Image Processing

Problem 4 (20 points) For a 3x3 feature a gradient vector has been found for each pixel. The magnitude and angle of each vector are shown in the figure below as a (magnitude, angle) pair. (5, 15)(1, 35) (8, 84 (M, 12) ,2) (2, 254) (1,168) (2,55) a) b) c) Create the histogram of the magnitude weighted angles. Use 12 bins each 30"wide, i.e. [0, 30), 30, 60),. If the bin with the max value corresponds to the dominant orientation of the feature, what is the dominant orientation? Use the upper limit of the bin, e.g. for bin [210, 240) use 240. If the feature needs to be rotated so that the dominant orientation is aligned to horizontal direction, what rotation matrix in homogeneous coordinates should be used to rotate the feature? If the rotation is to be performed using inverse warping approach, for each pixel in the rotated image (x,y) a pixel in the original image (x, y) needs to be found and its value copied. Express x and y as functions of x and y, i.e. find functions f1 and f2 such that x -fi(x',y) and d) Problem 4 (20 points) For a 3x3 feature a gradient vector has been found for each pixel. The magnitude and angle of each vector are shown in the figure below as a (magnitude, angle) pair. (5, 15)(1, 35) (8, 84 (M, 12) ,2) (2, 254) (1,168) (2,55) a) b) c) Create the histogram of the magnitude weighted angles. Use 12 bins each 30"wide, i.e. [0, 30), 30, 60),. If the bin with the max value corresponds to the dominant orientation of the feature, what is the dominant orientation? Use the upper limit of the bin, e.g. for bin [210, 240) use 240. If the feature needs to be rotated so that the dominant orientation is aligned to horizontal direction, what rotation matrix in homogeneous coordinates should be used to rotate the feature? If the rotation is to be performed using inverse warping approach, for each pixel in the rotated image (x,y) a pixel in the original image (x, y) needs to be found and its value copied. Express x and y as functions of x and y, i.e. find functions f1 and f2 such that x -fi(x',y) and d)