What are the applications of collinear equation?

Collinear equation is one of the most basic formulas in photogrammetry, which expresses the mathematical relationship between object point, image point and projection center (usually the lens center of a photo) on a straight line. Details are as follows:

1, collinear equation can be used to solve the transformation relationship between object space coordinates and image space coordinates. Through the known internal and external orientation elements of the image, the collinear equations of object space coordinates and image space coordinates can be derived, so as to realize the transformation from object space coordinates to image space coordinates and the inverse transformation from image space coordinates to object space coordinates.

2. Collinear equation can be used for polar image generation and digital differential correction. Epipolar image generation is a process of matching oblique photos with horizontal photos to obtain epipolar images. Through collinear equation, the points on the oblique photograph can be corresponding to the points on the horizontal photograph, thus generating the epipolar image.

3. Digital difference correction is to improve the accuracy and readability of the map by correcting the geometric deformation of the image. Using collinear equation, the mapping relationship between the corrected image point and the original image point can be established, and digital differential correction can be realized.

4. Collinear equation can also be used to solve directional elements and transform image points. Orientation elements include rotation matrix, translation vector and other parameters, which describe the relative position relationship between projection center and object space coordinates. Through the collinear equation, the directional elements can be solved, thus realizing the orientation and orientation of the object space.

5. Collinear equation can also be used for spatial geometric transformation and graphic clipping. In the fields of computer graphics and computer vision, collinear equations can be used to realize three-dimensional reconstruction of objects, scene rendering and virtual reality. In addition, in the field of geographic information system, collinear equation is also widely used in map making, remote sensing image processing and three-dimensional terrain visualization.

The application of collinear equation in photogrammetry is as follows:

1, aerial photogrammetry: collinear equation can be used for projection transformation and photo correction in aerial photogrammetry. Through the known internal and external orientation elements of the camera, the collinear equation can be established, so as to carry out geometric correction and radiation correction on the photo and obtain accurate geographical information.

2. 3D reconstruction: Collinear equation can be used for homonym point matching and coordinate transformation in 3D reconstruction. Through collinear equation, the mapping relationship between points with the same name can be established, and the transformation from two-dimensional image to three-dimensional model can be realized, which provides support for the digital protection and measurement of buildings, cultural relics and other objects.

3. Remote sensing image processing: Collinear equation can be used for image registration and fusion in remote sensing image processing. Through collinear equation, the images obtained by different sensors can be registered and fused, which can improve the quality and accuracy of remote sensing images and provide data support for environmental monitoring, resource investigation and other fields.

4. Medical image processing: Collinear equation can be used for image registration and segmentation in medical image processing. Through collinear equation, multiple medical images from different angles and different parts can be aligned and segmented, which provides accurate image information for disease diagnosis and treatment.

5. Visual navigation: Collinear equation can be used for target recognition and attitude estimation in visual navigation. Through collinear equation, the mapping relationship between camera coordinate system and navigation coordinate system can be established, and the recognition and attitude estimation of target objects can be realized, which provides technical support for autonomous navigation, robot vision and other fields.