Abstract: A point correspondence procedure is applied to a set of images of a specular object to produce sparse reflection correspondences. The set of images is subject to rotation while acquired by a camera. That is, either the camera, the environment or the object rotates. Either a linear system A?=0 is solved or a related second order cone program (SOCP) is solved, where ? is a vector of local surface parameters. Gradients of the surface are obtained from the local quadric surface parameters, and the gradients are integrated to obtain normals, wherein the normals define a shape of the surface.

Abstract: Embodiments of the invention disclose a system and a method for determining points of parabolic curvature on a surface of a specular object from a set of images of the object is acquired by a camera under a relative motion between a camera-object pair and the environment. The method determines directions of image gradients at each pixel of each image in the set of images, wherein pixels from different images corresponding to an identical point on the surface of the object form corresponding pixels. The corresponding pixels having substantially constant the direction of the image gradients are selected as pixels representing points of the parabolic curvature.

Abstract: A point correspondence procedure is applied to a set of images of a specular object to produce sparse reflection correspondences. The set of images is subject to rotation while acquired by a camera. That is, either the camera, the environment or the object rotates. Either a linear system A?=0 is solved or a related second order cone program (SOCP) is solved, where ? is a vector of local surface parameters. Gradients of the surface are obtained from the local quadric surface parameters, and the gradients are integrated to obtain normals, wherein the normals define a shape of the surface.

Abstract: Embodiments of the invention disclose a system and a method for determining points of parabolic curvature on a surface of a specular object from a set of images of the object is acquired by a camera under a relative motion between a camera-object pair and the environment. The method determines directions of image gradients at each pixel of each image in the set of images, wherein pixels from different images corresponding to an identical point on the surface of the object form corresponding pixels. The corresponding pixels having substantially constant the direction of the image gradients are selected as pixels representing points of the parabolic curvature.

Abstract: Invention describes a method and system for detecting and tracking an object in a sequence of images. For each image the invention determines an object descriptor from a tracking region in a current image in a sequence of images, in which the tracking region corresponds to a location of an object in a previous image. A regression function is applied to the descriptor to determine a motion of the object from the previous image to the current image, in which the motion has a matrix Lie group structure. The location of the tracking region is updated using the motion of the object.

Abstract: A method constructs a classifier from training data and detects moving objects in test data using the trained classifier. High-level features are generated from low-level features extracted from training data. The high level features are positive definite matrices on an analytical manifold. A subset of the high-level features is selected, and an intrinsic mean matrix is determined. Each high-level feature is mapped to a feature vector on a tangent space of the analytical manifold using the intrinsic mean matrix. An untrained classifier is trained with the feature vectors to obtain a trained classifier. Test high-level features are similarly generated from test low-level features. The test high-level features are classified using the trained classifier to detect moving objects in the test data.

Abstract: A computer implemented method constructs a classifier for classifying test data. High-level features are generated from low-level features extracted from training data. The high level features are positive definite matrices in a form of an analytical manifold. A subset of the high-level features is selected. An intrinsic mean matrix is determined from the subset of the selected high-level features. Each high-level feature is mapped to a feature vector onto a tangent space of the analytical manifold using the intrinsic mean matrix. Then, an untrained classifier model can be trained with the feature vectors to obtain a trained classifier. Subsequently, the trained classifier can classify unknown test data.

Abstract: Invention describes a method and system for detecting and tracking an object in a sequence of images. For each image the invention determines an object descriptor from a tracking region in a current image in a sequence of images, in which the tracking region corresponds to a location of an object in a previous image. A regression function is applied to the descriptor to determine a motion of the object from the previous image to the current image, in which the motion has a matrix Lie group structure. The location of the tracking region is updated using the motion of the object.

Abstract: A method constructs a classifier from training data and detects moving objects in test data using the trained classifier. High-level features are generated from low-level features extracted from training data. The high level features are positive definite matrices on an analytical manifold. A subset of the high-level features is selected, and an intrinsic mean matrix is determined. Each high-level feature is mapped to a feature vector on a tangent space of the analytical manifold using the intrinsic mean matrix. An untrained classifier is trained with the feature vectors to obtain a trained classifier. Test high-level features are similarly generated from test low-level features. The test high-level features are classified using the trained classifier to detect moving objects in the test data.

Abstract: A computer implemented method constructs a classifier for classifying test data. High-level features are generated from low-level features extracted from training data. The high level features are positive definite matrices in a form of an analytical manifold. A subset of the high-level features is selected. An intrinsic mean matrix is determined from the subset of the selected high-level features. Each high-level feature is mapped to a feature vector onto a tangent space of the analytical manifold using the intrinsic mean matrix. Then, an untrained classifier model can be trained with the feature vectors to obtain a trained classifier. Subsequently, the trained classifier can classify unknown test data.