Abstract: A dictionary of atoms for coding data is learned by first selecting samples from a set of samples. Similar atoms in the dictionary are clustered, and if a cluster has multiple atoms, the atoms in that cluster are merged into a single atom. The samples can be acquired online.

Abstract: A natural input image is upscaled, first by interpolation. Second, edges in the interpolated image are sharpened by a lion-parametric patch transform. The result is decomposed into an edge layer and a detail layer. Only pixels in the detail layer enhanced, and the enhanced detail layer is merged with the edge layer to produce a high resolution version of the input image.

Abstract: A method recovers an uncorrupted low-rank matrix, noise in corrupted data and a subspace from the data in a form of a high-dimensional matrix. An objective function minimizes the noise to solve for the low-rank matrix and the subspace without estimating the rank of the low-rank matrix. The method uses group sparsity and the subspace is orthogonal. Random subsampling of the data can recover subspace bases and their coefficients from a much smaller matrix to improve performance. Convergence efficiency can also be improved by applying an augmented Lagrange multiplier, and an alternating stepwise coordinate descent. The Lagrange function is solved by an alternating direction method.

Abstract: A method reduces multiplicative and additive noise in image pixels by clustering similar patches of the pixels into clusters. The clusters form nodes in an affinity net of nodes and vertices. From each cluster, a dictionary is learned by a sparse combination of corresponding atoms in the dictionaries. The patches are aggregated collaboratively using the dictionaries to construct a denoised image.

Abstract: A method reduces multiplicative and additive noise in image pixels by clustering similar patches of the pixels into clusters. The clusters form nodes in an affinity net of nodes and vertices. From each cluster, a dictionary is learned by a sparse combination of corresponding atoms in the dictionaries. The patches are aggregated collaboratively using the dictionaries to construct a denoised image.

Abstract: A test sample is classified by determining a nearest subspace residual from subspaces learned from multiple different classes of training samples, and a collaborative residual from a collaborative representation of a dictionary constructed from all of the test samples. The residuals are used to determine a regularized residual. The subspaces, the dictionary and the regularized residual are inputted into a classifier, wherein the classifier includes a collaborative representation classifier and a nearest subspace classifier, and a label is assigned to the test sample using the classifier, and wherein the regularization parameter balances a trade-off between the collaborative representation classifier the nearest subspace classifier.

Abstract: A method compresses an image partitioned into blocks of pixels, for each block the method converts the block to a 2D matrix. The matrix is decomposing into a column matrix and a row matrix, wherein a width of the column matrix is substantially smaller than a height of the column matrix and the height of the row matrix is substantially smaller than the width of the row matrix. The column matrix and the row matrix are compressed, and the compressed matrices are then combined to form a compressed image.

Abstract: Frequency features to be used for binary classification of data using a linear classifier are selected by determining a set of hypotheses in a d-dimensional space using d-dimensional labeled training data. A mapping function is constructed for each hypothesis. The mapping functions are applied to the training data to generate frequency features, and a subset of the frequency are selecting iteratively. The linear function is then trained using the subset of frequency features and labels of the training data.

Abstract: A multi-class classifier is trained by selecting a query image from a set of active images based on a membership probability determined by the classifier, wherein the active images are unlabeled. A sample image is selected from a set of training image based on the membership probability of the query image, wherein the training images are labeled. The query image and the sample images are displayed to a user on an output device. A response from the user is obtained with an input device, wherein the response is a yes-match or a no-match. The query image with the label of the sample image is added to the training set if the yes-match is obtained, and otherwise repeating the selecting, displaying, and obtaining steps until a predetermined number of no-match is reached to obtain the multi-class classifier.

Abstract: Symbols in information are encoded as a codeword using a differential orthogonal code. The codeword is stored in a substrate. A moving sensor acquires an image of the codeword in the substrate and decodes the codeword using a balanced differential decoder. The codeword can be painted as lane markings on a road surface.

Abstract: A method clusters samples using a mean shift procedure. A kernel matrix is determined from the samples in a first dimension. A constraint matrix and a scaling matrix are determined from a constraint set. The kernel matrix is projected to a feature space having a second dimension using the constraint matrix, wherein the second dimension is higher than the first dimension. Then, the samples are clustered according to the kernel matrix.

