Resonant Deformable Matching: Simultaneous Registration and Reconstruction
In the past decade we have seen the emergence of many efficient algorithms for estimating non-rigid deformations registering a template to target features. Registration of density functions is particularly popular. In contrast to the success enjoyed by th
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Abstract. In the past decade we have seen the emergence of many efficient algorithms for estimating non-rigid deformations registering a template to target features. Registration of density functions is particularly popular. In contrast to the success enjoyed by the density function representation, we have not seen similar success with the signed distance function representation. Resonant deformable matching (RDM) simultaneously estimates a non-rigid deformation and a set of unknown target normal directions by registering fields comprising signed distance and probability density information. Resonance occurs as the reconstruction estimate comes into agreement with the registered template. We perform experiments probing two problems: point-set registration and normal estimation. RDM compares favorably to top tier point registration and graph algorithms in terms of registration and reconstruction metrics.
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Introduction
Many problems in computer vision require us to determine correspondences between similar sets of features. However, we are often faced with scenarios where it is very difficult to even define what a correspondence between two objects should be—no natural map, moreover bijection, may exist at all—often due to mismatched representations. Work focused on determining point correspondences for matching organized features has been abundant, as we highlight below, but there remains a clear need for handling mismatched representations. This work provides a solution for the mismatched case where the template consists of oriented points and the target consists of points, under the assumption that both template and target are drawn from outlines of shapes. Given a set of point-features, correspondences can be obtained via registration. In this approach, sparse feature sets are often first converted into scalar field representations. Then non-rigid matching of the template field with that of the target yields dense point to point correspondences. For example, point features can be converted into a probability density function representation [1–3]. Registration is obtained by deforming the template density onto the target using regularized spatial deformations [4,5]. Implicit shape representations are not restricted to probability density functions estimated from sets of features. c Springer International Publishing AG 2016 B. Leibe et al. (Eds.): ECCV 2016, Part VI, LNCS 9910, pp. 51–68, 2016. DOI: 10.1007/978-3-319-46466-4 4
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J. Corring and A. Rangarajan
Implicit representations abound in the literature [6–8]. The signed distance function (SDF) is an example in which the sign encodes interior/exterior properties with the absolute value encoding the distance to the nearest point in the set of curves (surfaces) [9–11]. Contrast this with the unsigned distance function which lacks interior/exterior information. Surprisingly, there is little work on matching template and target SDFs. We address the technical reasons for this now. The signed distance bS : Rd → R for an open set S satisfies |∇bS | = 1 : bS |∂S = 0 wi
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