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49
A levelset approach to 3d reconstruction from range data
 International Journal of Computer Vision
, 1998
"... This paper presents a method that uses the level sets of volumes to reconstruct the shapes of 3D objects from range data. The strategy is to formulate 3D reconstruction as a statistical problem: find that surface which is mostly likely, given the data and some prior knowledge about the application d ..."
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Cited by 149 (20 self)
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This paper presents a method that uses the level sets of volumes to reconstruct the shapes of 3D objects from range data. The strategy is to formulate 3D reconstruction as a statistical problem: find that surface which is mostly likely, given the data and some prior knowledge about the application domain. The resulting optimization problem is solved by an incremental process of deformation. We represent a deformable surface as the level set of a discretely sampled scalar function of 3 dimensions, i.e. a volume. Such levelset models have been shown to mimic conventional deformable surface models by encoding surface movements as changes in the greyscale values of the volume. The result is a voxelbased modeling technology that offers several advantages over conventional parametric models, including flexible topology, no need for reparameterization, concise descriptions of differential structure, and a natural scale space for hierarchical representations. This paper builds on previous work in both 3D reconstruction and levelset modeling. It presents a fundamental result in surface estimation from range data: an analytical characterization of the surface that maximizes the posterior probability. It also presents a novel computational technique for levelset modeling, called the sparsefield algorithm, which combines the advantages of a levelset approach with the computational efficiency and accuracy of a parametric representation. The sparsefield algorithm is more efficient than other approaches, and because it assigns the level set to a specific set of grid points, it positions the levelset model more accurately than the grid itself. These properties, computational efficiency and subcell accuracy, are essential when trying to reconstruct the shapes of 3D objects. Results are shown for the reconstruction objects from sets of noisy and overlapping range maps.
Recognition of Shapes by Editing Shock Graphs
 In IEEE International Conference on Computer Vision
, 2001
"... This paper presents a novel recognition framework which is based on matching shock graphs of 2D shape outlines, where the distance between two shapes is defined to be the cost of the least action path deforming one shape to another. Three key ideas render the implementation of this framework practic ..."
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Cited by 93 (6 self)
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This paper presents a novel recognition framework which is based on matching shock graphs of 2D shape outlines, where the distance between two shapes is defined to be the cost of the least action path deforming one shape to another. Three key ideas render the implementation of this framework practical. First, the shape space is partitioned by defining an equivalence class on shapes, where two shapes with the same shock graph topology are considered to be equivalent. Second, the space of deformations is discretized by defining all deformations with the same sequence of shock graph transitions as equivalent. Shock transitions are points along the deformation where the shock graph topology changes. Third, we employ a graph edit distance algorithm that searches in the space of all possible transition sequences and finds the globally optimal sequence in polynomial time. The effectiveness of the proposed technique in the presence of a variety of visual transformations including occlusion, articulation and deformation of parts, shadow and highlights, viewpoint variation, and boundary perturbations is demonstrated. Indexing into two separate databases of roughly 100 shapes results in 100% accuracy for top three matches and 99:5% for the next three matches. 1
Autonomous Exploration: Driven by Uncertainty
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 1995
"... Passively accepting measurements of the world is not enough, as the data we obtain is always incomplete, and the inferences made from it uncertain to a degree which is often unacceptable. If we are to build machines that operate autonomously they will always be faced with this dilemma, and can only ..."
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Cited by 86 (8 self)
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Passively accepting measurements of the world is not enough, as the data we obtain is always incomplete, and the inferences made from it uncertain to a degree which is often unacceptable. If we are to build machines that operate autonomously they will always be faced with this dilemma, and can only be successful if they play a much more active role. This paper presents such a machine. It deliberately seeks out those parts of the world which maximize the fidelity of its internal representations, and keeps searching until those representations are acceptable. We call this paradigm autonomous exploration, and the machine an autonomous explorer. This paper has two major contributions. The first is a theory that tells us how to explore, and which confirms the intuitive ideas we have put forward previously. The second is an implementation of that theory. In our laboratory we have constructed a working autonomous explorer and here for the first time show it in action. The system is entirely bottomup and does not depend on any a priori knowledge of the environment. To our knowledge it is the first to have successfully closed the loop between gaze planning and the inference of complex 3D models.
