Affine transformations and analytic capacities

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...

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, Polynomials, and Proportionality

In the articles [1] and [3], standard tools and techniques of calculus are used to establish a variety of proportionality results concerning areas defined by the lines tangent to a cubic curve, and by the lengths of certain arcs of a parabola, where the arcs themselves are determined by an area-proportionality criterion. We demonstrate here that these results can be viewed as consequences of so...

3D affine coordinate 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...