate patterns

Semi-Continuity of Skeletons in Two-Manifold and Discrete Voronoi Approximation

The skeleton of a 2D shape is an important geometric structure in pattern analysis and computer vision. In this paper we study the skeleton of a 2D shape in a two-manifold M , based on a geodesic metric. We present a formal definition of the skeleton S(Ω) for a shape Ω in M and show several properties that make S(Ω) distinct from its Euclidean counterpart in R(2). We further prove that for a shape sequence {Ωi} that converge to a shape Ω in M, the mapping Ω→ S̅(Ω) is lower semi-continuous. A direct application of this result is that we can use a set P of sample points to approximate the boundary of a 2D shape Ω, and the Voronoi diagram of P inside Ω ⊂ M gives a good approximation to the skeleton S(Ω) . Examples of skeleton computation in topography and brain morphometry are illustrated.

Digital Topology and Geometry in Medical Imaging: A Survey

Digital topology and geometry refers to the use of topologic and geometric properties and features for images defined in digital grids. Such methods have been widely used in many medical imaging applications, including image segmentation, visualization, manipulation, interpolation, registration, surface-tracking, object representation, correction, quantitative morphometry etc. Digital topology and geometry play important roles in medical imaging research by enriching the scope of target outcomes and by adding strong theoretical foundations with enhanced stability, fidelity, and efficiency. This paper presents a comprehensive yet compact survey on results, principles, and insights of methods related to digital topology and geometry with strong emphasis on understanding their roles in various medical imaging applications. Specifically, this paper reviews methods related to distance analysis and path propagation, connectivity, surface-tracking, image segmentation, boundary and centerline detection, topology preservation and local topological properties, skeletonization, and object representation, correction, and quantitative morphometry. A common thread among the topics reviewed in this paper is that their theory and algorithms use the principle of digital path connectivity, path propagation, and neighborhood analysis.

A Robust and Efficient Curve Skeletonization Algorithm for Tree-Like Objects Using Minimum Cost Paths

Conventional curve skeletonization algorithms using the principle of Blum's transform, often, produce unwanted spurious branches due to boundary irregularities, digital effects, and other artifacts. This paper presents a new robust and efficient curve skeletonization algorithm for three-dimensional (3-D) elongated fuzzy objects using a minimum cost path approach, which avoids spurious branches without requiring post-pruning. Starting from a root voxel, the method iteratively expands the skeleton by adding new branches in each iteration that connects the farthest quench voxel to the current skeleton using a minimum cost path. The path-cost function is formulated using a novel measure of local significance factor defined by the fuzzy distance transform field, which forces the path to stick to the centerline of an object. The algorithm terminates when dilated skeletal branches fill the entire object volume or the current farthest quench voxel fails to generate a meaningful skeletal branch. Accuracy of the algorithm has been evaluated using computer-generated phantoms with known skeletons. Performance of the method in terms of false and missing skeletal branches, as defined by human experts, has been examined using in vivo CT imaging of human intrathoracic airways. Results from both experiments have established the superiority of the new method as compared to the existing methods in terms of accuracy as well as robustness in detecting true and false skeletal branches. The new algorithm makes a significant reduction in computation complexity by enabling detection of multiple new skeletal branches in one iteration. Specifically, this algorithm reduces the number of iterations from the number of terminal tree branches to the worst case performance of tree depth. In fact, experimental results suggest that, on an average, the order of computation complexity is reduced to the logarithm of the number of terminal branches of a tree-like object.

A computational model of the short-cut rule for 2D shape decomposition

We propose a new 2D shape decomposition method based on the short-cut rule. The short-cut rule originates from cognition research, and states that the human visual system prefers to partition an object into parts using the shortest possible cuts. We propose and implement a computational model for the short-cut rule and apply it to the problem of shape decomposition. The model we proposed generates a set of cut hypotheses passing through the points on the silhouette, which represent the negative minima of curvature. We then show that most part-cut hypotheses can be eliminated by analysis of local properties of each. Finally, the remaining hypotheses are evaluated in ascending length order, which guarantees that of any pair of conflicting cuts only the shortest will be accepted. We demonstrate that, compared with state-of-the-art shape decomposition methods, the proposed approach achieves decomposition results, which better correspond to human intuition as revealed in psychological experiments.

