Answer Happy

We have a Microsoft Kinect camera installed on a Quanser QBot 2 robot. The camera generates both the vision of the environment and distance and orientation of the obstacles as separate vision and depth images. The depth information, including distance and orientation of the obstacle, is transferred to the processing units as a 2D grey-scale image frame of the size of 480 x 640 pixels (i.e., 480 rows each with 640 pixels). a) Datasheet of Kinect says that its horizontal field of view (FOV) is 57°. What is the meaning of FOV and how it is related to the motion of the robot for mapping? Figure Q3-1 illustrates the way that Kinect stores the location and orientation information of obstacles within the depth image. If the value of d = 6.1m in Figure Q3-1 is stored in the 550th pixel, calculate the distance and orientation of the obstacle P (i.e., L and a). Figure Q3-1 Example of encoding of information related to the distance and orientation of obstacles in a row of the depth image [courtesy of Quanser]. [6 marks) b) According to the formal definition, a transformation (also known as a function) y(t) = T(X(t)) is linear if and only if: T(ax:(t) + bxz(t)) = a1(xz(t)) + b1(x2(t)) = ay(t) + byz(t) and is time-invariant if and only if for VT 2 0: T(x(t = 1)) = y(t-1) Using this definition, evaluate if the following functions are linear or not: 1. T(x) = e-tx(t) 2. T'(x) = x(t) dr(e) 3. T(x) = 1 [6 marks] IQuestion continued on next page di dx() dt

c) With providing a mathematical equation and a pseudo code explain the convolution operator between two functions f(x) and g(x) and the way it can be implemented as a software programme. Why convolution operator is important for the image processing algorithms? [8 marks)