Abstract: Example aspects of the present disclosure provide for an example computer-implemented method for generating alternative network paths, the example method including obtaining a network graph; determining flows respectively for edges of the network graph by: resolving a linear system of weights associated with the edges, the linear system resolved over a reduced network graph, and propagating a solution of the linear system into a respective partition of a plurality of partitions of the network graph to determine at least one of the flows within the respective partition; and determining a plurality of alternative paths across the network graph.

Abstract: Methods and systems for conditioning graph neural networks on affinity features. One of the methods includes obtaining graph data representing an input graph that comprises a set of nodes and a set of edges that each connect a respective pair of nodes, the graph data comprising respective node features for each of the nodes, edge features for each of the edges, and a respective weight for each of the edges; generating one or more affinity features, each affinity feature representing a property of one or more random walks through the graph guided by the respective weights for the edges; and processing the graph data using a graph neural network that is conditioned on the one or more affinity features to generate a task prediction for a machine learning task for the input graph.

Abstract: A method for reconstructing a signal from incomplete data in a signal processing device includes acquiring incomplete signal data. An initial reconstruction of the incomplete signal data is generated. A reconstruction is generated starting from the initial reconstruction by repeating the steps of: calculating a sparsity transform of the reconstruction, measuring an approximation of sparsity of the reconstruction by applying an m-estimator to the calculated sparsity transform, and iteratively optimizing the reconstruction to minimize output of the m-estimator thereby maximizing the approximation of sparsity for the reconstruction. The optimized reconstruction is provided as a representation of the incomplete data.

Abstract: Methods and systems for reconstruction of an image from parallel Magnetic Resonance Image (pMRI) data are disclosed. A reconstructed pMRI image may suffer from noise and aliasing. A method for reducing aliasing by applying a bounded error function is disclosed. A method for reducing noise in a reconstruction by applying an error term is also disclosed. Error terms are included in an expression that can be solved as a minimization problem. Creating a solution in an iterative way is also disclosed. Examples of specific solutions are provided. A system applying the methods is also provided.

Abstract: A method for interactive image segmentation includes receiving an image to be segmented, performing an offline computation of eigenvectors of a Laplacian of the image without using seed points, receiving seed points, and performing an online segmentation taking the seed points and the eigenvectors of the Laplacian as input and outputting a partition of the image.

Abstract: An improved method of graph-based segmentation of objects in images uses the property of rectilinear shape classes which optimize the ratio of specific metrics, that can be expressed as Laplacian matrices applied to indicator vectors. A relaxation of the binary formulation of this problem allows a solution via generalized eigenvectors. This segmentation algorithm incorporating shape information requires no initialization, is non -iterative and finds a steady-state (i.e., global optimum) solution. The method is generally applicable to segmentation of rectilinear shapes.

Abstract: A process for segmenting an object of interest from background, comprising: obtaining a master, high-resolution image of an object disposed within a background; applying a first band graph cut process to the master image generating a second image with the object being segmented from the background to a first approximation; and, comparing the second image with the master image to produce a comparison image with pixels identified by the comparison to be background images being removed from the comparison image.

Abstract: A computer readable medium embodying instructions executable by a processor to perform a method for seeded image segmentation using l? minimization, the method including providing an image comprising a set of pixels, wherein a foreground seed label is given for at least one pixel of the image and a background seed label is given for at least another pixel of the image, determining an affinity function for every pair of neighbor pixels, solving the l? minimization, which assigns a probability to each pixel, labeling each pixel as foreground pixel or background pixel according to a threshold of the probability, and outputting the image including the segmentation labels.

Abstract: A method for reconstructing a signal from incomplete data in a signal processing device includes acquiring incomplete signal data. An initial reconstruction of the incomplete signal data is generated. A reconstruction is generated starting from the initial reconstruction by repeating the steps of: calculating a sparsity transform of the reconstruction, measuring an approximation of sparsity of the reconstruction by applying an m-estimator to the calculated sparsity transform, and iteratively optimizing the reconstruction to minimize output of the m-estimator thereby maximizing the approximation of sparsity for the reconstruction. The optimized reconstruction is provided as a representation of the incomplete data.

Abstract: Methods and systems for reconstruction of an image from parallel Magnetic Resonance Image (pMRI) data are disclosed. A reconstructed pMRI image may suffer from noise and aliasing. A method for reducing aliasing by applying a bounded error function is disclosed. A method for reducing noise in a reconstruction by applying an error term is also disclosed. Error terms are included in an expression that can be solved as a minimization problem. Creating a solution in an iterative way is also disclosed. Examples of specific solutions are provided. A system applying the methods is also provided.

Abstract: A method for interactive image segmentation includes receiving an image to be segmented, performing an offline computation of eigenvectors of a Laplacian of the image without using seed points, receiving seed points, and performing an online segmentation taking the seed points and the eigenvectors of the Laplacian as input and outputting a partition of the image.

Abstract: A computer readable medium embodying instructions executable by a processor to perform a method for seeded image segmentation using l? minimization, the method including providing an image comprising a set of pixels, wherein a foreground seed label is given for at least one pixel of the image and a background seed label is given for at least another pixel of the image, determining an affinity function for every pair of neighbor pixels, solving the l? minimization, which assigns a probability to each pixel, labeling each pixel as foreground pixel or background pixel according to a threshold of the probability, and outputting the image including the segmentation labels.

Abstract: A process for segmenting an object of interest from background, comprising: obtaining a master, high-resolution image of an object disposed within a background; applying a first band graph cut process to the master image generating a second image with the object being segmented from the background to a first approximation; and, comparing the second image with the master image to produce a comparison image with pixels identified by the comparison to be background images being removed from the comparison image.