Symmetrybased Indexing of Image Databases
 J. VISUAL COMMUNICATION AND IMAGE REPRESENTATION
, 1998
"... The use of shape as a cue for indexing into pictorial databases has been traditionally based on global invariant statistics and deformable templates, on the one hand, and local edge correlation on the other. This paper proposes an intermediate approach based on a characterization of the symmetry in ..."
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Cited by 76 (5 self)
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The use of shape as a cue for indexing into pictorial databases has been traditionally based on global invariant statistics and deformable templates, on the one hand, and local edge correlation on the other. This paper proposes an intermediate approach based on a characterization of the symmetry in edge maps. The use of symmetry matching as a joint correlation measure between pairs of edge elements further constrains the comparison of edge maps. In addition, a natural organization of groups of symmetry into a hierarchy leads to a graphbased representation of relational structure of components of shape that allows for deformations by changing attributes of this relational graph. A graduate assignment graph matching algorithm is used to match symmetry structure in images to stored prototypes or sketches. The results of matching sketches and greyscale images against a small database consisting of a variety of fish, planes, tools, etc., are depicted.
Object Representation by Cores: Identifying and Representing Primitive Spatial Regions
, 1994
"... We propose a model of the spatial visual processes underlying the identification and representation of the shape of primitive spatial regions. We propose that a region's boundaries are sensed at multiple scales by boundariness detectors that give graded responses, that stimulated boundariness detect ..."
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Cited by 71 (19 self)
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We propose a model of the spatial visual processes underlying the identification and representation of the shape of primitive spatial regions. We propose that a region's boundaries are sensed at multiple scales by boundariness detectors that give graded responses, that stimulated boundariness detectors of similar scale, s, connect to one another across a distance that is proportional to their scale, and that they connect via cores, where a core encodes the middles and widths of the region and hence is a trace in (x,y,s), i.e., 3D scale space. 3 INTRODUCTION One of the more impressive feats that the human visual system performs is the identification of individual objects from the continuous distribution of light that falls on the retina. To accomplish this task, the observer uses information from the image to identify regions of interest on the basis of spatial changes in luminance, color, texture, motion, etc. He also interprets information from the image on the basis of prior experi...
Convexity Rule for Shape Decomposition Based on Discrete Contour Evolution
 Computer Vision and Image Understanding
, 1999
"... We concentrate here on decomposition of 2D objects into meaningful parts of visual form,orvisual parts. It is a simple observation that convex parts of objects determine visual parts. However, the problem is that many significant visual parts are not convex, since a visual part may have concavities. ..."
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Cited by 69 (19 self)
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We concentrate here on decomposition of 2D objects into meaningful parts of visual form,orvisual parts. It is a simple observation that convex parts of objects determine visual parts. However, the problem is that many significant visual parts are not convex, since a visual part may have concavities. We solve this problem by identifying convex parts at different stages of a proposed contour evolution method in which significant visual parts will become convex object parts at higher stages of the evolution. We obtain a novel rule for decomposition of 2D objects into visual parts, called the hierarchical convexity rule, which states that visual parts are enclosed by maximal convex (with respect to the object) boundary arcs at different stages of the contour evolution. This rule determines not only parts of boundary curves but directly the visual parts of objects. Moreover, the stages of the evolution hierarchy induce a hierarchical structure of the visual parts. The more advanced the stage of contour evolution, the more significant is the shape contribution of the obtained visual parts. c ○ 1999 Academic Press Key Words: visual parts; discrete curve evolution; digital curves; digital straight line segments; total curvature; shape hierarchy; digital geometry. 1.
A Society of Models for Video and Image Libraries
, 1996
"... The average person with a computer will soon have access to the world's collections of digital video and images. However, unlike text which can be alphabetized or numbers which can be ordered, image and video has no general language to aid in its organization. Although tools which can "see" and "und ..."
