Transform the scene in the world coordinate system to the viewing coordinate system with viewpoint at (1,1,2). The view plane normal vector is(−4,2,5) and the view up vector is (1,4,0
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- Complete the transititon function in the image:Perform histogram equalization on the following 6*6 image the gray scalelevel distribution of the image is given belowThis problem is on Computer Graphics and is based on the topic 'Perspective Projection'. Please provide a step-by-step solution to the problem and explain the steps. The solution must include the General purpose perspective projection matrix. Question: Let a 3D point (423, -423, 423) be projected on a projection plane. Given that the center of the projection plane is (0.0, 0.0, -423.0) and the coordinate of the COP is (4, 2, 3). Determine the coordinate of that 3D point on the projection plane using a general purpose perspective projection matrix.
- If the origin is taken as the centre of projection, then what will be the perspective projection when the projection plane passes through the point P(4;5;3) and has normal vector (1;2;-1).The attatched image is the 2D profile of an image, showing I(x,y). True or False: The spatial frequency in the x direction (kx) is π; the spatial frequency in the y direction (ky) is π; and the inital phase is π. To create this 2D intensity, we need to add together multiple 2D sine waves. The Fourier transformation of this image will contain a single peak at a single frequency (not counting peaks at zero and the overtones) The wave in the 2D profile is plotted for 3 wavelengthsConsider a room with world coordinate system U-V-W as shown. Two cameras are mounted in the room, forming a stereo pair. The world coordinate origin is in one corner of the room, with UV-W axes shown. The "Left" camera Cl is located at world coordinates (10,1,3) and it's xl-yl-zl axes are oriented as shown. The "Right" camera Cr is located at world coordinates (7.1,2) and its xr-yr-zr axes are oriented as shown. Both cameras have a focal length of 1. U (1) What is the 3x4 matrix that maps 3D points in world coordinates into 2D points in film plane coordinates (when points are represented as homogeneous coordinates), for the left camera CI? (2) What is the 3x3 essential matrix for the two cameras, treating them as a stereo pair where Cl is the "left camera" and Cr is the "right" camera?
- Q1 Suppose an image has a line having three points with (x,y) coordinates (1,2), (2,3), and (3,4) (assume the image coordinates starts from (0,0)). What will these points be in the Hough space (m, b)? Draw them in Hough space with exact coordinates mentioned, where (m, b) are the parameters representing the slope and intercept of the line. What information do you get from the resultant Hough space?Create a vector (v). which consists of 25 equally spaced points in the range from -21 to 3TT. Then, perform each of the following: d) Remove the last element in (v). e) Plot f cos(v) with linewidth - 2 and title Sinusoidal WaveformWrite a function mountains example on how the function works is given in the image.
- Suppose images f(x,y) and g(x,y) have histograms h; and hg. Suppose you form image k(x,y) as the sum of these two images: k(x,y) = f(x,y) + g(x,y). (a) Under what conditions (on images f and g) can you determine the histogram hų of image k in terms of the histograms hf and hg? (That is, under what conditions can you determine hu if you are only given hj and he? Hint: this turns out to be fairly restrictive.) (b) Explain how you would derive hỵ in this case.Problem 3: The histograms of two images are illustrated below. Sketch a transformation function for each image that will make the image have a better contrast. Use the axis provided below to sketch your transformation functions. 1/128 1/200 64 192 255 100 155 255A point in 3D space has coordinates [-10,-40,500] mm relative to the camera reference frame. If the camera has an image plane at distance f'=33 mm from its optical centre, the CCD array is 10 mm by 14 mm and is divided into 340 by 240 pixels, and the image principal point is at coordinates [170,120] pixels, then determine the coordindates (in pixels) where the point will appear in the image using the pinhole camera model of image formation. ANSWER: Coordinates of point in image: (