Message-passing labeling inference algorithms {belief propagation} can compute many graphical-distribution statistics, each with few values, to calculate disparities by finding large-neighborhood minima. Belief propagation uses sum-product to find minimum or max-product to find maximum a posteriori (MAP) estimate. For stereo vision, Markov random-field model describes disparity, and inference algorithm determines nodes.
Algorithms {binary space partitioning} (BSP) can recursively divide space or polygon into two regions using hyperplanes, to make halves, quarters, eights, sixteenths, and so on.
orientation
Hyperplanes can have any orientation, making unequal regions. Hyperplanes that cut at medians make both regions equal.
polygons
Polygons can have angles greater than 180 degrees {reflex angle, polygon} or less than 180 degrees. Dividing polygon recursively makes regions with angles less than 180 degrees {convex set}.
recursion
Recursion steps define trees {BSP tree} and make stored lists {visibility list} that order polygons from front to rear. Convex sets become smaller until they include only point {BSP-tree leaves}.
multiple hyperplanes
Binary space partitioning can use hyperplane pairs or triples for cuts. Hyperplane pair divides space into four regions {quadtree}. Hyperplane triple divides space into eight regions {octree}.
Methods {iterative closest points method} can use point-sample clouds to align two images.
Modified BSP-tree algorithms {kd-tree} {k-dimensional tree} can use only hyperplanes perpendicular to space axes and use axis sequences, typically splitting at axis or polygon medians. If space has k axes, kd-tree has k cuts and tree branchings. kd-tree algorithms are better for searches using nearest neighbors, because they match space coordinate parameters and split hyperplanes go through points. Because hyperplanes are across axes, all regions have nodes or points.
Gauss-Helmert methods can use least squares {least-squares adjustment} to estimate best fit.
Painters paint background first, then layer objects on canvas from rear to front {painter's algorithm}, drawing over things that become behind.
Stereo images project onto aligned image plane by transformation {rectification of image}.
Cameras can use epipolar transform and absolute conic image in Kruppa equation to find standard metric {self-calibration}.
Robots can find their locations in environments {self-localization}, using self-localization alignment methods (SLAM).
Algorithms {z-buffering} {depth buffering} can store object-part depths for image generation or object recognition. z-buffers {depth buffer} represent two-dimensional images, for object identification. z-culling algorithms compare object-part depths and store object with smallest depth in buffer. The same visual angle covers more space farther away. To control for increasing spread with increasing distance, use variant w-buffers.
3-Computer Science-Systems-Computer Vision-Algorithms
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Date Modified: 2022.0225