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The distance (or perpendicular distance) from a point to a line is the shortest distance from a fixed point to any point on a fixed infinite line in Euclidean geometry. It is the length of the line segment which joins the point to the line and is perpendicular to the line. The formula for calculating it can be derived and expressed in several ways.
The main idea is to determine the correspondences between 2D image features and points on the 3D model curve. (a) Reconstruct projection rays from the image points (b) Estimate the nearest point of each projection ray to a point on the 3D contour (c) Estimate the pose of the contour with the use of this correspondence set (d) goto (b)
The image to the left illustrates the epipolar geometry of a pair of stereo cameras of pinhole model. A point x (3D point) in 3D space is projected onto the respective image plane along a line (green) which goes through the camera's focal point, and , resulting in the two corresponding image points and .
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 ...
CloudCompare an open source point and model processing tool that includes an implementation of the ICP algorithm. Released under the GNU General Public License. PCL (Point Cloud Library) is an open-source framework for n-dimensional point clouds and 3D geometry processing. It includes several variants of the ICP algorithm.
The simplest method of drawing a line involves directly calculating pixel positions from a line equation. Given a starting point (,) and an end point (,), points on the line fulfill the equation = +, with = = being the slope of the line. The line can then be drawn by evaluating this equation via a simple loop, as shown in the following pseudocode: