Erlang Shen (二郎神), or Erlang is a Chinese God with a third truth-seeing eye in the middle of his forehead.

Er-lang Shen may be a deified version of several semi-mythical folk heroes who help regulate China’s torrential floods, dating variously from the Qin, Sui and Jin dynasties. A later Buddhist source identify him as the second son of the Northern Heavenly King Vaishravana.

In the Ming semi-mythical novels Creation of the Gods and Journey to the West Erlang Shen is the nephew of the Jade Emperor. In the former he assisted the Zhou army in defeating the Shang. In the latter, he is the second son of a mortal and Jade emperor’s brother. In the legend, he is known as the greatest warrior god of heaven.

 

這小汽車不知打哪聽來一定要有『兩個鏡頭』才能看見『Epipolar』

Epipolar geometry

Epipolar geometry is the geometry of stereo vision. When two cameras view a 3D scene from two distinct positions, there are a number of geometric relations between the 3D points and their projections onto the 2D images that lead to constraints between the image points. These relations are derived based on the assumption that the cameras can be approximated by the pinhole camera model.

Typical use case for epipolar geometry
Two cameras take a picture of the same scene from different points of view. The epipolar geometry then describes the relation between the two resulting views.

 

，因此經常自怨自艾。洛水小神龜於心不忍，特告之道︰當年我曾有緣得逢『二郎神君』，問過『三眼好處』！神君言︰『天眼』斷『來歷』，『慧眼』識『物心』，此『眼』非彼『眼』也。爾今一『眼』足矣！

先修習『投射入睛』

Projective geometry

Projective geometry is a topic of mathematics. It is the study of geometric properties that are invariant with respect to projective transformations. This means that, compared to elementary geometry, projective geometry has a different setting, projective space, and a selective set of basic geometric concepts. The basic intuitions are that projective space has more points than Euclidean space, for a given dimension, and that geometric transformations are permitted that transform the extra points (called “points at infinity“) to Euclidean points, and vice versa.

Properties meaningful for projective geometry are respected by this new idea of transformation, which is more radical in its effects than can be expressed by a transformation matrix and translations (the affine transformations). The first issue for geometers is what kind of geometry is adequate for a novel situation. It is not possible to refer to angles in projective geometry as it is in Euclidean geometry, because angle is an example of a concept not invariant with respect to projective transformations, as is seen in perspective drawing. One source for projective geometry was indeed the theory of perspective. Another difference from elementary geometry is the way in which parallel lines can be said to meet in a point at infinity, once the concept is translated into projective geometry’s terms. Again this notion has an intuitive basis, such as railway tracks meeting at the horizon in a perspective drawing. See projective plane for the basics of projective geometry in two dimensions.

While the ideas were available earlier, projective geometry was mainly a development of the 19th century. This included the theory of complex projective space, the coordinates used (homogeneous coordinates) being complex numbers. Several major types of more abstract mathematics (including invariant theory, the Italian school of algebraic geometry, and Felix Klein‘s Erlangen programme resulting in the study of the classical groups) were based on projective geometry. It was also a subject with a large number of practitioners for its own sake, as synthetic geometry. Another topic that developed from axiomatic studies of projective geometry is finite geometry.

The topic of projective geometry is itself now divided into many research subtopics, two examples of which are projective algebraic geometry (the study of projective varieties) and projective differential geometry (the study of differential invariants of the projective transformations).

The Fundamental Theory of Projective Geometry

 

可從

Projective Geometry for Machine Vision — tutorial by Joe Mundy and Andrew Zisserman.

入室

 

後登堂自可知矣◎

《Multiple View Geometry in Computer Vision》