Results 1  10
of
25
Approximate convex decomposition of polygons
 In Proc. 20th Annual ACM Symp. Computat. Geom. (SoCG
, 2004
"... We propose a strategy to decompose a polygon, containing zero or more holes, into “approximately convex” pieces. For many applications, the approximately convex components of this decomposition provide similar benefits as convex components, while the resulting decomposition is significantly smaller ..."
Abstract

Cited by 42 (6 self)
 Add to MetaCart
(Show Context)
We propose a strategy to decompose a polygon, containing zero or more holes, into “approximately convex” pieces. For many applications, the approximately convex components of this decomposition provide similar benefits as convex components, while the resulting decomposition is significantly smaller and can be computed more efficiently. Moreover, our approximate convex decomposition (ACD) provides a mechanism to focus on key structural features and ignore less significant artifacts such as wrinkles and surface texture. We propose a simple algorithm that computes an ACD of a polygon by iteratively removing (resolving) the most significant nonconvex feature (notch). As a by product, it produces an elegant hierarchical representation that provides a series of ‘increasingly convex ’ decompositions. A user specified tolerance determines the degree of concavity that will be allowed in the lowest level of the hierarchy. Our algorithm computes an ACD of a simple polygon with n vertices and r notches in O(nr) time. In contrast, exact convex decomposition is NPhard or, if the polygon has no holes, takes O(nr 2) time. Models and movies can be found on our webpages at:
ArticulationInvariant Representation of Nonplanar Shapes
"... Abstract. Given a set of points corresponding to a 2D projection of a nonplanar shape, we would like to obtain a representation invariant to articulations (under no selfocclusions). It is a challenging problem since we need to account for the changes in 2D shape due to 3D articulations, viewpoint ..."
Abstract

Cited by 22 (1 self)
 Add to MetaCart
Abstract. Given a set of points corresponding to a 2D projection of a nonplanar shape, we would like to obtain a representation invariant to articulations (under no selfocclusions). It is a challenging problem since we need to account for the changes in 2D shape due to 3D articulations, viewpoint variations, as well as the varying effects of imaging process on different regions of the shape due to its nonplanarity. By modeling an articulating shape as a combination of approximate convex parts connected by nonconvex junctions, we propose to preserve distances between a pair of points by (i) estimating the parts of the shape through approximate convex decomposition, by introducing a robust measure of convexity and (ii) performing partwise affine normalization by assuming a weak perspective camera model, and then relating the points using the inner distance which is insensitive to planar articulations. We demonstrate the effectiveness of our representation on a dataset with nonplanar articulations, and on standard shape retrieval datasets like MPEG7.
A new convexity measure based on a probabilistic interpretation of images
 IEEE Transactions on Pattern Analysis and Machine Intelligence
"... In this article we present a novel convexity measure for object shape analysis. The proposed method is based on the idea of generating pairs of points from a set, and measuring the probability that a point dividing the corresponding line segments belongs to the same set. The measure is directly appl ..."
Abstract

Cited by 12 (0 self)
 Add to MetaCart
(Show Context)
In this article we present a novel convexity measure for object shape analysis. The proposed method is based on the idea of generating pairs of points from a set, and measuring the probability that a point dividing the corresponding line segments belongs to the same set. The measure is directly applicable to image functions representing shapes, and also to grayscale images which approximate image binarizations. The approach introduced gives rise to a variety of convexity measures, which makes it possible to obtain more information about the object shape. The proposed measure turns out to be easy to implement using the Fast Fourier Transform and we will consider this in detail. Finally, we illustrate the behavior of our measure in different situations and compare it to other similar ones.
A symmetric convexity measure
 Computer Vision Image Understanding
, 2006
"... A new areabased convexity measure for polygons is described. It has the desirable properties that it is not sensitive to small boundary defects, and it is symmetric with respect to intrusions and protrusions. The measure requires a maximally overlapping convex polygon, and this is efficiently estim ..."
Abstract

Cited by 12 (5 self)
 Add to MetaCart
(Show Context)
A new areabased convexity measure for polygons is described. It has the desirable properties that it is not sensitive to small boundary defects, and it is symmetric with respect to intrusions and protrusions. The measure requires a maximally overlapping convex polygon, and this is efficiently estimated using a genetic algorithm. Examples of the measures application to medical image analysis are shown. 1.
The image torque operator: A new tool for midlevel vision
 In CVPR
, 2012
"... Contours are a powerful cue for semantic image understanding. Objects and parts of objects in the image are delineated from their surrounding by closed contours which make up their boundary. In this paper we introduce a new bottomup visual operator to capture the concept of closed contours, which w ..."
Abstract

