(b) Fig. 2 shows the gradient magnitudes and orientations (magnitude/gradient) of a region in an image....

  

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(b) Fig. 2 shows the gradient magnitudes and orientations (magnitude/gradient) of a region in an image. 6868 0/ 0/ 0/ 0/ 0/ 0 0 0 0 0 0/ 0/ 0/ 250/ 200 0 0 0 90 190 0/ 0/ 141/ 141/ 250 0 0 45 45 190 0/ 141/ 141/ 0/ 0/ 0 45 45 141/ 141/ 0/ 0/ 0/ 45 45 0 0 0 Fig. 2 (i) Assume that gradients are quantized into 8 orientations (i.e. 0, 45, 90, 135, 180, 225, 270, and 315). Determine the histogram of oriented gradients (HOG) of the image region shown in Fig. 2. (ii) Assume that the size of an image is 4020 pixels, the cell size for HOG representation is 5x5, and gradients are quantized into 8 orientations. Determine the dimension of the HOG descriptor used to represent the image. Explain why normalization is usually applied to the HOG descriptors. (iii) The SIFT descriptor can be used to describe an image region. The centre pixel in Fig. 2 is a detected keypoint. Assume that a window size of 55 is considered. Based on the result in (b)(i), determine the dominant orientation(s) of the keypoint. How many SIFT descriptors will be constructed for this keypoint? Discuss how the dominant orientation(s) are used to improve the image- matching performance. (b) Fig. 2 shows the gradient magnitudes and orientations (magnitude/gradient) of a region in an image. 6868 0/ 0/ 0/ 0/ 0/ 0 0 0 0 0 0/ 0/ 0/ 250/ 200 0 0 0 90 190 0/ 0/ 141/ 141/ 250 0 0 45 45 190 0/ 141/ 141/ 0/ 0/ 0 45 45 141/ 141/ 0/ 0/ 0/ 45 45 0 0 0 Fig. 2 (i) Assume that gradients are quantized into 8 orientations (i.e. 0, 45, 90, 135, 180, 225, 270, and 315). Determine the histogram of oriented gradients (HOG) of the image region shown in Fig. 2. (ii) Assume that the size of an image is 4020 pixels, the cell size for HOG representation is 5x5, and gradients are quantized into 8 orientations. Determine the dimension of the HOG descriptor used to represent the image. Explain why normalization is usually applied to the HOG descriptors. (iii) The SIFT descriptor can be used to describe an image region. The centre pixel in Fig. 2 is a detected keypoint. Assume that a window size of 55 is considered. Based on the result in (b)(i), determine the dominant orientation(s) of the keypoint. How many SIFT descriptors will be constructed for this keypoint? Discuss how the dominant orientation(s) are used to improve the image- matching performance.