Part II: Separable kernels Show whether the following convolution kernels are separable or not. If separa-...

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Part II: Separable kernels Show whether the following convolution kernels are separable or not. If separa- ble, indicate the separations per case. [2 0 f = 0 1 0 0 3 1 g= -2 0 -3 0 0 1 2 (a) the Harris detector (b) the Hessian detector Part III: Image features Considering the image y, an interest point detector typically computes the ma- trix Mp which captures the changes of pixel intensities in a neighborhood N (p) of each pixel location p. A pixel intensity change at location p can be computed by filtering y with a filter g. h = 1. Give the expressions of a (3 3) filter g and the expression of Mp, each time explaining your notation, for: [3 6 9 0 1 0 3 6 9 (a) 0 0 of the Hessian detector? (c) == 0 of the Hessian detector? (d) X = X = 0 of the Harris detector? (e) 0 < or 0 < x of the Harris detector? 2. Let X and X2 denote the eigenvalues of Mp. What kind of image feature is present at p when: 3. What are the invariance properties of: (a) the Harris detector? (b) the Hessian detector? 2 4. The SIFT decriptor is known for its scale invariance property where the idea is to find local extrema in the scale space parametriezed by the stan- dard deviation of, such that: Z= (fos - fkos)* y (3) where k is a fixed scalar factor, and for is a Gaussian kernel with variance of. (a) Why is the kernel f chosen to be Gaussian? (b) Show that z is an approximation of the Laplacian of y. (c) How is the factor k typically chosen? Part II: Separable kernels Show whether the following convolution kernels are separable or not. If separa- ble, indicate the separations per case. [2 0 f = 0 1 0 0 3 1 g= -2 0 -3 0 0 1 2 (a) the Harris detector (b) the Hessian detector Part III: Image features Considering the image y, an interest point detector typically computes the ma- trix Mp which captures the changes of pixel intensities in a neighborhood N (p) of each pixel location p. A pixel intensity change at location p can be computed by filtering y with a filter g. h = 1. Give the expressions of a (3 3) filter g and the expression of Mp, each time explaining your notation, for: [3 6 9 0 1 0 3 6 9 (a) 0 0 of the Hessian detector? (c) == 0 of the Hessian detector? (d) X = X = 0 of the Harris detector? (e) 0 < or 0 < x of the Harris detector? 2. Let X and X2 denote the eigenvalues of Mp. What kind of image feature is present at p when: 3. What are the invariance properties of: (a) the Harris detector? (b) the Hessian detector? 2 4. The SIFT decriptor is known for its scale invariance property where the idea is to find local extrema in the scale space parametriezed by the stan- dard deviation of, such that: Z= (fos - fkos)* y (3) where k is a fixed scalar factor, and for is a Gaussian kernel with variance of. (a) Why is the kernel f chosen to be Gaussian? (b) Show that z is an approximation of the Laplacian of y. (c) How is the factor k typically chosen?

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The kernel 4 is chosen to be computed when the input image is filtered with the Harris detector The Harris detector is an interest point detector that identifies points in an image that are likely to ... View the full answer