Contractive similarities are affine transformations
of the form [F.
were applied to express translations and rotations (linear transformations and vector addition, resp.
In particular, features-based methods (based on SIFT or others feature descriptors) have been demonstrated so far to be effective against copy-move attack and constitute one of the most promising techniques addressing this issue because they are resistant to JPEG compression, scaling, rotation, and affine transformations
and also to digital/analog/digital conversion [10, 11].
Coloring the cells of the grid, stereo learners revisit arithmetic and algebra, meet tessellations, polyominoes, moires, affine transformations
, cellular automata, methods of computer graphics and animation.
It covers various topics including representing real numbers, vectors and points, linear transformations and matrices, affine transformations
, orientation representation, interpolation, viewing and projection, geometry and programmable shading, lighting, rasterization, random numbers, intersection testing, and rigid-body dynamics.
In general rigid and affine transformations
are used as global transformations and curved transformations are local.
The most notable invariants of grayscale images with respect to affine transformations
are affine moment invariants.
Now, there is no question of finding vectors, affine transformations
, decompositions, or other elements of the developed field of modern linear algebra in the records of f[a.
To reduce the number of parameters of the affine transformations
we applied PCA on the parameters W, which resulted in vector [p.
It is well known that this functional is invariant under unimodular affine transformations
Understanding the correspondence between matrices and affine transformations
can help to clarify the meaning of such key notions from Linear algebra and Geometry such as the linear map, affine map, image and kernel of an affine map, composition of affine maps and transformation of the coordinate system.
of Technology, Sydney) describes how to write a ray tracer step-by-step, starting with design and programming and some essential mathematics and theoretical foundations, moving to such details as antialiasing, sampling techniques, mapping samples to a disk or a hemisphere, perspective viewing and developing a practical viewing system, nonlinear projections, stereoscopy, lights and materials, specular reflection, shadows, ambient occlusion, area lights, ray-object interconnections, affine transformations
, transforming objects, regular grids, triangle meshes, mirror reflections, global illumination, simple and realistic transparency, texture mapping, procedural textures and noise-based textures.