Ben Appleton

Globally minimal surfaces by continuous maximal flows

In this paper, we address the computation of globally minimal curves and surfaces for image segmentation and stereo reconstruction. We present a solution, simulating a continuous maximal flow by a novel system of partial differential equations. Existing methods are either grid-biased (graph-based methods) or suboptimal (active contours and surfaces). The solution simulates the flow of an ideal fluid with isotropic velocity constraints. Velocity constraints are defined by a metric derived from image data. An auxiliary potential function is introduced to create a system of partial differential equations. It is proven that the algorithm produces a globally maximal continuous flow at convergence, and that the globally minimal surface may be obtained trivially from the auxiliary potential. The bias of minimal surface methods toward small objects is also addressed. An efficient implementation is given for the flow simulation. The globally minimal surface algorithm is applied to segmentation in 2D and 3D as well as to stereo matching. Results in 2D agree with an existing minimal contour algorithm for planar images. Results in 3D segmentation and stereo matching demonstrate that the new algorithm is robust and free from grid bias.

Globally Optimal Geodesic Active Contours

An approach to optimal object segmentation in the geodesic active contour framework is presented with application to automated image segmentation. The new segmentation scheme seeks the geodesic active contour of globally minimal energy under the sole restriction that it contains a specified internal point pint. This internal point selects the object of interest and may be used as the only input parameter to yield a highly automated segmentation scheme. The image to be segmented is represented as a Riemannian space S with an associated metric induced by the image. The metric is an isotropic and decreasing function of the local image gradient at each point in the image, encoding the local homogeneity of image features. Optimal segmentations are then the closed geodesics which partition the object from the background with minimal similarity across the partitioning. An efficient algorithm is presented for the computation of globally optimal segmentations and applied to cell microscopy, x-ray, magnetic resonance and cDNA microarray images.

Circular Shortest Paths by Branch and Bound

Shortest path algorithms are used for a large variety of optimisation problems in network and transportation analysis. They are also used in image analysis for object segmentation, disparity estimation, path finding and crack detection. Sometimes the topology of the problem demands that the path be circular. Such circular path constraints occur in polar object segmentation, disparity estimation for panoramic stereo images and in shortest paths around a cylinder. In this paper we present a new efficient algorithm for circular shortest path determination on a

An energy minimisation approach to stereo-temporal dense reconstruction

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Towards Optimal Image Stitching for Virtual Microscopy

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Fast stereo matching by iterated dynamic programming and quadtree subregioning

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Multiple paths extraction in images using a constrained expanded trellis

trellis in

Iterated dynamic programming and quadtree subregioning for fast stereo matching

O(u^{1.6} v)

Efficient Path Openings and Closings

average time. We impose a binary search tree on the set of path endpoints and use a best-first Branch and Bound search technique to efficiently obtain the global minimum circular path. The typical running time of our circular shortest path algorithm on a 256

Effect of cardiac motion on body surface electrocardiographic potentials: an MRI-based simulation study

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