Abstract: One or more aspects of the subject disclosure are directed towards identifying objects within an image via image searching/matching. In one aspect, an image is processed into bounding boxes, with the bounding boxes further processed to each surround a possible object. A sub-image of pixels corresponding to the bounding box is featurized for matching with tagged database images. The information (tags) associated with any matched images is processed to identify/categorize the sub-image and thus the object corresponding thereto.

Abstract: One or more aspects of the subject disclosure are directed towards identifying objects within an image via image searching/matching. In one aspect, an image is processed into bounding boxes, with the bounding boxes further processed to each surround a possible object. A sub-image of pixels corresponding to the bounding box is featurized for matching with tagged database images. The information (tags) associated with any matched images is processed to identify/categorize the sub-image and thus the object corresponding thereto.

Abstract: A method for colorization of images is presented. The method comprises the following steps: Displaying an image (102); applying multiple color markings (at least two colors are different) to the displayed image (104); automatically coloring the image by applying a constrained optimization to a cost function that is responsive to the marked colors and the intensity differences of the neighborhoods of some of all of the pixels (106); the resultant image is subsequently stored (110), displayed (108), or transferred (112).

Abstract: A method for colorization of images is presented. The method comprises the following steps: Displaying an image (102); applying multiple color markings (at least two colors are different) to the displayed image (104); automatically coloring the image by applying a constrained optimization to a cost function that is responsive to the marked colors and the intensity differences of the neighborhoods of some of all of the pixels (106); the resultant image is subsequently stored (110), displayed (108), or transferred (112).

Abstract: In a method and system for matting a foreground object F having an opacity ? constrained by associating a characteristic with selected pixels in an image having a background B, weights are determined for all edges of neighboring pixels for the image and used to build a Laplacian matrix L. The equation ? is solved where ?=arg min ?T L? s.t.?i=si, ?i?S, S is the group of selected pixels, and si is the value indicated by the associated characteristic. The equation Ii=?iFi+(1??i)Bi is solved for F and B with additional smoothness assumptions on F and B; after which the foreground object F may be composited on a selected background B? that may be the original background B or may be a different background, thus allowing foreground features to be extracted from the original image and copied to a different background.

Abstract: In a method and system for matting a foreground object F having an opacity ? constrained by associating a characteristic with selected pixels in an image having a background B, weights are determined for all edges of neighboring pixels for the image and used to build a Laplacian matrix L. The equation ? is solved where ?=arg min ?T L? s.t.?i=si, ?i?S, S is the group of selected pixels, and si is the value indicated by the associated characteristic. The equation Ii=?iFi+(1??i)Bi is solved for F and B with additional smoothness assumptions on F and B; after which the foreground object F may be composited on a selected background B? that may be the original background B or may be a different background, thus allowing foreground features to be extracted from the original image and copied to a different background.

Abstract: In a method and system for matting a foreground object F having an opacity ? constrained by associating a characteristic with selected pixels in an image having a background B, weights are determined for all edges of neighboring pixels for the image and used to build a Laplacian matrix L. The equation ? is solved where ?=arg min ?T L? s.t.?i=si, ?i ? S, S is the group of selected pixels, and si is the value indicated by the associated characteristic. The equation Ii=?iFi+(1??i)Bi is solved for F and B with additional smoothness assumptions on F and B; after which the foreground object F may be composited on a selected background B? that may be the original background B or may be a different background, thus allowing foreground features to be extracted from the original image and copied to a different background.

Abstract: A method maximizes a candidate solution to a cardinality-constrained combinatorial optimization problem of sparse principal component analysis. An approximate method has as input a covariance matrix A, a candidate solution, and a sparsity parameter k. A variational renormalization for the candidate solution vector x with regards to the eigenvalue structure of the covariance matrix A and the sparsity parameter k is then performed by means of a sub-matrix eigenvalue decomposition of A to obtain a variance maximized k-sparse eigenvector x that is the best possible solution. Another method solves the problem by means of a nested greedy search technique that includes a forward and backward pass. An exact solution to the problem initializes a branch-and-bound search with an output of a greedy solution.

Abstract: A computer implemented method maximizes candidate solutions to a cardinality-constrained combinatorial optimization problem of sparse linear discriminant analysis. A candidate sparse solution vector x with k non-zero elements is inputted, along with a pair of covariance matrices A, B measuring between-class and within-class covariance of binary input data to be classified, the sparsity parameter k denoting a desired cardinality of a final solution vector. A variational renormalization of the candidate solution vector x is performed with regards to the pair of covariance matrices A, B and the sparsity parameter k to obtain a variance maximized discriminant eigenvector {circumflex over (x)} with cardinality k that is locally optimal for the sparsity parameter k and zero-pattern of the candidate sparse solution vector x, and is the final solution vector for the sparse linear discriminant analysis optimization problem.

Abstract: A method determines the probabilities of states of a system represented by a model including of nodes connected by links. Each node represents possible states of a corresponding part of the system, and each link represents statistical dependencies between possible states of related nodes. The nodes are grouped into arbitrary sized clusters such that every node is included in at least one cluster. A minimal number of marginalization constraints to be satisfied between the clusters are determined. A super-node network is constructed so that each cluster of nodes is represented by exactly one super-node. Super-nodes that share one of the marginalization constraints are connected by super-links. The super-node network is searched to locate closed loops of super-nodes containing at least one common node. A normalization operator for each closed loop is determined, and messages between the super-nodes are defined.