We address the problem of identifying individual cetaceans from images showing the trailing edge of their fins. Given the trailing edge from an unknown individual, we produce a ranking of known individuals from a database. The nicks and notches along the trailing edge define an individual's unique signature. We define a representation based on integral curvature that is robust to changes in viewpoint and pose, and captures the pattern of nicks and notches in a local neighborhood at multiple scales. We explore two ranking methods that use this representation. The first uses a dynamic programming time-warping algorithm to align two representations, and interprets the alignment cost as a measure of similarity. This algorithm also exploits learned spatial weights to downweight matches from regions of unstable curvature. The second interprets the representation as a feature descriptor. Feature keypoints are defined at the local extrema of the representation. Descriptors for the set of known individuals are stored in a tree structure, which allows us to perform queries given the descriptors from an unknown trailing edge. We evaluate the top-k accuracy on two real-world datasets to demonstrate the effectiveness of the curvature representation, achieving top-1 accuracy scores of approximately 95 and 80 for bottlenose dolphins and humpback whales, respectively.
The curvature computed at points along a contour is often used to represent shape information @cite_20 @cite_15 @cite_0 . For differential curvature, this is defined as the change of the angle of the normal vector along the length of the contour @cite_26 . This representation is sensitive to noise, however, and instead we use integral curvature. A fixed shape is placed at points along the contour, while measuring the area of the intersection of the shape with the contour @cite_22 . Using integral curvature to capture shape information is a key part of the Leafsnap system @cite_24 , which classifies leaves by using curvature histograms at multiple scales as shape features. We briefly compare to Leafsnap in .
@cite_26 @cite_22 @cite_0 @cite_24 @cite_15 @cite_20
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A new theorem is discussed that relates the apparent curvature of the occluding contour of a visual shape to the intrinsic curvature of the surface and the radial curvature. This theorem allows the formulation of general laws for the apparent curvature, independent of viewing distance and regardless of the fact that the rim (the boundary between the visible and invisible parts of the object) is a general, thus twisted, space curve. Consequently convexities, concavities, or inflextions of contours in the retinal image allow the observer to draw inferences about local surface geometry with certainty. These results appear to be counterintuitive, witness to the treatment of the problem by recent authors. It is demonstrated how well-known examples, used to show how concavities and convexities of the contour have no obvious relation to solid shape, are actually good illustrations of the fact that convexities are due to local ovoid shapes, concavities to local saddle shapes. We define a new notion of total curvature, called net total curvature, for finite graphs embedded inR n , and investigate its properties. Two guiding principles ar e given by Milnor's way of measuring the local crookedness of a Jorda n curve via a Crofton-type formula, and by considering the double cover of a given graph as an Eulerian circuit. The strength of combining these ideas in defining the curvature f unctional is (1) it allows us to interpret the singular non-eulidean behavior at the vertices of the graph as a superposition of vertices of a 1-dimensional manifold, and thus (2) one can compute the total curva- ture for a wide range of graphs by contrasting local and global properties of the graph utilizing the integral geometric representation of the cur vature. A collection of results on upper lower bounds of the total curvature on isotopy homeomorphism classes of embed- dings is presented, which in turn demonstrates the effectiveness of net total curvature as a new functional measuring complexity of spatial graphs in differential-geometric terms. For smooth curved surfaces the dominant image feature is the apparent contour, or outline. This is the projection of the contour generator, the locus of points on the surface which separate visible and occluded parts. The contour generator is dependent of the local surface geometry and the viewpoint. Each viewpoint will generate a different contour generator. This paper addresses the problem of recovering the three–dimensional shape and motion of curves and surfaces from image sequences of apparent contours. @PARASPLIT For known viewer motion the visible surfaces can then be reconstructed by exploiting a spatio–temporal parametrization of the apparent contours and contour generators under viewer motion. A natural parametrization exploits the contour generators and the epipolar geometry between successive viewpoints. The epipolar parametrization leads to simplified expressions for the recovery of depth and surface curvatures from image velocities and accelerations and known viewer motion. @PARASPLIT The parametrization is, however, degenerate when the apparent contour is singular since the ray is tangent to the contour generator and at frontier points when the epipolar plane is a tangent plane to the surface. At these isolated points the epipolar parametrization can no longer be used to recover the local surface geometry. This paper reviews the epipolar parametrization and shows how the degenerate cases can be used to recover surface geometry and unknown viewer motion from apparent contours of curved surfaces. Practical implementations are outlined. In this paper, an effective shape-based leaf image retrieval system is presented. A new contour descriptor is defined which reduces the number of points for the shape representation considerably. This shape representation is based on the curvature of the leaf contour and it deals with the scale factor in a novel and compact way. A two-step algorithm for retrieval is used. In a first step, the database is reduced using some geometrical features. Then a similarity measure between the contour representations is used to rank conveniently leaf images on the database. We implemented a prototype system based on these features and performed several experiments to show its effectiveness for plant species identification.