DTW–RADON-BASED SHAPE DESCRIPTOR FOR PATTERN RECOGNITION

In this paper, we present a pattern recognition method that uses dynamic programming for the alignment of Radon features. The key characteristic of the method is to use dynamic time warping (DTW) to match corresponding pairs of the Radon features for all possible projections. Thanks to DTW, we avoid compressing the feature matrix into a single vector which would otherwise miss information. To reduce the possible number of matchings, we rely on a initial normalization based on the pattern orientation. A comprehensive study is made using major state-of-the-art shape descriptors over several public datasets of shapes such as graphical symbols (both printed and hand-drawn), handwritten characters and footwear prints. In all tests, the method proves its generic behavior by providing better recognition performance. Overall, we validate that our method is robust to deformed shape due to distortion, degradation and occlusion.

Local field potentials and border ownership: A conjecture about computation in visual cortex

Border ownership is an intermediate-level visual task: it must integrate (upward flowing) image information about edges with (downward flowing) shape information. This highlights the familiar local-to-global aspect of border formation (linking of edge elements to form contours) with the much less studied global-to-local aspect (which edge elements form part of the same shape). To address this task we show how to incorporate certain high-level notions of distance and geometric arrangement into a form that can influence image-based edge information. The center of the argument is a reaction-diffusion equation that reveals how (global) aspects of the distance map (that is, shape) can be "read out" locally, suggesting a solution to the border ownership problem. Since the reaction-diffusion equation defines a field, a possible information processing role for the local field potential can be defined. We argue that such fields also underlie the Gestalt notion of closure, especially when it is refined using modern experimental techniques. An important implication of this theoretical argument is that, if true, then network modeling must be extended to include the substrate surrounding spiking neurons, including glia.

Development of a semi-automated method for mitral valve modeling with medial axis representation using 3D ultrasound

PURPOSE

Precise 3D modeling of the mitral valve has the potential to improve our understanding of valve morphology, particularly in the setting of mitral regurgitation (MR). Toward this goal, the authors have developed a user-initialized algorithm for reconstructing valve geometry from transesophageal 3D ultrasound (3D US) image data.

METHODS

Semi-automated image analysis was performed on transesophageal 3D US images obtained from 14 subjects with MR ranging from trace to severe. Image analysis of the mitral valve at midsystole had two stages: user-initialized segmentation and 3D deformable modeling with continuous medial representation (cm-rep). Semi-automated segmentation began with user-identification of valve location in 2D projection images generated from 3D US data. The mitral leaflets were then automatically segmented in 3D using the level set method. Second, a bileaflet deformable medial model was fitted to the binary valve segmentation by Bayesian optimization. The resulting cm-rep provided a visual reconstruction of the mitral valve, from which localized measurements of valve morphology were automatically derived. The features extracted from the fitted cm-rep included annular area, annular circumference, annular height, intercommissural width, septolateral length, total tenting volume, and percent anterior tenting volume. These measurements were compared to those obtained by expert manual tracing. Regurgitant orifice area (ROA) measurements were compared to qualitative assessments of MR severity. The accuracy of valve shape representation with cm-rep was evaluated in terms of the Dice overlap between the fitted cm-rep and its target segmentation.

RESULTS

The morphological features and anatomic ROA derived from semi-automated image analysis were consistent with manual tracing of 3D US image data and with qualitative assessments of MR severity made on clinical radiology. The fitted cm-reps accurately captured valve shape and demonstrated patient-specific differences in valve morphology among subjects with varying degrees of MR severity. Minimal variation in the Dice overlap and morphological measurements was observed when different cm-rep templates were used to initialize model fitting.

CONCLUSIONS

This study demonstrates the use of deformable medial modeling for semi-automated 3D reconstruction of mitral valve geometry using transesophageal 3D US. The proposed algorithm provides a parametric geometrical representation of the mitral leaflets, which can be used to evaluate valve morphology in clinical ultrasound images.

