Understanding Rigid Object Motion in Computer Vision Defining the Motion Field The motion field describes the apparent movement of pixels in an image sequence. It's a 2D vector field, where each vector represents the velocity of a corresponding pixel. For rigid objects, all points move coherently, unlike non-rigid objects with independent movements. Motion of a Rigid Object: Translation Pure translation involves only a change in position. Let `(x, y)` be the pixel coordinates and `(u, v)` be the displacement vector. Then, `u = t_x` and `v = t_y`, where `t_x` and `t_y` are the components of the translation vector. Motion of a Rigid Object: Rotation Pure rotation around a point (e.g., the object's center) is described using a rotation matrix. The rotation matrix R is a 2x2 matrix dependent on the rotation angle θ. The rotation equations are: `x' = x cosθ - y sinθ` and `y' = x sinθ + y cosθ`. `x', y'` are the rotated coordinates. Combi...