Non‐Rigid Puzzles

Shape correspondence is a fundamental problem in computer graphics and vision, with applications in various problems including animation, texture mapping, robotic vision, medical imaging, archaeology and many more. In settings where the shapes are allowed to undergo non‐rigid deformations and only partial views are available, the problem becomes very challenging. To this end, we present a non‐rigid multi‐part shape matching algorithm. We assume to be given a reference shape and its multiple parts undergoing a non‐rigid deformation. Each of these query parts can be additionally contaminated by clutter, may overlap with other parts, and there might be missing parts or redundant ones. Our method simultaneously solves for the segmentation of the reference model, and for a dense correspondence to (subsets of) the parts. Experimental results on synthetic as well as real scans demonstrate the effectiveness of our method in dealing with this challenging matching scenario.     

Hypercolumn-array based image representation and its application to shape-based object detection

Biological and psychological evidence increasingly reveals that high-level geometrical and topological features are the keys to shape-based object recognition in the brain. Attracted by the excellent performance of neural visual systems, we simulate the mechanism of hypercolumns in the mammalian cortical area V1 that selectively responds to oriented bar stimuli. We design an orderly-arranged hypercolumn array to extract and represent linear or near-linear stimuli in an image. Each unit of this array covers stimuli of various orientations in a small area, and multiple units together produce a low-dimensional vector to describe shape. Based on the neighborhood of units in the array, we construct a graph whose node represents a short line segment with a certain position and slope. Therefore, a contour segment in the image can be represented with a route in this graph. The graph converts an image, comprised of typically unstructured raw data, into structured and semantic-enriched data. We search along the routes in the graph and compare them with a shape template for object detection. The graph greatly upgrades the level of image representation, remarkably reduces the load of combinations, significantly improves the efficiency of object searching, and facilitates the intervening of high-level knowledge. This work provides a systematic infrastructure for shape-based object recognition.     

A shape-based voting algorithm for pedestrian detection and tracking

This paper presents the MOUGH (mixture of uniform and Gaussian Hough) Transform for shape-based object detection and tracking. We show that the edgels of a rigid object at a given orientation are approximately distributed according to a Gaussian mixture model (GMMs). A variant of the generalized Hough transform is proposed, voting using GMMs and optimized via Expectation-Maximization, that is capable of searching images for a mildly-deformable shape, based on a training dataset of (possibly noisy) images with only crude estimates of scale and centroid of the object in each image. Further modifications are proposed to optimize the algorithm for tracking. The method is able to locate and track objects reliably even against complex backgrounds such as dense moving foliage, and with a moving camera. Experimental results indicate that the algorithm is superior to previously published variants of the Hough transform and to active shape models in tracking pedestrians from a side view.     

A comparison of local parametric C Bézier interpolants for triangular meshes

Parametric curved shape surface schemes interpolating vertices and normals of a given triangular mesh with arbitrary topology are widely used in computer graphics for gaming and real-time rendering due to their ability to effectively represent any surface of arbitrary genus. In this context, continuous curved shape surface schemes using only the information related to the triangle corresponding to the patch under construction, emerged as attractive solutions responding to the requirements of resource-limited hardware environments. In this paper we provide a unifying comparison of the local parametric C⁰ curved shape schemes we are aware of, based on a reformulation of their original constructions in terms of polynomial Bézier triangles. With this reformulation we find a geometric interpretation of all the schemes that allows us to analyse their strengths and shortcomings from a geometrical point of view. Further, we compare the four schemes with respect to their computational costs, their reproduction capabilities of analytic surfaces and their response to different surface interrogation methods on arbitrary triangle meshes with a low triangle count that actually occur in their real-world use.     

Exoskeleton: Curve network abstraction for 3D shapes

In this paper, we introduce the concept of an exoskeleton as a new abstraction of arbitrary shapes that succinctly conveys both the perceptual and the geometric structure of a 3D model. We extract exoskeletons via a principled framework that combines segmentation and shape approximation. Our method starts from a segmentation of the shape into perceptually relevant parts and then constructs the exoskeleton using a novel extension of the Variational Shape Approximation method. Benefits of the exoskeleton abstraction to graphics applications such as simplification and chartification are presented.     

Robust skeletonization using the discrete λ-medial axis

Medial axes and skeletons are notoriously sensitive to contour irregularities. This lack of stability is a serious problem for applications in e.g. shape analysis and recognition. In 2005, Chazal and Lieutier introduced the λ-medial axis as a new concept for computing the medial axis of a shape subject to single parameter filtering. The λ-medial axis is stable under small shape perturbations, as proved by these authors. In this article, a discrete λ-medial axis (DLMA) is introduced and compared with the recently introduced integer medial axis (GIMA). We show that DLMA provides measurably better results than GIMA, with regard to stability and sensibility to rotations. We give efficient algorithms to compute the DLMA, and we also introduce a variant of the DLMA which may be computed in linear-time.     

A shape prior constraint for implicit active contours

We present a shape prior constraint to guide the evolution of implicit active contours. Our method includes three core techniques. Firstly, a rigid registration is introduced, using a line search method within a level set framework. The method automatically finds the time step for the iterative optimization processes. The order for finding the optimal translation, rotation and scale is derived experimentally. Secondly, a single reconstructed shape is created from a shape distribution of a previously acquired learning set. The reconstructed shape is applied to guide the active contour evolution. Thirdly, our method balances the impact of the shape prior versus the image guidance of the active contour. A mixed stopping condition is defined based on the stationarity of the evolving curve and the shape prior constraint. Our method is completely non-parametric and avoids taking linear combinations of non-linear signed distance functions, which would cause problems because distance functions are not closed under linear operations. Experimental results show that our method is able to extract the desired objects in several circumstances, namely when noise is present in the image, when the objects are in slightly different poses and when parts of the object are invisible in the image.