tailieunhanh - Lecture Digital image processing - Lecture 6: Transformations
After studying this chapter you will be able to understand: Different distance measures, application of distance measures, arithmetic and logical operations on images, neighborhood operation on images, some basic mathematical transformations, the inverse transformations of these different mathematical transformations. | Digital Image Processing CCS331 Basic Transformations 1 Summery of previous lecture Different distance measures Application of distance measures used to find the distance transformation of a binary image and using the distance transformation, we can find out the skeleton of the image which gives a compact representation or compact description of the shape. Arithmetic and logical operations on images Neighborhood operation on images 2 3 Todays lecture some basic mathematical transformations translation, rotation and scaling in 2D and 3D The inverse transformations of these different mathematical transformations. 4 What is the translation operation? 5 translation the equation in the form of a matrix, 6 combine all the operation in a single matrix form 7 8 Rotate point P 9 Expanding the equation 10 Matrix equation 11 12 Translation and rotation 13 3D coordinate system Transformations we consider translation, rotation and scaling 3D in dimensional coordinate system. 14 Translation We have 3 coordinates x, y and z and all these 3D coordinates, The 3 coordinate are to be translated by the translation vector x0 y0 z0 and then new translation at the new point we get as x star, y star and z star. 15 Matrix for 3D Translaation we have added the additional component which is equal to 1 But this is not uniform matrix 16 unified representations we will represent the matrix by uppercase letter T. 17 Unified matrix representation if you have a vector V, a position vector V which is translated by the transformation matrix A, the transformation matrix A is a 4 by 4 transformation matrix; V the original position vector was X, Y, Z, we have added and additional component 1 to it in our unified matrix representation. So, V now a 4 dimensional vector having components X, Y, Z and 1. Similarly, the transformed position vector V star is also a 4 dimensional vector 18 Transformation matrix We can have the transformation matrix which is represented, for translating a point in point 3D by | Digital Image Processing CCS331 Basic Transformations 1 Summery of previous lecture Different distance measures Application of distance measures used to find the distance transformation of a binary image and using the distance transformation, we can find out the skeleton of the image which gives a compact representation or compact description of the shape. Arithmetic and logical operations on images Neighborhood operation on images 2 3 Todays lecture some basic mathematical transformations translation, rotation and scaling in 2D and 3D The inverse transformations of these different mathematical transformations. 4 What is the translation operation? 5 translation the equation in the form of a matrix, 6 combine all the operation in a single matrix form 7 8 Rotate point P 9 Expanding the equation 10 Matrix equation 11 12 Translation and rotation 13 3D coordinate system Transformations we consider translation, rotation and scaling 3D in dimensional coordinate system. 14 Translation We have
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