Ben Appleton
Ben Appleton completed the PhD degree in the area of image analysis at the University of Queensland (UQ), Australia, in 2005. He received degrees in engineering and science from the University of Queensland in 2001 and was awarded a university medal. He is particularly interested in optimization theory as well as its applications to image analysis.
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Image-based 3D reconstruction remains a competitive field of research as state-of-the-art algorithms continue to improve. This paper presents a voxel-based algorithm that adapts the earliest space-carving methods and utilises a minimal surface technique to obtain a cleaner result. Embedded Voxel Colouring is built in two stages: (a) progressive voxel carving is used to build a volume of embedded surfaces and (b) the volume is processed to obtain a surface that maximises photo-consistency data in the volume. This algorithm combines the strengths of classical carving techniques with those of minimal surface approaches. We require only a single pass through the voxel volume, this significantly reduces computation time and is the key to the speed of our approach. We also specify three requirements for volumetric reconstruction: monotonic carving order, causality of carving and water-tightness. Experimental results are presented that demonstrate the strengths of this approach.
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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 sub-optimal (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.
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