Combinations of Deformable Shape Prototypes

We propose to investigate a model-based technique for encoding non-rigid object classes in terms of object prototypes. Objects from the same class can be parameterized by identifying shape and appearance invariants of the class to devise low-level representations. The approach presented here creates a flexible model for an object class from a set of prototypes. This model is then used to estimate the parameters of low-level representation of novel objects as combinations of the prototype parameters. Variations in the object shape are modeled as non-rigid deformations. Appearance variations are modeled as intensity variations. In the training phase, the system is presented with several example prototype images. These prototype images are registered to a reference image by a finite element-based technique called Active Blobs. The deformations of the finite element model to register a prototype image with the reference image provide the shape description or shape vector for the prototype. The shape vector for each prototype, is then used to warp the prototype image onto the reference image and obtain the corresponding texture vector. The prototype texture vectors, being warped onto the same reference image have a pixel by pixel correspondence with each other and hence are "shape normalized". Given sufficient number of prototypes that exhibit appropriate in-class variations, the shape and the texture vectors define a linear prototype subspace that spans the object class. Each prototype is a vector in this subspace. The matching phase involves the estimation of a set of combination parameters for synthesis of the novel object by combining the prototype shape and texture vectors. The strengths of this technique lie in the combined estimation of both shape and appearance parameters. This is in contrast with the previous approaches where shape and appearance parameters were estimated separately.

Intersubject Regularity in the Intrinsic Shape of Human V1

Previous studies have reported considerable intersubject variability in the three-dimensional geometry of the human primary visual cortex (V1). Here we demonstrate that much of this variability is due to extrinsic geometric features of the cortical folds, and that the intrinsic shape of V1 is similar across individuals. V1 was imaged in ten ex vivo human hemispheres using high-resolution (200 μm) structural magnetic resonance imaging at high field strength (7 T). Manual tracings of the stria of Gennari were used to construct a surface representation, which was computationally flattened into the plane with minimal metric distortion. The instrinsic shape of V1 was determined from the boundary of the planar representation of the stria. An ellipse provided a simple parametric shape model that was a good approximation to the boundary of flattened V1. The aspect ration of the best-fitting ellipse was found to be consistent across subject, with a mean of 1.85 and standard deviation of 0.12. Optimal rigid alignment of size-normalized V1 produced greater overlap than that achieved by previous studies using different registration methods. A shape analysis of published macaque data indicated that the intrinsic shape of macaque V1 is also stereotyped, and similar to the human V1 shape. Previoud measurements of the functional boundary of V1 in human and macaque are in close agreement with these results.

A Neural Model of 3D Shape-From-Texture: Multiple-Scale Filtering, Boundary Grouping, and Surface Filling-In

A neural model is presented of how cortical areas V1, V2, and V4 interact to convert a textured 2D image into a representation of curved 3D shape. Two basic problems are solved to achieve this: (1) Patterns of spatially discrete 2D texture elements are transformed into a spatially smooth surface representation of 3D shape. (2) Changes in the statistical properties of texture elements across space induce the perceived 3D shape of this surface representation. This is achieved in the model through multiple-scale filtering of a 2D image, followed by a cooperative-competitive grouping network that coherently binds texture elements into boundary webs at the appropriate depths using a scale-to-depth map and a subsequent depth competition stage. These boundary webs then gate filling-in of surface lightness signals in order to form a smooth 3D surface percept. The model quantitatively simulates challenging psychophysical data about perception of prolate ellipsoids (Todd and Akerstrom, 1987, J. Exp. Psych., 13, 242). In particular, the model represents a high degree of 3D curvature for a certain class of images, all of whose texture elements have the same degree of optical compression, in accordance with percepts of human observers. Simulations of 3D percepts of an elliptical cylinder, a slanted plane, and a photo of a golf ball are also presented.

