The near-ring of affine transformations

Implementation of Affine Transformations

1. Pointwise. Each point in the dest is determined from the corresponding point in the src. We start with 3 points specifying the initial coordinate space and the 3 corresponding points that specify the transformed coordinate space, and transform an entire image pointwise by the transformation (1). 2. Sequential. The entire image is successively transformed by a sequence of shear, scale and tra...

Learning affine transformations

Under the assumption of weak perspective, two views of the same planar object are related through an affine transformation. In this paper, we consider the problem of training a simple neural network to learn to predict the parameters of the affine transformation. Although the proposed scheme has similarities with other neural network schemes, its practical advantages are more profound. First of...

Affine transformations and convexity

The purpose of this document is to prove some basic properties of affine transformations involving convex sets. Here are a few online references for background information: http://math.ucr.edu/∼res/progeom/pgnotes02.pdf http://math.ucr.edu/∼res/math133/metgeom.pdf Recall that an affine transformation of R is a map of the form F (x) = b+A(x), where b ∈ E is some fixed vector and A is an invertib...

3D affine coordinate transformations

Acceleration of Affine Hybrid Transformations

This work addresses the computation of the set of reachable configurations of linear hybrid automata. The approach relies on symbolic state-space exploration, using acceleration in order to speed up the computation and to make it terminate for a broad class of systems. Our contribution is an original method for accelerating the control cycles of linear hybrid automata, i.e., to compute their un...