The time course of configural change detection for novel 3-D objects

The present study investigated the time course of visual information processing that is responsible for successful object change detection involving the configuration and shape of 3-D novel object parts. Using a one-shot change detection task, we manipulated stimulus and interstimulus mask durations (40-500 msec). Experiments 1A and 1B showed no change detection advantage for configuration at very short (40-msec) stimulus durations, but the configural advantage did emerge with durations between 80 and 160 msec. In Experiment 2, we showed that, at shorter stimulus durations, the number of parts changing was the best predictor of change detection performance. Finally, in Experiment 3, with a stimulus duration of 160 msec, configuration change detection was found to be highly accurate for each of the mask durations tested, suggesting a fast processing speed for this kind of change information. However, switch and shape change detection reached peak levels of accuracy only when mask durations were increased to 160 and 320 msec, respectively. We conclude that, with very short stimulus exposures, successful object change detection depends primarily on quantitative measures of change. However, with longer stimulus exposures, the qualitative nature of the change becomes progressively more important, resulting in the well-known configural advantage for change detection.

Optimal embedding for shape indexing in medical image databases

This paper addresses the problem of indexing shapes in medical image databases. Shapes of organs are often indicative of disease, making shape similarity queries important in medical image databases. Mathematically, shapes with landmarks belong to shape spaces which are curved manifolds with a well defined metric. The challenge in shape indexing is to index data in such curved spaces. One natural indexing scheme is to use metric trees, but metric trees are prone to inefficiency. This paper proposes a more efficient alternative. We show that it is possible to optimally embed finite sets of shapes in shape space into a Euclidean space. After embedding, classical coordinate-based trees can be used for efficient shape retrieval. The embedding proposed in the paper is optimal in the sense that it least distorts the partial Procrustes shape distance. The proposed indexing technique is used to retrieve images by vertebral shape from the NHANES II database of cervical and lumbar spine X-ray images maintained at the National Library of Medicine. Vertebral shape strongly correlates with the presence of osteophytes, and shape similarity retrieval is proposed as a tool for retrieval by osteophyte presence and severity. Experimental results included in the paper evaluate (1) the usefulness of shape similarity as a proxy for osteophytes, (2) the computational and disk access efficiency of the new indexing scheme, (3) the relative performance of indexing with embedding to the performance of indexing without embedding, and (4) the computational cost of indexing using the proposed embedding versus the cost of an alternate embedding. The experimental results clearly show the relevance of shape indexing and the advantage of using the proposed embedding.

Scale-space behavior of planar-curve corners

The curvature scale-space (CSS) technique is suitable for extracting curvature features from objects with noisy boundaries. To detect corner points in a multiscale framework, Rattarangsi and Chin investigated the scale-space behavior of planar-curve corners. Unfortunately, their investigation was based on an incorrect assumption, viz., that planar curves have no shrinkage under evolution. In the present paper, this mistake is corrected. First, it is demonstrated that a planar curve may shrink nonuniformly as it evolves across increasing scales. Then, by taking into account the shrinkage effect of evolved curves, the CSS trajectory maps of various corner models are investigated and their properties are summarized. The scale-space trajectory of a corner may either persist, vanish, merge with a neighboring trajectory, or split into several trajectories. The scale-space trajectories of adjacent corners may attract each other when the corners have the same concavity, or repel each other when the corners have opposite concavities. Finally, we present a standard curvature measure for computing the CSS maps of digital curves, with which it is shown that planar-curve corners have consistent scale-space behavior in the digital case as in the continuous case.

Skeletal shape abstraction from examples

Learning a class prototype from a set of exemplars is an important challenge facing researchers in object categorization. Although the problem is receiving growing interest, most approaches assume a one-to-one correspondence among local features, restricting their ability to learn true abstractions of a shape. In this paper, we present a new technique for learning an abstract shape prototype from a set of exemplars whose features are in many-to-many correspondence. Focusing on the domain of 2D shape, we represent a silhouette as a medial axis graph whose nodes correspond to "parts" defined by medial branches and whose edges connect adjacent parts. Given a pair of medial axis graphs, we establish a many-to-many correspondence between their nodes to find correspondences among articulating parts. Based on these correspondences, we recover the abstracted medial axis graph along with the positional and radial attributes associated with its nodes. We evaluate the abstracted prototypes in the context of a recognition task.