Cited by 6 (5 self)
 Add to MetaCart
(Show Context)
Contours are a powerful cue for semantic image understanding. Objects and parts of objects in the image are delineated from their surrounding by closed contours which make up their boundary. In this paper we introduce a new bottomup visual operator to capture the concept of closed contours, which we call the ’Torque ’ operator. Its computation is inspired by the mechanical definition of torque or moment of force, and applied to image edges. The torque operator takes as input edges and computes over regions of different size a measure of how well the edges are aligned to form a closed, convex contour. We explore fundamental properties of this measure and demonstrate that it can be made a useful tool for visual attention, segmentation, and boundary edge detection by verifying its benefits on these applications. 1.
A New Convexity Measurement for 3D Meshes
"... This paper presents a novel convexity measurement for 3D meshes. The new convexity measure is calculated by minimizing the ratio of the summed area of valid regions in a mesh’s six views, which are projected on faces of the bounding box whose edges are parallel to the coordinate axes, to the sum of ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
(Show Context)
This paper presents a novel convexity measurement for 3D meshes. The new convexity measure is calculated by minimizing the ratio of the summed area of valid regions in a mesh’s six views, which are projected on faces of the bounding box whose edges are parallel to the coordinate axes, to the sum of three orthogonal projected areas of the mesh. The complete definition, theoretical analysis, and a computing algorithm of our convexity measure are explicitly described. This paper also proposes a new 3D shape descriptor CD (i.e., Convexity Distribution) based on the distribution of abovementioned ratios, which are computed by randomly rotating the mesh around its center, to better describe the object’s convexityrelated properties compared to existing convexity measurements. Our experiments not only show that the proposed convexity measure corresponds well with human intuition, but also demonstrate the effectiveness of the new convexity measure and the new shape descriptor by significantly improving the performance of other methods in the application of 3D shape retrieval. 1.
Classification of pathological shapes using convexity measures
 Pattern Recognition Letters
"... Two new shape measures for quantifying the degree of convexity are described. When applied to assessment of skin lesions they are shown to be an effective indicator of malignancy, outperforming Lee et al.’s OII scalespace based irregularity measure. In addition, the new measures were applied to th ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
(Show Context)
Two new shape measures for quantifying the degree of convexity are described. When applied to assessment of skin lesions they are shown to be an effective indicator of malignancy, outperforming Lee et al.’s OII scalespace based irregularity measure. In addition, the new measures were applied to the classification of mammographic masses and lung field boundaries and were shown to perform well relative to a large set of common shape measures that appear in the literature such as moments, compactness, symmetry, etc.
Efficient Computation of Shortest PathConcavity for 3D Meshes
"... In the context of shape segmentation and retrieval objectwide distributions of measures are needed to accurately evaluate and compare local regions of shapes. Lien et al. [16] proposed two pointwise concavity measures in the context of Approximate Convex Decompositions of polygons measuring the ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
In the context of shape segmentation and retrieval objectwide distributions of measures are needed to accurately evaluate and compare local regions of shapes. Lien et al. [16] proposed two pointwise concavity measures in the context of Approximate Convex Decompositions of polygons measuring the distance from a point to the polygon’s convex hull: an accurate Shortest PathConcavity (SPC) measure and a Straight LineConcavity (SLC) approximation of the same. While both are practicable on 2D shapes, the exponential costs of SPC in 3D makes it inhibitively expensive for a generalization to meshes [14]. In this paper we propose an efficient and straight forward approximation of the Shortest PathConcavity measure to 3D meshes. Our approximation is based on discretizing the space between mesh and convex hull, thereby reducing the continuous Shortest Path search to an efficiently solvable graph problem. Our approach works outofthebox on complex mesh topologies and requires no complicated handling of genus. Besides presenting a rigorous evaluation of our method on a variety of input meshes, we also define an SPCbased Shape Descriptor and show its superior retrieval and runtime performance compared with the recently presented results on the Convexity Distribution by Lian et al. [12]. 1.
Classification of cell nuclei using shape and texture indexes
"... In this paper, we present a study on the characterization and the classification of binary digital objects. This study is performed using a set of values obtained by the computation of "shape and texture indexes". To get the shape indexes, we extract a set of data called "measures &qu ..."
Abstract
 Add to MetaCart
(Show Context)
In this paper, we present a study on the characterization and the classification of binary digital objects. This study is performed using a set of values obtained by the computation of "shape and texture indexes". To get the shape indexes, we extract a set of data called "measures " from 2D shapes, like for example surface and perimeter. These indexes are then used as parameters of a function returning a real value that gives information about geometrical and morphological features of the shape to analyze. A model characterizing the shape (and the texture) of objects is subsequently built. An application to the classification of cell nuclei (in order to diagnose patients affected by the Progeria syndrome) is proposed. Keywords: Pattern recognition, shape and textures indexes, Haralick’s features, cell nuclei classification.
CORCORAN ET AL.: A CONVEXITY MEASURE FOR OPEN AND CLOSED CONTOURS 1 A Convexity Measure for Open and Closed Contours
"... Convexity represents a fundamental descriptor of object shape. This paper presents a new convexity measure for both open and closed simple contours. Given such a contour this measure extracts two corresponding open convex hulls. The shape similarity between these two hulls and the original contour i ..."
Abstract
 Add to MetaCart
(Show Context)
Convexity represents a fundamental descriptor of object shape. This paper presents a new convexity measure for both open and closed simple contours. Given such a contour this measure extracts two corresponding open convex hulls. The shape similarity between these two hulls and the original contour is then computed and normalized to give a measure of convexity. The time complexity of the proposed technique is O(n). The authors believe this technique represents the first measure of convexity which uses shape similarity and which can be applied to both open and closed contours. The proposed technique is shown to provide similar or greater performance relative to two other state of the art techniques. 1