Quantum Monte Carlo in the Interaction Representation --- Application to a Spin-Peierls Model

A quantum Monte Carlo algorithm is constructed starting from the standard perturbation expansion in the interaction representation. The resulting configuration space is strongly related to that of the Stochastic Series Expansion (SSE) method, which is based on a direct power series expansion of exp(-beta*H). Sampling procedures previously developed for the SSE method can therefore be used also in the interaction representation formulation. The new method is first tested on the S=1/2 Heisenberg chain. Then, as an application to a model of great current interest, a Heisenberg chain including phonon degrees of freedom is studied. Einstein phonons are coupled to the spins via a linear modulation of the nearest-neighbor exchange. The simulation algorithm is implemented in the phonon occupation number basis, without Hilbert space truncations, and is exact. Results are presented for the magnetic properties of the system in a wide temperature regime, including the T-->0 limit where the chain undergoes a spin-Peierls transition. Some aspects of the phonon dynamics are also discussed. The results suggest that the effects of dynamic phonons in spin-Peierls compounds such as GeCuO3 and NaV2O5 must be included in order to obtain a correct quantitative description of their magnetic properties, both above and below the dimerization temperature.

A study of stone fragmentation in shock wave lithotripsy by customizing the acoustic field and waveform shape

Shock wave lithotripsy is the preferred treatment modality for kidney stones in the United States. Despite clinical use for over twenty-five years, the mechanisms of stone fragmentation are still under debate. A piezoelectric array was employed to examine the effect of waveform shape and pressure distribution on stone fragmentation in lithotripsy. The array consisted of 170 elements placed on the inner surface of a 15 cm-radius spherical cap. Each element was driven independently using a 170 individual pulsers, each capable of generating 1.2 kV. The acoustic field was characterized using a fiber optic probe hydrophone with a bandwidth of 30 MHz and a spatial resolution of 100 μm. When all elements were driven simultaneously, the focal waveform was a shock wave with peak pressures p+ =65±3MPa and p−=−16±2MPa and the −6 dB focal region was 13 mm long and 2 mm wide. The delay for each element was the only control parameter for customizing the acoustic field and waveform shape, which was done with the aim of investigating the hypothesized mechanisms of stone fragmentation such as spallation, shear, squeezing, and cavitation. The acoustic field customization was achieved by employing the angular spectrum approach for modeling the forward wave propagation and regression of least square errors to determine the optimal set of delays. Results from the acoustic field customization routine and its implications on stone fragmentation will be discussed.

Search by Shape Examples: Modeling Nonrigid Deformation

We describe our work on shape-based image database search using the technique of modal matching. Modal matching employs a deformable shape decomposition that allows users to select example objects and have the computer efficiently sort the set of objects based on the similarity of their shape. Shapes are compared in terms of the types of nonrigid deformations (differences) that relate them. The modal decomposition provides deformation "control knobs" for flexible matching and thus allows for selecting weighted subsets of shape parameters that are deemed significant for a particular category or context. We demonstrate the utility of this approach for shape comparison in 2-D image databases; however, the general formulation is applicable to signals of any dimensionality.

Deformable Prototypes for Encoding Shape Categories in Image Databases

We describe a method for shape-based image database search that uses deformable prototypes to represent categories. Rather than directly comparing a candidate shape with all shape entries in the database, shapes are compared in terms of the types of nonrigid deformations (differences) that relate them to a small subset of representative prototypes. To solve the shape correspondence and alignment problem, we employ the technique of modal matching, an information-preserving shape decomposition for matching, describing, and comparing shapes despite sensor variations and nonrigid deformations. In modal matching, shape is decomposed into an ordered basis of orthogonal principal components. We demonstrate the utility of this approach for shape comparison in 2-D image databases.

Color Region Grouping and Shape Recognition with Deformable Models

A new deformable shape-based method for color region segmentation is described. The method includes two stages: over-segmentation using a traditional color region segmentation algorithm, followed by deformable model-based region merging via grouping and hypothesis selection. During the second stage, region merging and object identification are executed simultaneously. A statistical shape model is used to estimate the likelihood of region groupings and model hypotheses. The prior distribution on deformation parameters is precomputed using principal component analysis over a training set of region groupings. Once trained, the system autonomously segments deformed shapes from the background, while not merging them with similarly colored adjacent objects. Furthermore, the recovered parametric shape model can be used directly in object recognition and comparison. Experiments in segmentation and image retrieval are reported.

Program Representation Size in an Intermediate Language with Intersection and Union Types

The CIL compiler for core Standard ML compiles whole programs using a novel typed intermediate language (TIL) with intersection and union types and flow labels on both terms and types. The CIL term representation duplicates portions of the program where intersection types are introduced and union types are eliminated. This duplication makes it easier to represent type information and to introduce customized data representations. However, duplication incurs compile-time space costs that are potentially much greater than are incurred in TILs employing type-level abstraction or quantification. In this paper, we present empirical data on the compile-time space costs of using CIL as an intermediate language. The data shows that these costs can be made tractable by using sufficiently fine-grained flow analyses together with standard hash-consing techniques. The data also suggests that non-duplicating formulations of intersection (and union) types would not achieve significantly better space complexity.

