Curve-Based Shape Matching Methods and Applications

One of the main cues we use in our everyday life when interacting with the environment is shape. For example, we use shape information to recognise a chair, grasp a cup, perceive traffic signs and solve jigsaw puzzles. We also use shape when dealing with more sophisticated tasks, such as the medical diagnosis of radiographs or the restoration of archaeological artifacts. While the perception of shape and its use is a natural ability of human beings, endowing machines with such skills is not straightforward. However, the exploitation of shape cues is important for the development of competent computer methods that will automatically perform tasks such as those just mentioned. With this aim, the present work proposes computer methods which use shape to tackle two important tasks, namely packing and object recognition. The packing problem arises in a variety of applications in industry, where the placement of a set of two-dimensional shapes on a surface such that no shapes overlap and the uncovered surface area is minimised is important. Given that this problem is NP-complete, we propose a heuristic method which searches for a solution of good quality, though not necessarily the optimal one, within a reasonable computation time. The proposed method adopts a pictorial representation and employs a greedy algorithm which uses a shape matching module in order to dynamically select the order and the pose of the parts to be placed based on the “gaps” appearing in the layout during the execution. This thesis further investigates shape matching in the context of object recognition and first considers the case where the target object and the input scene are represented by their silhouettes. Two distinct methods are proposed; the first method follows a local string matching approach, while the second one adopts a global optimisation approach using dynamic programming. Their use of silhouettes, however, rules out the consideration of any internal contours that might appear in the input scene, and in order to address this limitation, we later propose a graph-based scheme that performs shape matching incorporating information from both internal and external contours. Finally, we lift the assumption made that input data are available in the form of closed curves, and present a method which can robustly perform object recognition using curve fragments (edges) as input evidence. Experiments conducted with synthetic and real images, involving rigid and deformable objects, show the robustness of the proposed methods with respect to geometrical transformations, heavy clutter and substantial occlusion

MoSS: Monocular Shape Sensing for Continuum Robots

Continuum robots are promising candidates for interactive tasks in medical and industrial applications due to their unique shape, compliance, and miniaturization capability. Accurate and real-time shape sensing is essential for such tasks yet remains a challenge. Embedded shape sensing has high hardware complexity and cost, while vision-based methods require stereo setup and struggle to achieve real-time performance. This paper proposes the first eye-to-hand monocular approach to continuum robot shape sensing. Utilizing a deep encoder-decoder network, our method, MoSSNet, eliminates the computation cost of stereo matching and reduces requirements on sensing hardware. In particular, MoSSNet comprises an encoder and three parallel decoders to uncover spatial, length, and contour information from a single RGB image, and then obtains the 3D shape through curve fitting. A two-segment tendon-driven continuum robot is used for data collection and testing, demonstrating accurate (mean shape error of 0.91 mm, or 0.36% of robot length) and real-time (70 fps) shape sensing on real-world data. Additionally, the method is optimized end-to-end and does not require fiducial markers, manual segmentation, or camera calibration. Code and datasets will be made available at https://github.com/ContinuumRoboticsLab/MoSSNet.Comment: 8 pages, 6 figures, submitted to RA-

Optimized normal and distance matching for heterogeneous object modeling

This paper presents a new optimization methodology of material blending for heterogeneous object modeling by matching the material governing features for designing a heterogeneous object. The proposed method establishes point-to-point correspondence represented by a set of connecting lines between two material directrices. To blend the material features between the directrices, a heuristic optimization method developed with the objective is to maximize the sum of the inner products of the unit normals at the end points of the connecting lines and minimize the sum of the lengths of connecting lines. The geometric features with material information are matched to generate non-self-intersecting and non-twisted connecting surfaces. By subdividing the connecting lines into equal number of segments, a series of intermediate piecewise curves are generated to represent the material metamorphosis between the governing material features. Alternatively, a dynamic programming approach developed in our earlier work is presented for comparison purposes. Result and computational efficiency of the proposed heuristic method is also compared with earlier techniques in the literature. Computer interface implementation and illustrative examples are also presented in this paper

Face analysis using curve edge maps

This paper proposes an automatic and real-time system for face analysis, usable in visual communication applications. In this approach, faces are represented with Curve Edge Maps, which are collections of polynomial segments with a convex region. The segments are extracted from edge pixels using an adaptive incremental linear-time fitting algorithm, which is based on constructive polynomial fitting. The face analysis system considers face tracking, face recognition and facial feature detection, using Curve Edge Maps driven by histograms of intensities and histograms of relative positions. When applied to different face databases and video sequences, the average face recognition rate is 95.51%, the average facial feature detection rate is 91.92% and the accuracy in location of the facial features is 2.18% in terms of the size of the face, which is comparable with or better than the results in literature. However, our method has the advantages of simplicity, real-time performance and extensibility to the different aspects of face analysis, such as recognition of facial expressions and talking

A relaxed approach for curve matching with elastic metrics

In this paper we study a class of Riemannian metrics on the space of unparametrized curves and develop a method to compute geodesics with given boundary conditions. It extends previous works on this topic in several important ways. The model and resulting matching algorithm integrate within one common setting both the family of $H^2$-metrics with constant coefficients and scale-invariant $H^2$-metrics on both open and closed immersed curves. These families include as particular cases the class of first-order elastic metrics. An essential difference with prior approaches is the way that boundary constraints are dealt with. By leveraging varifold-based similarity metrics we propose a relaxed variational formulation for the matching problem that avoids the necessity of optimizing over the reparametrization group. Furthermore, we show that we can also quotient out finite-dimensional similarity groups such as translation, rotation and scaling groups. The different properties and advantages are illustrated through numerical examples in which we also provide a comparison with related diffeomorphic methods used in shape registration.Comment: 27 page

Piecewise rigid curve deformation via a Finsler steepest descent

This paper introduces a novel steepest descent flow in Banach spaces. This extends previous works on generalized gradient descent, notably the work of Charpiat et al., to the setting of Finsler metrics. Such a generalized gradient allows one to take into account a prior on deformations (e.g., piecewise rigid) in order to favor some specific evolutions. We define a Finsler gradient descent method to minimize a functional defined on a Banach space and we prove a convergence theorem for such a method. In particular, we show that the use of non-Hilbertian norms on Banach spaces is useful to study non-convex optimization problems where the geometry of the space might play a crucial role to avoid poor local minima. We show some applications to the curve matching problem. In particular, we characterize piecewise rigid deformations on the space of curves and we study several models to perform piecewise rigid evolution of curves