Perspective transformation Perspective transformation is often used, for example, in the research of mobile robot visual navigation, because there is a Inclination angle , rather than straight down（ Orthographic projection ）Sometimes, if you want to correct the image to the form of orthographic projection, you need to use perspective transformation. The process of transforming three-dimensional objects or objects in the space coordinate system into two-dimensional image representation is called projection transformation. According to the difference in the distance between the viewpoint (projection center) and the projection plane, projection can be divided into parallel projection and perspective projection. Perspective projection is perspective transformation. The distance between the viewpoint (projection center) of parallel projection and the projection plane is infinite, while for perspective projection (transformation), this distance is limited. Perspective projection has the feature of perspective reduction effect, that is, the size of perspective projection of 3D objects or objects is inversely proportional to the distance from the body to the viewpoint (projection center). For example, two line segments of equal length are parallel to the projection plane. However, the perspective projection of the line near the projection center is large, while the perspective projection of the line far from the projection center is small. The visual effect produced by this effect is similar to that of human visual system. Compared with parallel projection, perspective projection has a stronger sense of depth and looks more realistic, but perspective projection can not truly reflect the exact size and shape of objects. [1]
For perspective projection, the projection of a parallel line parallel to the projection plane can remain parallel, while the projection of a parallel line not parallel to the projection plane will gather to a point, which is called Vanishing point (Vanishing Point)。 The vanishing point can be regarded as the projection of an infinitely distant point on the projection plane. There can be an infinite number of vanishing points of perspective projection. Parallel lines in different directions can form different vanishing points on the projection plane. The vanishing points formed by parallel lines in the direction of coordinate axis on the projection plane are also called principal vanishing points. Perspective projection can be divided into one point perspective, two point perspective and three points according to the number of main vanishing points perspective 。 Take a point perspective as an example. One point perspective has only one main vanishing point, that is, the projection plane is orthogonal to one coordinate axis and parallel to the other two coordinate axes. When performing a point perspective projection transformation, the layout of the drawing should be well considered to avoid the accumulation of planar regions or lines of 3D objects or objects into points that affect the intuition. To be specific, the following points should be considered: ① the relative position between the three-dimensional shape or object and the picture; ② Sight distance, i.e viewpoint Distance between (projection center) and projection plane; ③ The height of the viewpoint. [1-2] Perspective transformation is also an operation to change the size and shape of objects. A plane figure can produce a three-dimensional effect after perspective transformation. Taking a rectangle as an example, the stagger transformation only moves two vertices on the same edge, and the two vertices move in the same direction, while the two vertices on the opposite side remain unchanged. However, the perspective transformation may move all the vertices of the rectangle, and the two vertices on the same side move in opposite directions.
In fact, when an object is undergoing perspective transformation, the four corners of its limit box are not necessarily limited to their side lengths, and the four corners can also move, thus obtaining more complex perspective transformation effects. [3]
The most general form of linear transformation is perspective transformation. Its main feature is that straight lines are still straight lines after transformation, but parallel straight lines may intersect after transformation. Perspective transformation is not very useful for processing data of tomographic images. Perspective transformation is mainly used in the following aspects:
(1) A point source interacts with an object to produce a radial image of a projected image on a plane.
(2) For photos, the acquisition light passes through the focus of the lens. [4]