Retrieval by Shape Population: An Index Tree Approach

Based on our previous work in deformable shape model-based object detection, a new method is proposed that uses index trees for organizing shape features to support content-based retrieval applications. In the proposed strategy, different shape feature sets can be used in index trees constructed for object detection and shape similarity comparison respectively. There is a direct correspondence between the two shape feature sets. As a result, application-specific features can be obtained efficiently for shape-based retrieval after object detection. A novel approach is proposed that allows retrieval of images based on the population distribution of deformed shapes in each image. Experiments testing these new approaches have been conducted using an image database that contains blood cell micrographs. The precision vs. recall performance measure shows that our method is superior to previous methods.

An Appearance-Based Framework for 3D Hand Shape Classification and Camera Viewpoint Estimation

An appearance-based framework for 3D hand shape classification and simultaneous camera viewpoint estimation is presented. Given an input image of a segmented hand, the most similar matches from a large database of synthetic hand images are retrieved. The ground truth labels of those matches, containing hand shape and camera viewpoint information, are returned by the system as estimates for the input image. Database retrieval is done hierarchically, by first quickly rejecting the vast majority of all database views, and then ranking the remaining candidates in order of similarity to the input. Four different similarity measures are employed, based on edge location, edge orientation, finger location and geometric moments.

Deformable Shape Detection and Description via Model-Based Region Grouping

A method for deformable shape detection and recognition is described. Deformable shape templates are used to partition the image into a globally consistent interpretation, determined in part by the minimum description length principle. Statistical shape models enforce the prior probabilities on global, parametric deformations for each object class. Once trained, the system autonomously segments deformed shapes from the background, while not merging them with adjacent objects or shadows. The formulation can be used to group image regions based on any image homogeneity predicate; e.g., texture, color, or motion. The recovered shape models can be used directly in object recognition. Experiments with color imagery are reported.

Non-Rigid Shape from Image Streams

We present a framework for estimating 3D relative structure (shape) and motion given objects undergoing nonrigid deformation as observed from a fixed camera, under perspective projection. Deforming surfaces are approximated as piece-wise planar, and piece-wise rigid. Robust registration methods allow tracking of corresponding image patches from view to view and recovery of 3D shape despite occlusions, discontinuities, and varying illumination conditions. Many relatively small planar/rigid image patch trackers are scattered throughout the image; resulting estimates of structure and motion at each patch are combined over local neighborhoods via an oriented particle systems formulation. Preliminary experiments have been conducted on real image sequences of deforming objects and on synthetic sequences where ground truth is known.

Index Trees for Efficient Deformable Shape-based Retrieval

An improved method for deformable shape-based image indexing and retrieval is described. A pre-computed index tree is used to improve the speed of our previously reported on-line model fitting method; simple shape features are used as keys in a pre-generated index tree of model instances. In addition, a coarse to fine indexing scheme is used at different levels of the tree to further improve speed while maintaining matching accuracy. Experimental results show that the speedup is significant, while accuracy of shape-based indexing is maintained. A method for shape population-based retrieval is also described. The method allows query formulation based on the population distributions of shapes in each image. Results of population-based image queries for a database of blood cell micrographs are shown.

MosaicShape: Stochastic Region Grouping with Shape Prior

A novel method that combines shape-based object recognition and image segmentation is proposed for shape retrieval from images. Given a shape prior represented in a multi-scale curvature form, the proposed method identifies the target objects in images by grouping oversegmented image regions. The problem is formulated in a unified probabilistic framework and solved by a stochastic Markov Chain Monte Carlo (MCMC) mechanism. By this means, object segmentation and recognition are accomplished simultaneously. Within each sampling move during the simulation process,probabilistic region grouping operations are influenced by both the image information and the shape similarity constraint. The latter constraint is measured by a partial shape matching process. A generalized parallel algorithm by Barbu and Zhu,combined with a large sampling jump and other implementation improvements, greatly speeds up the overall stochastic process. The proposed method supports the segmentation and recognition of multiple occluded objects in images. Experimental results are provided for both synthetic and real images.