Q. 3. a) A point in space is captured by two cameras with identical focal length of 6" separated by 3". The disparity of the image points along the axis joining the camera centers is 0.53". Calculate the depth of the camera point. (2 marks) b) What is content addressable image retrieval and why is it necessary? Discuss a simple scheme for image retrieval based on color distribution in the query and database images. (2 marks) The RGB to HSI conversion formulas are: . R R+G+B G R+G+B B ;b= R+G+B h = cos 0.5{(r-g)+(r-b)} 0/2 When h=[0,7] for bsg r-g)+(r-b)(g-b) h=2x-h (Computed above) when h (computed above) e [,2] for b> g s=1-3min(r.g,b) se[01]; i=(R+G+B)/(3*255) ie [0,1] H =hx180/7,S=sx100, and -i*255 Q. 1. a) Outline the procedure for deriving the formula for cos(h), where h is the hue of the color in radians, from the normalized (rgb) color triangle (only an outline, not a detailed derivation, is required). Compute HSI values for the color (R. G, B) (25, 50, 125). (3 for outline +3 for calculations = 6 Marks) = Pe (2 Marks) b) Show how the translations, rotations, and scaling of an object may be represented by an affine transform in homogeneous coordinates. Discuss in no more than two lines the need for homogeneous coordinates. Q.2. In a texture segmentation problem, the proportion of horizontal and vertical edgels among 25 pixels in (5x5) window around each pixel are considered as two measurements at each pixel site in the image, and 2-dimensional pattern vectors representing the texture at the pixel are obtained. When mapped into the pattern space with Pe and Pve as coordinates, the pixels form, as shown in the adjacent diagram, two clusters are formed with means as 4,[11] and [2-0.5], and covariance matrices as Σ,= and Σ,= = [2 1] inverse of a non-singular matrix is given by 1 d -b a ad-bc-c = (0.01 ul 11 X = [1.5 0.25] Now, given that the H2 12 -0.51 is given by , find the cluster to which the point X=[1.5 0.25] will be assigned using the Mahalanobis distance in the next iteration of the ISODATA algorithm. Also, given that a cluster with semi-major axis greater than the split threshold of 2 needs to be split, which one of the two clusters will be split up? What will be the coordinates of the new cluster centers in case of split up? (4+4=8 marks) Note: The semi-principal axis size (equivalently the spread along the principal axis) will be equal to the square root of the corresponding eigenvalue. Q. 3. a) A point in space is captured by two cameras with identical focal length of 6" separated by 3". The disparity of the image points along the axis joining the camera centers is 0.53". Calculate the depth of the camera point. (2 marks) b) What is content addressable image retrieval and why is it necessary? Discuss a simple scheme for image retrieval based on color distribution in the query and database images. The RGB to HSI conversion formulas are:= R h=cos 0.5(-8)+(-b)) r-8)+(r-bg-b)" 11/2 R+G+B G B R+G+B R+G+B When h=[0.] for bsg h=2x-h (Computed above) when h (computed above) [2] for b>g € s-1-3min(r.g,b) se[01]; i=(R+G+B)/(3*255) ie [0,1] H=hx180/л,S=sx100, and 11*255 (2 marks)