Extracting invariants based on coordinate transformations

Tensor-Product Adaptive Grids Based on Coordinate Transformations

In this paper we discuss a two-dimensional adaptive grid method that is based on a tensor-product approach. Adaptive grids are a commonly used tool for increasing the accuracy and reducing computational costs when solving both Partial Differential Equations (PDEs) and Ordinary Differential Equations (ODEs). A traditional and widely used form of adaptivity is the concept of equidistribution, whi...

Introducing a method for extracting features from facial images based on applying transformations to features obtained from convolutional neural networks

In pattern recognition, features are denoting some measurable characteristics of an observed phenomenon and feature extraction is the procedure of measuring these characteristics. A set of features can be expressed by a feature vector which is used as the input data of a system. An efficient feature extraction method can improve the performance of a machine learning system such as face recognit...

3D affine coordinate transformations

Landsat MSS Coordinate Transformations

, A number of image a n a l y s i s t a s k s r e q u i r e t h e r e g i s t r a t i o n of a s u r f a c e model w i t h an image. I n t h e case o f s a t e l l i t e images, t h e s u r f a c e model may be a map o r d i g i t a l t e r r a i n model i n t h e form o f surface e l e v a t i o n s on a g r i d o f p o i n t s. We develop here an a f f i n e transformation between coordinates...

Vectors, Matrices and Coordinate Transformations

For our purposes we will think of a vector as a mathematical representation of a physical entity which has both magnitude and direction in a 3D space. Examples of physical vectors are forces, moments, and velocities. Geometrically, a vector can be represented as arrows. The length of the arrow represents its magnitude. Unless indicated otherwise, we shall assume that parallel translation does n...