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Deep Learning Algorithms for Brain Image Analysis
Published in Mridu Sahu, G. R. Sinha, Brain and Behavior Computing, 2021
Sai Darahas Akkineni, S. P. K. Karri
In rigid registration, the input images that need to be registered are considered as rigid bodies, which can be spatially transformed into each other. The objects in the images are assumed to be nondeformable. In the case of affine transformation, the transformation matrix of size 3×3 for image and 4×4 for volume holds parameters of translation, rotation, and scaling across all dimensions. The projective transformation has two additional parameters in the matrix for the image.
Role of discontinuity on stress field in wall-control blasting
Published in B. Mohanty, Rock Fragmentation by Blasting, 2020
in which [K]n is the element stiffness matrix in the global coordinate system and [T] is the transformation matrix. The global stiffness matrix of the whole structure [K] is obtained using the summation of the element stiffness matrices. This process can be represented symbolically by: [K]=∑n=1N[k]n
Affine Transformation
Published in Ravishankar Chityala, Sridevi Pudipeddi, Image Processing and Acquisition using Python, 2020
Ravishankar Chityala, Sridevi Pudipeddi
Translation is the process of shifting the image along the various axes (x-, y- and z-axis). For a 2D image, we can perform translation along one or both axes independently. The transformation matrix for translation is defined as: T=(100010txty1)
Mesh modeling and simulation for three-dimensional warp-knitted tubular fabrics
Published in The Journal of The Textile Institute, 2022
Haisang Liu, Gaoming Jiang, Zhijia Dong
Assuming that p(x,y,z,1) is one point on the flat fabric as shown in Figure 3(a). When the flat fabric moves from its original position to another position as illustrated in Figure 3(b), a new coordinate of this point is generated which is defined as p’(x’, y’, z’,1). The translation can be represented by a transformation matrix M1 shown by Equation (2), where the translation vectors of point p in x-y-z directions are introduced as Tx, Ty, Tz. According to the original coordinate p(x,y,z,1) and a transformation matrix M1, the new point p’(x’, y’,z’,1) can be derived as Equation (3).