Correcting curvature-density effects in the Hamilton-Jacobi skeleton

The Hainilton-Jacobi approach has proven to be a powerful and elegant method for extracting the skeleton of two-dimensional (2-D) shapes. The approach is based on the observation that the normalized flux associated with the inward evolution of the object boundary at nonskeletal points tends to zero as the size of the integration area tends to zero, while the flux is negative at the locations of skeletal points. Nonetheless, the error in calculating the flux on the image lattice is both limited by the pixel resolution and also proportional to the curvature of the boundary evolution front and, hence, unbounded near endpoints. This makes the exact location of endpoints difficult and renders the performance of the skeleton extraction algorithm dependent on a threshold parameter. This problem can be overcome by using interpolation techniques to calculate the flux with subpixel precision. However, here, we develop a method for 2-D skeleton extraction that circumvents the problem by eliminating the curvature contribution to the error. This is done by taking into account variations of density due to boundary curvature. This yields a skeletonization algorithm that gives both better localization and less susceptibility to boundary noise and parameter choice than the Hamilton-Jacobi method

Fast Contour Matching Using Approximate Earth Mover's Distance

Weighted graph matching is a good way to align a pair of shapes represented by a set of descriptive local features; the set of correspondences produced by the minimum cost of matching features from one shape to the features of the other often reveals how similar the two shapes are. However, due to the complexity of computing the exact minimum cost matching, previous algorithms could only run efficiently when using a limited number of features per shape, and could not scale to perform retrievals from large databases. We present a contour matching algorithm that quickly computes the minimum weight matching between sets of descriptive local features using a recently introduced low-distortion embedding of the Earth Mover's Distance (EMD) into a normed space. Given a novel embedded contour, the nearest neighbors in a database of embedded contours are retrieved in sublinear time via approximate nearest neighbors search. We demonstrate our shape matching method on databases of 10,000 images of human figures and 60,000 images of handwritten digits

Drexel University

We present a 3D matching framework based on a many-to-many matching algorithm that works with skeletal representations of 3D volumetric objects. We demonstrate the performance of this approach on a large database of 3D objects containing more than 1000 exemplars. The method is especially suited to matching objects with distinct part structure and is invariant to part articulation. Skeletal matching has an intuitive quality that helps in defining the search and visualizing the results. In particular, the matching algorithm produces a direct correspondence between two skeletons and their parts, which can be used for registration and juxtaposition. 1

A three-level signature by graph for Reverse Engineering of mechanical assemblies

Several approaches exist to provide Reverse Engineering solutions on mechanical parts. Mechanical assemblies and the expertise information retrieved at the same time with the model geometry are not really taken into account in the literature. Thus, the main challenge of this contribution is to propose a methodology to retrieve the Digital Mock-Up of a mechanical assembly from its meshed data (from digitalization). The output DMU consists of expertise information and parameterized CAD models. The methodology proposed relies on a signature by a three-level graph. It enables to provide an adequate level of details by identifying the corresponding functional surfaces in meshed data. The first-level graph is a connectivity graph; the intermediate level is the same as the first with the geometric type of face added to each node (plane, cylinder and sphere) and the deepest level corresponds to a precedence graph. This one provides information such as functional surfaces and position between them (perpendicularity, coaxiality etc.). The solutions developed and the results are presented in this paper. The methodology is illustrated thanks to an industrial use-case with a scan of an assembly with a connecting rod and a piston. The conclusion and perspectives will complete this paper

An Efficiency Criterion for 2D Shape Model Selection

We propose efficiency of representation as a criterion for evaluating shape models, then apply this criterion to compare the boundary curve representation with the medial axis. We estimate the å-entropy of two compact classes of curves. We then construct two adaptive encodings for noncompact classes of shapes, one using the boundary curve and the other using the medial axis, and determine precise conditions for when the medial axis is more efficient. Along the way we construct explicit near-optimal boundarybased approximations for compact classes of shapes and an explicit compression scheme for non-compact classes of shapes based on the medial axis. We end with an application of the criterion to shape data

Mesure de similarité de graphes par noyau de sacs de chemins

La classification de graphes s'appuie généralement sur une mesure de similarité entre graphes utilisée ensuite par un classifieur. Nous proposons ici l'utilisation des méthodes à noyaux pour une application de reconnaissance de formes représentées à l'aide de graphes. Nous introduisons tout d'abord la notion de noyau de graphe que nous étendons en proposant des noyaux entre des sacs de chemins. Nos premiers résultats montrent l'intérêt de cette approche par rapport aux approches classiques de comparaison de graphes

A novel shape descriptor based on salient keypoints detection for binary image matching and retrieval

We introduce a shape descriptor that extracts keypoints from binary images and automatically detects the salient ones among them. The proposed descriptor operates as follows: First, the contours of the image are detected and an image transformation is used to generate background information. Next, pixels of the transformed image that have specific characteristics in their local areas are used to extract keypoints. Afterwards, the most salient keypoints are automatically detected by filtering out redundant and sensitive ones. Finally, a feature vector is calculated for each keypoint by using the distribution of contour points in its local area. The proposed descriptor is evaluated using public datasets of silhouette images, handwritten math expressions, hand-drawn diagram sketches, and noisy scanned logos. Experimental results show that the proposed descriptor compares strongly against state of the art methods, and that it is reliable when applied on challenging images such as fluctuated handwriting and noisy scanned images. Furthermore, we integrate our descripto