Abstract: A method compresses an image partitioned into blocks of pixels, for each block the method converts the block to a 2D matrix. The matrix is decomposing into a column matrix and a row matrix, wherein a width of the column matrix is substantially smaller than a height of the column matrix and the height of the row matrix is substantially smaller than the width of the row matrix. The column matrix and the row matrix are compressed, and the compressed matrices are then combined to form a compressed image.

Abstract: A tumor is tracked in sequences of biplane images by generating a set of segmentation hypotheses using a 3D model of the tumor, a biplane geometry, and a previous location of the tumor as determined from the pairs of biplane images. Volume prior probabilities are constructed based on the set of hypotheses. Seed pixels are selected using the volume prior probabilities, and a bi-plane dual image graph is constructed using intensity gradients and the seed pixels to obtaining segmentation masks corresponding to tumor boundaries using the image intensities to determine a current location of the tumor.

Abstract: Frequency features to be used for binary classification of data using a linear classifier are selected by determining a set of hypotheses in a d-dimensional space using d-dimensional labeled training data. A mapping function is constructed for each hypothesis. The mapping functions are applied to the training data to generate frequency features, and a subset of the frequency are selecting iteratively. The linear function is then trained using the subset of frequency features and labels of the training data.

Abstract: A 3D object is represented by a descriptor, wherein a model of the 3D object is a 3D point cloud. A local support for each point p in the 3D point cloud is located, and reference x, y, and z axes are generated for the local support. A polar grid is applied according to the references x, y, and z axes a along an azimuth and a radial directions on an xy plane centered on the point p such that each patch on the grid is a bin for a 2D histogram, wherein the 2D histogram is a 2D matrix F on the grid and each coefficient of the 2D matrix F corresponds to the patch on the grid. For each grid location (k, l), an elevation value F(k, l) is estimated by interpolating the elevation values of the 3D points within the patches to produce the descriptor for the point p.

Abstract: A shape of an object is represented by a set of points inside and outside the shape. A decision function is learned from the set of points an object. Feature points in the set of points are selected using the decision function, or a gradient of the decision function, and then a local descriptor is determined for each feature point.

Abstract: A 3D object is represented by a descriptor, wherein a model of the 3D object is a 3D point cloud. A local support for each point p in the 3D point cloud is located, and reference x, y, and z axes are generated for the local support. A polar grid is applied according to the references x, y, and z axes a along an azimuth and a radial directions on an xy plane centered on the point p such that each patch on the grid is a bin for a 2D histogram, wherein the 2D histogram is a 2D matrix F on the grid and each coefficient of the 2D matrix F corresponds to the patch on the grid. For each grid location (k, l), an elevation value F(k, l) is estimated by interpolating the elevation values of the 3D points within the patches to produce the descriptor for the point p.

Abstract: A multi-class classifier is trained by selecting a query image from a set of active images based on a membership probability determined by the classifier, wherein the active images are unlabeled. A sample image is selected from a set of training image based on the membership probability of the query image, wherein the training images are labeled. The query image and the sample images are displayed to a user on an output device. A response from the user is obtained with an input device, wherein the response is a yes-match or a no-match. The query image with the label of the sample image is added to the training set if the yes-match is obtained, and otherwise repeating the selecting, displaying, and obtaining steps until a predetermined number of no-match is reached to obtain the multi-class classifier.

Abstract: A method clusters samples using a mean shift procedure. A kernel matrix is determined from the samples in a first dimension. A constraint matrix and a scaling matrix are determined from a constraint set. The kernel matrix is projected to a feature space having a second dimension using the constraint matrix, wherein the second dimension is higher than the first dimension. Then, the samples are clustered according to the kernel matrix.

Abstract: Symbols in information are encoded as a codeword using a differential orthogonal code. The codeword is stored in a substrate. A moving sensor acquires an image of the codeword in the substrate and decodes the codeword using a balanced differential decoder. The codeword can be painted as lane markings on a road surface.