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Cited by 53 (0 self)
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The average person with a computer will soon have access to the world's collections of digital video and images. However, unlike text which can be alphabetized or numbers which can be ordered, image and video has no general language to aid in its organization. Although tools which can "see" and "understand" the content of imagery are still in their infancy, they are now at the point where they can provide substantial assistance to users in navigating through visual media. This paper describes new tools based on "vision texture" for modeling image and video. The focus of this research is the use of a society of lowlevel models for performing relatively highlevel tasks, such as retrieval and annotation of image and video libraries. This paper surveys our recent and present research in this fastgrowing area. 1 Introduction: Vision Texture Suppose you have a set of vacation photos of Paris and the surrounding countryside, and you accidentally drop them on the floor. They get out of or...
ImageBased Object Recognition in Man, Monkey and Machine
, 1998
"... Theories of visual object recognition must solve the problem of recognizing 3D objects given that perceivers only receive 2D patterns of light on their retinae. Recent findings from human psychophysics, neurophysiology and machine vision provide converging evidence for `imagebased' models in whi ..."
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Cited by 53 (4 self)
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Theories of visual object recognition must solve the problem of recognizing 3D objects given that perceivers only receive 2D patterns of light on their retinae. Recent findings from human psychophysics, neurophysiology and machine vision provide converging evidence for `imagebased' models in which objects are represented as collections of viewpointspecific local features. This approach is contrasted with `structuraldescription' models in which objects are represented as configurations of 3D volumes or parts. We then review recent behavioral results that address the biological plausibility of both approaches, as well as some of their computational advantages and limitations. We conclude that, although the imagebased approach holds great promise, it has potential pitfalls that may be best overcome by including structural information. Thus, the most viable model of object recognition may be one that incorporates the most appealing aspects of both imagebased and structuraldescription theories. 1998 Elsevier Science B.V. All rights reserved Keywords: Object recognition; Imagebased model; Structural description 1.
Zoominvariant vision of figural shape: The mathematics of cores
 Computer Vision and Image Understanding
"... Believing that figural zoom invariance and the crossfigural boundary linking implied by medial loci are important aspects of object shape, we present the mathematics of and algorithms for the extraction of medial loci directly from image intensities. The medial loci called cores are defined as gene ..."
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Cited by 52 (19 self)
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Believing that figural zoom invariance and the crossfigural boundary linking implied by medial loci are important aspects of object shape, we present the mathematics of and algorithms for the extraction of medial loci directly from image intensities. The medial loci called cores are defined as generalized maxima in scale space of a form of medial information that is invariant to translation, rotation, and in particular, zoom. These loci are very insensitive to image disturbances, in strong contrast to previously available medial loci, as demonstrated in a companion paper. Corerelated geometric properties and image object representations are laid out which, together with the aforementioned insensitivities, allow the core to be used effectively for a variety of image analysis objectives. 2
Geometric Heat Equation and Nonlinear Diffusion of Shapes and Images
 Computer Vision and Image Understanding
, 1993
"... We propose a geometric smoothing method based on local curvature in shapes and images which is governed by the geometric heat equation and is a special case of the reactiondiffusion framework proposed by [28]. For shapes, the approach is analogous to the classical heat equation smoothing, but with ..."
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Cited by 40 (5 self)
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We propose a geometric smoothing method based on local curvature in shapes and images which is governed by the geometric heat equation and is a special case of the reactiondiffusion framework proposed by [28]. For shapes, the approach is analogous to the classical heat equation smoothing, but with a renormalization by arclength at each infinitesimal step. For images, the smoothing is similar to anisotropic diffusion in that, since the component of diffusion in the direction of the brightness gradient is nil, edge location and sharpness are left intact. We present several properties of curvature deformation smoothing of shape: it preserves inclusion order, annihilates extrema and inflection points without creating new ones, decreases total curvature, satisfies the semigroup property allowing for local iterative computations, etc. Curvature deformation smoothing of an image is based on viewing it as a collection of isointensity level sets, each of which is smoothed by curvature and the...