Disconnected skeleton: shape at its absolute scale

We present a new skeletal representation along with a matching framework to address the deformable shape recognition problem. The disconnectedness arises as a result of excessive regularization that we use to describe a shape at an attainably coarse scale. Our motivation is to rely on stable properties the shape instead of inaccurately measured secondary details. The new representation does not suffer from the common instability problems of the traditional connected skeletons, and the matching process gives quite successful results on a diverse database of 2D shapes. An important difference of our approach from the conventional use of skeleton is that we replace the local coordinate frame with a global Euclidean frame supported by additional mechanisms to handle articulations and local boundary deformations. As a result, we can produce descriptions that are sensitive to any combination of changes in scale, position, orientation and articulation, as well as invariant ones.

Continuous medial representation of brain structures using the biharmonic PDE

A new approach for constructing deformable continuous medial models for anatomical structures is presented. Medial models describe geometrical objects by first specifying the skeleton of the object and then deriving the boundary surface corresponding to the skeleton. However, an arbitrary specification of a skeleton will not be "valid" unless a certain set of sufficient conditions is satisfied. The most challenging of these is the non-linear equality constraint that must hold along the boundaries of the manifolds forming the skeleton. The main contribution of this paper is to leverage the biharmonic partial differential equation as a mapping from a codimension-0 subset of Euclidean space to the space of skeletons that satisfy the equality constraint. The PDE supports robust numerical solution on freeform triangular meshes, providing additional flexibility for shape modeling. The approach is evaluated by generating continuous medial models for a large dataset of hippocampus shapes. Generalizations to modeling more complex shapes and to representing branching skeletons are demonstrated.

Privileged coding of convex shapes in human object-selective cortex

What is the neural code for object shape? Despite intensive research, the precise nature of object representations in high-level visual cortex remains elusive. Here we use functional magnetic resonance imaging (fMRI) to show that convex shapes are encoded in a privileged fashion by human lateral occipital complex (LOC), a region that has been implicated in object recognition. On each trial, two convex or two concave shapes that were either identical or different were presented sequentially. Critically, the convex and concave stimuli were the same except for a binocular disparity change that reversed the figure-ground assignment. The fMRI response in LOC for convex stimuli was higher for different than that for identical shape pairs, indicating sensitivity to differences in convex shape. However, when the same stimuli were seen as concave, the response for different and identical pairs was the same, indicating lower sensitivity to changes in concave shape than convex shape. This pattern was more pronounced in the anterior than that in the posterior portion of LOC. These results suggest that convex contours could be important elements in cortical object representations.

Path similarity skeleton graph matching

This paper presents a novel framework to for shape recognition based on object silhouettes. The main idea is to match skeleton graphs by comparing the shortest paths between skeleton endpoints. In contrast to typical tree or graph matching methods, we completely ignore the topological graph structure. Our approach is motivated by the fact that visually similar skeleton graphs may have completely different topological structures. The proposed comparison of shortest paths between endpoints of skeleton graphs yields correct matching results in such cases. The skeletons are pruned by contour partitioning with Discrete Curve Evolution, which implies that the endpoints of skeleton branches correspond to visual parts of the objects. The experimental results demonstrate that our method is able to produce correct results in the presence of articulations, stretching, and occlusion.

Shape-based normalization of the corpus callosum for DTI connectivity analysis

The continuous medial representation (cm-rep) is an approach that makes it possible to model, normalize, and analyze anatomical structures on the basis of medial geometry. Having recently presented a partial differential equation (PDE)-based approach for 3-D cm-rep modeling [1], here we present an equivalent 2-D approach that involves solving an ordinary differential equation. This paper derives a closed form solution of this equation and shows how Pythagorean hodograph curves can be used to express the solution as a piecewise polynomial function, allowing efficient and robust medial modeling. The utility of the approach in medical image analysis is demonstrated by applying it to the problem of shape-based normalization of the midsagittal section of the corpus callosum. Using diffusion tensor tractography, we show that shape-based normalization aligns subregions of the corpus callosum, defined by connectivity, more accurately than normalization based on volumetric registration. Furthermore, shape-based normalization helps increase the statistical power of group analysis in an experiment where features derived from diffusion tensor tractography are compared between two cohorts. These results suggest that cm-rep is an appropriate tool for normalizing the corpus callosum in white matter studies.