Preliminary understanding of some knowledge points _ 3 (stereoscopic vision, ing ...)

I recently read some stereoscopic visual materials. I feel that there are too many things involved in stereoscopic vision, and there are strong mathematical theories, especially geometric aspects, the following is a preliminary summary of the information about stereoscopic vision in the past week. I have learned a lot about this concept. If I am deeply familiar with it, I will continue to understand it in the future, there are mainly some terms. Writing down is a small Summary of yourself:

1. ry knowledge.

This includes plane and spatial projective ry. Inner ry only introduces Infinite Elements in Euclidean ry, such as Infinity, infinite straight lines, infinite curves, and surfaces. Therefore, two parallel lines can interwork In the projective ry. The intersection is infinite distance, and the two parallel planes are also in a straight line in the infinite distance.

Therefore, a two-dimensional projective plane is introduced in two-dimensional Projective ry, which consists of a Euclidean Plane and an infinite straight line. The related knowledge points involved include the Second coordinate and the Second coordinate, the cross product, the intersection ratio, the projection parameter, the dual, the expression of the infinite distance straight line, the quadratic curve, the dual quadratic curve, and the degraded quadratic curve, ring point, unifit, degree of freedom, equidistance transformation, similarity transformation, affine transformation, difference between projection transformation, geometric distortion, transformation group and invariant.

The three-dimensional projective ry is very similar to the two-dimensional ones, but in the three-dimensional projective space, the straight line is the most difficult to express, and the straight line has four degrees of freedom, while the point and the surface have only three degrees of freedom, and the points and surfaces are dual, line self-dual. Related Knowledge points include Quadratic Surface, dual Quadratic Surface, cubic torsion curve, and absolute quadratic curve. All spherical cross infinite far plane in absolute quadratic curve, all circular cross absolute quadratic curve at 2 points, that is, the ring point. It is an absolute dual quadratic surface, a constant, and calculation of the hidden points and hidden lines.

Why do we need to introduce ry in stereoscopic vision? Because the imaging of images does not maintain the Euclidean immutability, the camera imaging process is a process of projection transformation.

 

Ii. Camera Model.

It is mainly a small hole imaging model and a central perspective projection model. The concepts introduced include depth of field, angle of view, perspective distortion, physical coordinate system, camera coordinate system, object image coordinate system, pixel coordinate system, Master point offset, and camera parameters (5, Master point coordinate 2, focal lengths in two directions, one scaling factor), camera external parameters (2, rotation and Heping), radial distortion, centrifugal distortion, thin lens distortion, and affine cameras, camera matrix.

In general, the analysis principles in stereoscopic vision are the small hole imaging model, but the center perspective projection model is used.

 

3. multi-view ry.

Because restoring the structure and depth of a single image may cause ambiguity, multi-view ry is introduced, which mainly includes binary and tri-view ry.

Two-view ry refers to obtaining two photos at the same time. For example, two cameras or one camera moves twice. Its concept includes outer pole ry, outer pole, baseline, outer pole plane, outer pole, outer pole constraint, essential matrix, basic matrix, and 8 points.AlgorithmEstimate the basic matrix, single-fit matrix, fixed point and non-dynamic line.

The generation of Three-view ry is because the two-view ry cannot constrain the straight line. The constraints between two images are determined by the basic matrix, and the constraints between three images are determined by the trifocal tensor, there is no independent constraint between three or more images.

The knowledge of multi-view ry is of great help to camera calibration and 3D reconstruction.

 

Iv. Camera calibration theory.

Camera calibration is used to obtain the internal and external parameters of the camera. The knowledge points involved include direct linear transformation, degradation configuration, geometric error, gold standard algorithm, matrix decomposition, constraints on the parameters in the circle points and cameras, and constraints on parallel lines and parameters in the camera, constraints of kruppa equation and camera parameters, constraints of absolute quadratic curve on camera parameters, constraints of absolute Quadratic Surface and camera parameters, active visual system, and active visual calibration.

 

V. 3D reconstruction theory.

The current computer theoretical framework is based on the MARR theory. Marr theory holds that 3D reconstruction is the main problem of human vision and is also the main research direction of computer vision. Therefore, 3D reconstruction plays an important role in computer vision. The general steps of 3D reconstruction are to find corresponding feature points in multiple images, then match the corresponding feature points, and then according to the geometric constraints and color value constraints of the corresponding feature points, motion Model constraints and other constraints are used to estimate the depth of corresponding points in the space. The most difficult part is how to match the points in each image, that is, the multi-object fusion problem.

At present, 3D Reconstruction involves the reconstruction process, human vision theory, binocular fusion, gray correlation, cross correlation, similarity constraints, window search, multi-scale edge matching, dynamic planning, multi-view stereo reconstruction, multi-Baseline Stereo reconstruction, Parallax, depth, stereo element, space cutting, silhouette reconstruction, intersection body, cutting-Based Visual shell, layered reconstruction theory, projection reconstruction, affine reconstruction, infinite distance, similarity reconstruction, structured light reconstruction, texture-based reconstruction, color value-based reconstruction, Motion Model-Based Reconstruction, large-scale scene reconstruction, etc.

Vi. References:

1. Wu fuchao (2008). Mathematical Methods in computer vision, Science Press.
2. Computer Vision PPT of the institute of automation of the Chinese Emy of sciences, stereo vision.
3. Szeliski, r. (2010). Computer Vision: algorithms and applications, Springer-Verlag New York Inc.
4. Shapiro, L. G. and G. C. Stockman (2001). Computer Vision, Prentice Hall.
5. Hartley, R., A. zisserman, et al. (2003). Multiple View Geometry in computer vision, Cambridge Univ press.
6. Forsyth, D. A. and J. Ponce (2002). Computer Vision: a modern approach, Prentice Hall professional technical reference.
7. Bradski, G. and A. kaehler (2008). Learning opencv: computer vision with the opencv library, O 'Reilly media.

The water in the stereoscopic vision is deep, and the road is long. I will go up and down to seek help!

 

 

Author: tornadomeet Source: http://www.cnblogs.com/tornadomeet welcome to repost or share, but please be sure to declare Article Source.