Nonparametric statistical methods for image segmentation and shape analysis

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2005.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Page 131 blank.Includes bibliographical references (p. 125-130).Image segmentation, the process of decomposing an image into meaningful regions, is a fundamental problem in image processing and computer vision. Recently, image segmentation techniques based on active contour models with level set implementation have received considerable attention. The objective of this thesis is in the development of advanced active contour-based image segmentation methods that incorporate complex statistical information into the segmentation process, either about the image intensities or about the shapes of the objects to be segmented. To this end, we use nonparametric statistical methods for modeling both the intensity distributions and the shape distributions. Previous work on active contour-based segmentation considered the class of images in which each region can be distinguished from others by second order statistical features such as the mean or variance of image intensities of that region. This thesis addresses the problem of segmenting a more general class of images in which each region has a distinct arbitrary intensity distribution. To this end, we develop a nonparametric information-theoretic method for image segmentation. In particular, we cast the segmentation problem as the maximization of the mutual information between the region labels and the image pixel intensities. The resulting curve evolution equation is given in terms of nonparametric density estimates of intensity distributions, and the segmentation method can deal with a variety of intensity distributions in an unsupervised fashion. The second component of this thesis addresses the problem of estimating shape densities from training shapes and incorporating such shape prior densities into the image segmentation process.(cont.) To this end, we propose nonparametric density estimation methods in the space of curves and the space of signed distance functions. We then derive a corresponding curve evolution equation for shape-based image segmentation. Finally, we consider the case in which the shape density is estimated from training shapes that form multiple clusters. This case leads to the construction of complex, potentially multi-modal prior densities for shapes. As compared to existing methods, our shape priors can: (a) model more complex shape distributions; (b) deal with shape variability in a more principled way; and (c) represent more complex shapes.by Junmo Kim.Ph.D

Data-Driven Shape Analysis and Processing

Data-driven methods play an increasingly important role in discovering geometric, structural, and semantic relationships between 3D shapes in collections, and applying this analysis to support intelligent modeling, editing, and visualization of geometric data. In contrast to traditional approaches, a key feature of data-driven approaches is that they aggregate information from a collection of shapes to improve the analysis and processing of individual shapes. In addition, they are able to learn models that reason about properties and relationships of shapes without relying on hard-coded rules or explicitly programmed instructions. We provide an overview of the main concepts and components of these techniques, and discuss their application to shape classification, segmentation, matching, reconstruction, modeling and exploration, as well as scene analysis and synthesis, through reviewing the literature and relating the existing works with both qualitative and numerical comparisons. We conclude our report with ideas that can inspire future research in data-driven shape analysis and processing.Comment: 10 pages, 19 figure

Interactive object contour extraction for shape modeling

In this paper we present a semi-automatic segmentation approach suitable for extracting object contours as a precursor to 2D shape modeling. The approach is a modified and extended version of an existing state-of-the-art approach based on the concept of a Binary Partition Tree (BPT) [1]. The resulting segmentation tool facilitates quick and easy extraction of an object’s contour via a small amount of user interaction that is easy to perform, even in complicated scenes. Illustrative segmentation results are presented and the usefulness of the approach in generating object shape models is discussed

Robust Temporally Coherent Laplacian Protrusion Segmentation of 3D Articulated Bodies

In motion analysis and understanding it is important to be able to fit a suitable model or structure to the temporal series of observed data, in order to describe motion patterns in a compact way, and to discriminate between them. In an unsupervised context, i.e., no prior model of the moving object(s) is available, such a structure has to be learned from the data in a bottom-up fashion. In recent times, volumetric approaches in which the motion is captured from a number of cameras and a voxel-set representation of the body is built from the camera views, have gained ground due to attractive features such as inherent view-invariance and robustness to occlusions. Automatic, unsupervised segmentation of moving bodies along entire sequences, in a temporally-coherent and robust way, has the potential to provide a means of constructing a bottom-up model of the moving body, and track motion cues that may be later exploited for motion classification. Spectral methods such as locally linear embedding (LLE) can be useful in this context, as they preserve "protrusions", i.e., high-curvature regions of the 3D volume, of articulated shapes, while improving their separation in a lower dimensional space, making them in this way easier to cluster. In this paper we therefore propose a spectral approach to unsupervised and temporally-coherent body-protrusion segmentation along time sequences. Volumetric shapes are clustered in an embedding space, clusters are propagated in time to ensure coherence, and merged or split to accommodate changes in the body's topology. Experiments on both synthetic and real sequences of dense voxel-set data are shown. This supports the ability of the proposed method to cluster body-parts consistently over time in a totally unsupervised fashion, its robustness to sampling density and shape quality, and its potential for bottom-up model constructionComment: 31 pages, 26 figure

Single-picture reconstruction and rendering of trees for plausible vegetation synthesis

State-of-the-art approaches for tree reconstruction either put limiting constraints on the input side (requiring multiple photographs, a scanned point cloud or intensive user input) or provide a representation only suitable for front views of the tree. In this paper we present a complete pipeline for synthesizing and rendering detailed trees from a single photograph with minimal user effort. Since the overall shape and appearance of each tree is recovered from a single photograph of the tree crown, artists can benefit from georeferenced images to populate landscapes with native tree species. A key element of our approach is a compact representation of dense tree crowns through a radial distance map. Our first contribution is an automatic algorithm for generating such representations from a single exemplar image of a tree. We create a rough estimate of the crown shape by solving a thin-plate energy minimization problem, and then add detail through a simplified shape-from-shading approach. The use of seamless texture synthesis results in an image-based representation that can be rendered from arbitrary view directions at different levels of detail. Distant trees benefit from an output-sensitive algorithm inspired on relief mapping. For close-up trees we use a billboard cloud where leaflets are distributed inside the crown shape through a space colonization algorithm. In both cases our representation ensures efficient preservation of the crown shape. Major benefits of our approach include: it recovers the overall shape from a single tree image, involves no tree modeling knowledge and minimal authoring effort, and the associated image-based representation is easy to compress and thus suitable for network streaming.Peer ReviewedPostprint (author's final draft