Geometry represents Euclidean space as n-dimensional sphere {conformal geometry}, not as vector space. Operations are linear. It has projective geometry.
Stereo-vision constraints {epipolar constraint} can reduce searching to along image curve {epipolar line}, using fundamental matrix, which gives camera relative orientation and position, or essential matrix, which describes epipolar geometry using focal length, chip size, or optical-center coordinates. Other camera has focal-point projection {epipole}. First-camera pixels have corresponding pixels on second-camera epipolar line.
Images have vertical orthogonal planes {homography} at focal points.
The same scene point is at different pixel coordinates {disparity of images} in rectified images from two cameras, with distance between them. Disparity is directly proportional to depth.
Two images have disparities between corresponding pixels and have disparity-change rates {disparity rate}.
Image objects have special points, lines, or angles {image features}, whose enumeration or configuration can describe objects. Training on standard images can teach object features and configuration. Features have parameters, such as length, angle, color, and distance. Feature scale, noise, illumination, and distortion can differ.
Camera image can have virtual shapes superimposed on it {augmented reality}, to serve as landmarks or features.
Curves have models {curve functions}. Hyperbolas have curvature, arc length, and separation. Clothoid curves have arc length related to bending. G2-splines have arc length related to bending. B-splines are closed curves. Fifth-degree Cartesian polynomials are closed curves. Polar splines are closed curves.
Three-dimensional curves use ellipsoids, spheroids, cylinders, quartics, and splines and try to find optimum position, orientation, scale, and mathematical function.
Principal component analysis can find axes.
Image features {descriptor, image}, such as points and regions, relate to object recognition. Features can be independent or combine. Descriptors include binary, spatial, shape, texture, and local colors. Texture can be gradient location-orientation histogram. Corner detection, SIFT, and SURF use descriptors.
Three-dimensional spheres, cubes, cylinders, cones, and wedges {geon} can be object-representation components. Different geon types look different from different viewpoints {viewpoint-invariance, geon}. Occluded, overlapped, noisy, blurry, or deformed geon types look different from other occluded, overlapped, noisy, blurry, or deformed geon types {stability, geon}. Object representations have geons and relations among geons {recognition-by-components, geon} (Irving Biederman) [1987].
Small areas {Monge patch} can have three-dimensional image patterns.
3-Computer Science-Systems-Computer Vision
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Date Modified: 2022.0225