Geodesic Methods for Shape and Surface Processing

Abstract-We present a novel face representation based on locally adaptive regression kernel (LARK) descriptors [1]. Our LARK descriptor measures a self-similarity based on "signal-induced distance" between a center pixel and surrounding pixels in a local neighborhood. By applying principal component analysis (PCA) and a logistic function to LARK consecutively, we develop a new binary-like face representation which achieves state of the art face verification performance on the challenging benchmark "Labeled Faces in the Wild" (LFW) dataset [2]. In the case where training data are available, we employ one-shot similarity (OSS) [3], [4] based on linear discriminant analysis (LDA) [5]. The proposed approach achieves state of the art performance on both the unsupervised setting and the image restrictive training setting (72.23% and 78.90% verification rates) respectively as a single descriptor representation, with no preprocessing step. As opposed to [4] which combined 30 distances to achieve 85.13%, we achieve comparable performance (85.1%) with only 14 distances while significantly reducing computational complexity.

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“…This can be thought of a non-linear mapping to the eigenvalues in order to turn the structure tensor into a Riemannian metric [32].…”

Section: Locally Adaptive Regression Kernels (Lark)mentioning

confidence: 99%

Face Verification Using the LARK Representation

Seo

Milanfar

2011

IEEE Trans.Inform.Forensic Secur.

140

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“…Different distance metrics have been studied. Peyré and Cohen [13] constructed geodesic CVT on mesh surfaces and used it for shape segmentation and remeshing. Alternatively, Yan et al [14] computed the constrained and restricted CVT on mesh surfaces based on Euclidean distance metric, in the context of isotropic remeshing.…”

Section: A Related Workmentioning

confidence: 99%

Computing 2D Periodic Centroidal Voronoi Tessellation

Yan

Wang

Lévy

et al. 2011

2011 Eighth International Symposium on Voronoi Diagrams in Science and Engineering

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Abstract-In this paper, we propose an efficient algorithm to compute the centroidal Voronoi tessellation in 2D periodic space. We first present a simple algorithm for constructing the periodic Voronoi diagram (PVD) from a Euclidean Voronoi diagram. The presented PVD algorithm considers only a small set of periodic copies of the input sites, which is more efficient than previous approaches requiring full copies of the sites (9 in 2D and 27 in 3D). The presented PVD algorithm is applied in a fast Newton-based framework for computing the centroidal Voronoi tessellation (CVT). We observe that full-hexagonal patterns can be obtained via periodic CVT optimization attributed to the convergence of the Newton-based CVT computation.

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“…In order to efficiently compute the anisotropic geodesic paths, a Fast Marching Method (FMM) developed for computing geodesic distances with generic Riemannian metrics [31] is used. Compared to Dijkstra algorithm [11], the FMM computes geodesics with the same computational complexity but more accurate estimation [28]. When computing geodesic paths with Eq.…”

Section: Morphological Thin Lines Enhancementmentioning

confidence: 99%

“…2, bottom). Since j+ ~ j-, a path "( has a shorter local length if its speed "('(t) is collinear to c [28]. This way, the front propagates faster along the direction of the potential network, i.e.…”

Section: Morphological Thin Lines Enhancementmentioning

confidence: 99%

A new generic method for semi-automatic extraction of river and road networks in low- and mid-resolution satellite images

Grazzini

Dillard

Soille³

2010

SPIE Proceedings

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This paper addresses the problem of semi-automatic extraction of road or hydrographic networks in satellite images. For that purpose, we propose an approach combining concepts arising from mathematical morphology and hydrology. The method exploits both geometrical and topological characteristics of rivers/roads and their tributaries in order to reconstruct the complete networks. It assumes that the images satisfy the following two general assumptions, which are the minimum conditions for a road/river network to be identifiable and are usually verified in low-to mid-resolution satellite images: (i) visual constraint: most pixels composing the network have similar spectral signature that is distinguishable from most of the surrounding areas; (ii) geometric constraint;: a line is a region that is relatively long and narrow , compared with other objects in the image. While t.his approach fully exploits local (roads/rivers are modeled as elongated regions with a smooth spectral signature in the image and a maximum width) and global (they are structured like a tree) characteristics of the networks, further directional information about the image structures is incorporated. Namely, an appropriate anisotropic metric is designed by using both the characteristic features of the target network and the eigen-decomposition of the gradient structure tensor of the image. Following, the geodesic propagation from a given network seed with this metric is combined with hydrological operators for overland flow simulation to extract the paths which contain most line evidence and identify them with the target network.

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Geodesic Methods for Shape and Surface Processing

Cited by 19 publications

References 25 publications

Face Verification Using the LARK Representation

Face Verification Using the LARK Representation

Computing 2D Periodic Centroidal Voronoi Tessellation

A new generic method for semi-automatic extraction of river and road networks in low- and mid-resolution satellite images

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