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Assume that we want to find intersection of two infinite lines in 2-dimensional space, defined as a 1 x + b 1 y + c 1 = 0 and a 2 x + b 2 y + c 2 = 0. We can represent these two lines in line coordinates as U 1 = (a 1, b 1, c 1) and U 2 = (a 2, b 2, c 2). The intersection P′ of two lines is then simply given by [4]
The grid structure of a chessboard naturally defines two sets of parallel lines in an image of it. Therefore, one expects that line detection algorithms should successfully detect these lines in practice. Indeed, the following figure demonstrates Hough transform-based line detection applied to a perspective-transformed chessboard image. Clearly ...
The resulting image points are y 1 and y 2. The green lines intersect at x. In practice, the image points y 1 and y 2 cannot be measured with arbitrary accuracy. Instead points y' 1 and y' 2 are detected and used for the triangulation. The corresponding projection lines (blue) do not, in general, intersect in 3D space and may also not intersect ...
The problem of finding the object (described with a model) in an image can be solved by finding the model's position in the image. With the generalized Hough transform, the problem of finding the model's position is transformed to a problem of finding the transformation's parameter that maps the model into the image.
The Hough transform [3] can be used to detect lines and the output is a parametric description of the lines in an image, for example ρ = r cos(θ) + c sin(θ). [1] If there is a line in a row and column based image space, it can be defined ρ, the distance from the origin to the line along a perpendicular to the line, and θ, the angle of the perpendicular projection from the origin to the ...
A two-line element set (TLE, or more rarely 2LE) or three-line element set (3LE) is a data format encoding a list of orbital elements of an Earth-orbiting object for a given point in time, the epoch. Using a suitable prediction formula, the state (position and velocity) at any point in the past or future can be estimated to some accuracy.
Point set registration is the process of aligning two point sets. Here, the blue fish is being registered to the red fish. In computer vision, pattern recognition, and robotics, point-set registration, also known as point-cloud registration or scan matching, is the process of finding a spatial transformation (e.g., scaling, rotation and translation) that aligns two point clouds.
Orbital position vector, orbital velocity vector, other orbital elements. In astrodynamics and celestial dynamics, the orbital state vectors (sometimes state vectors) of an orbit are Cartesian vectors of position and velocity that together with their time () uniquely determine the trajectory of the orbiting body in space.