We introduce new results connecting differential and morphological operators that provide a formal and theoretically grounded approach for stable and fast contour evolution. Contour evolution algorithms have been extensively used for boundary detection and tracking in computer vision. The standard solution based on partial differential equations and level-sets requires the use of numerical methods of integration that are costly computationally and may have stability issues. We present a morphological approach to contour evolution based on a new curvature morphological operator valid for surfaces of any dimension. We approximate the numerical solution of the curve evolution PDE by the successive application of a set of morphological operators defined on a binary level-set and with equivalent infinitesimal behavior. These operators are very fast, do not suffer numerical stability issues, and do not degrade the level set function, so there is no need to reinitialize it. Moreover, their implementation is much easier since they do not require the use of sophisticated numerical algorithms. We validate the approach providing a morphological implementation of the geodesic active contours, the active contours without borders, and turbopixels. In the experiments conducted, the morphological implementations converge to solutions equivalent to those achieved by traditional numerical solutions, but with significant gains in simplicity, speed, and stability.

Abstract-Emerging applications of computer vision and pattern recognition in mobile devices and networked computing require the development of resourcelimited algorithms. Linear classification techniques have an important role to play in this context, given their simplicity and low computational requirements. The paper reviews the state-of-the-art in gender classification, giving special attention to linear techniques and their relations. It discusses why linear techniques are not achieving competitive results and shows how to obtain state-of-the-art performances. Our work confirms previous results reporting very close classification accuracies for Support Vector Machines (SVMs) and boosting algorithms on single-database experiments. We have proven that Linear Discriminant Analysis on a linearly selected set of features also achieves similar accuracies. We perform cross-database experiments and prove that single database experiments were optimistically biased. If enough training data and computational resources are available, SVM's gender classifiers are superior to the rest. When computational resources are scarce but there is enough data, boosting or linear approaches are adequate. Finally, if training data and computational resources are very scarce, then the linear approach is the best choice.

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Face alignment algorithms locate a set of landmark points in images of faces taken in unrestricted situations. State-of-the-art approaches typically fail or lose accuracy in the presence of occlusions, strong deformations, large pose variations and ambiguous configurations. In this paper we present 3DDE, a robust and efficient face alignment algorithm based on a coarse-to-fine cascade of ensembles of regression trees. It is initialized by robustly fitting a 3D face model to the probability maps produced by a convolutional neural network. With this initialization we address self-occlusions and large face rotations. Further, the regressor implicitly imposes a prior face shape on the solution, addressing occlusions and ambiguous face configurations. Its coarse-to-fine structure tackles the combinatorial explosion of parts deformation. In the experiments performed, 3DDE improves the state-of-the-art in 300W, COFW, AFLW and WFLW data sets. Finally, we perform cross-dataset experiments that reveal the existence of a significant data set bias in these benchmarks.

Abstract. The main result of this paper is a procedure for self-calibration of a moving camera from instantaneous optical ow. Under certain assumptions, this procedure allows the ego-motion and some intrinsic parameters of the camera to be determined solely from the instantaneous positions and velocities of a set of image features. The proposed method relies upon the use of a di erential epipolar equation that relates optical ow to the ego-motion and internal geometry of the camera. The paper presents a detailed derivation of this equation. This aspect of the work may be seen as a recasting into an analytical framework of the pivotal research o f V i eville and Faugeras. 1 The information about the camera's ego-motion and internal geometry enters the di erential epipolar equation via two matrices. It emerges that the optical ow determines the composite ratio of some of the entries of the two matrices. It is shown that a camera with unknown focal length undergoing arbitrary motion can be self-calibrated via closed-form expressions in the composite ratio. The corresponding formulae specify ve ego-motion parameters, as well as the focal length and its derivative. An accompanying procedure is presented for reconstructing the viewed scene, up to scale, from the derived self-calibration data and the optical ow data. Experimental results are given to demonstrate the correctness of the approach. IntroductionOf considerable interest in recent y ears has been to generate computer vision algorithms able to operate with uncalibrated cameras. One challenge has been to reconstruct a scene, up to scale, from a stereo pair of images obtained by cameras whose internal geometry is not fully known, and whose relative orientation is unknown. Remarkably, such a reconstruction is sometimes attainable solely by consideration of corresponding points (that depict a common scene point) identied within the two images. A key process involved here is that of self-calibration, whereby the unknown relative orientation and intrinsic parameters of the cameras are automatically determined. 2,3 In this paper, we d e v elop a method for self-calibration of a single moving camera from instantaneous optical ow. Here self-calibration amounts to automatically determining the unknown instantaneous ego-motion and intrinsic parameters of the camera, and is analogous to self-calibration of a stereo vision set-up using corresponding points.The proposed method of self-calibration rests on a di erential epipolar equation that relates optical ow to the ego-motion and intrinsic parameters of the camera. A substantial portion of the paper is devoted to a detailed derivation of this equation. The di erential epipolar equation has as its counterpart in stereo vision