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.
Descriptors based on orientation histograms are widely used in computer vision. The spatial pooling involved in these representations provides important invariance properties, yet it is also responsible for the loss of important details. In this paper, we suggest a way to preserve the details described by the local curvature. We propose a descriptor that comprises the direction and magnitude of curvature and naturally expands classical orientation histograms like SIFT and HOG. We demonstrate the general benefit of the expansion exemplarily for image classification, object detection, and descriptor matching. Differential invariants of curves and surfaces such as curvatures and their derivatives play a central role in Geometry Processing. They are, however, sensitive to noise and minor perturbations and do not exhibit the desired multi-scale behavior. Recently, the relationships between differential invariants and certain integrals over small neighborhoods have been used to define efficiently computable integral invariants which have both a geometric meaning and useful stability properties. This paper considers integral invariants defined via distance functions, and the stability analysis of integral invariants in general. Such invariants proved useful for many tasks where the computation of shape characteristics is important. A prominent and recent example is the automatic reassembling of broken objects based on correspondences between fracture surfaces.  We describe the first mobile app for identifying plant species using automatic visual recognition. The system --- called Leafsnap --- identifies tree species from photographs of their leaves. Key to this system are computer vision components for discarding non-leaf images, segmenting the leaf from an untextured background, extracting features representing the curvature of the leaf's contour over multiple scales, and identifying the species from a dataset of the 184 trees in the Northeastern United States. Our system obtains state-of-the-art performance on the real-world images from the new Leafsnap Dataset --- the largest of its kind. Throughout the paper, we document many of the practical steps needed to produce a computer vision system such as ours, which currently has nearly a million users.  We present an approach that directly uses curvature cues in a discriminative way to perform object recognition. We show that integrating curvature information substantially improves detection results over descriptors that solely rely upon histograms of orientated gradients (HoG). The proposed approach is generic in that it can be easily integrated into state-of-the-art object detection systems. Results on two challenging datasets are presented: ETHZ Shape Dataset and INRIA horses Dataset, improving state-of the-art results using HoG by 7.6 and 12.3 in average precision (AP), respectively. In particular, we achieve higher recall at lower false positive rates.