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The Pinhole Camera
Published in Aditi Majumder, M. Gopi, Introduction to Visual Computing, 2018
Homography is a mathematical relationship between the position and orientation of two cameras in a constrained situation where two cameras see the same points on a plane. This relationship can be easily recovered without going through an explicit camera calibration. Figure 7.3 illustrates the situation. Let us assume a point Pπ on the plane π. Let the normal to the plane be appropriately defined as N=(a,b,c) $ N = (a, b, c) $ such that the plane equation can be written (N1).P=0 $$ (\,N\,\,\,~1\,\,).P = 0 $$
Literature Survey on Recent Methods for 2D to 3D Video Conversion
Published in Ling Guan, Yifeng He, Sun-Yuan Kung, Multimedia Image and Video Processing, 2012
Raymond Phan, Richard Rzeszutek, Dimitrios Androutsos
Finally, Yan et al. [29] first use the scale invariant feature transform (SIFT) [30] between two consecutive frames, and then formulate a homography transformation between the frames. In addition, the current frame is oversegmented using the mean-shift [14] segmentation algorithm. After, the oversegmented result and the homography transformation are formulated into a graph cuts segmentation problem and the depths are solved in that fashion [31]. Essentially, homography estimation is used to determine the motion layers, or layers in the scene that roughly share the same motion. Motion vectors in the same motion layer most likely correspond to the same depth. Therefore, a region-based graph cuts segmentation is performed with the previous information. The result is a depth assignment that is coherent with respect to each motion layer. Figure 27.13 illustrates a block diagram describing this approach.
Multiple-View Geometry
Published in Jian Chen, Bingxi Jia, Kaixiang Zhang, Multi-View Geometry Based Visual Perception and Control of Robotic Systems, 2018
Jian Chen, Bingxi Jia, Kaixiang Zhang
Traditional two-view geometric models include the homography and epipolar geometry. The homography relies on the relative pose information (among the object and the cameras) and describes the relationship between the projections in two views of planar objects. Epipopar geometry does not rely on the scene structure and describes the relationship between the projections in two views of 3D points. However, the estimation of epipolar geometry is degenerated. In this section, the homography and epipolar geometry are introduced for planar and nonplanar scenes. Besides, a general two-view geometry is constructed for general scenes (both planar and nonplanar) with respect to a reference plane.
Vehicle trajectory data extraction from the horizontal curves of mountainous roads
Published in Transportation Letters, 2022
V.A. Bharat Kumar Anna, Suvin P. Venthuruthiyil, Mallikarjuna Chunchu
A homography is a matrix (H) that maps a given set of points from one plane to another plane. Often, homography is used in transportation studies to transform the pixel coordinates to real-world coordinates during image-processing based traffic data collection. Figure 2 shows a pictorial representation of point-to-point correspondence between the real-world and image planes. A homography matrix maps this point-to-point correspondence as a transformation.
Intelligent driving system at opencast mines during foggy weather
Published in International Journal of Mining, Reclamation and Environment, 2022
Sushma Kumari, Monika Choudhary, Khushboo Kumari, Virendra Kumar, Abhishek Chowdhury, Swades Kumar Chaulya, Girendra Mohan Prasad, Sujit Kumar Mandal
After getting good feature points on both images, the homography matrix is estimated. The homography is the 3 × 3 transformation matrix, which maps the points on an image to the corresponding point in another image [32]. Let (x1, y1) is the corresponding point on the first image to the point (x2, y2) on the second image, then the transformation is given by:
Homography Transformation Correction Method for Position Error Generated in Readout Circuit Based on Resistive Network for the Compton Imaging System
Published in Nuclear Technology, 2020
Su-Jin Jeon, Jae-Sang Lee, Do-Hyun Kim, Seok-Ho Hong, Chun-Sik Lee, Young-Wan Choi
Homography is a coordinate transformation method that is used to convert 2-D images to three-dimensional (3-D) panoramic images.20,21 All possible 3-D transformations of 2-D planar objects can be represented by homography. Moreover, all points in a 2-D image can be projected onto another 2-D image. The homography transformation in this work is based on matrix expression (1):