精品文档---下载后可任意编辑1. Fourier Transform problem. 1）For an image given by the function f(x,y)=(x+y)3 where x,y are continuous varibales; evaluate f(x,y)δ(x-1,y-2) and f(x,y)* δ(x-1,y-2),whereδ is the Dorac Delta function.2）For the optical imaging system shoen below,consisting of an image scaling and two forward Fourier transforms show that the output image is a scale and inverted replica of the original image f(x,y).f(x,y)Scalingf(ax,by)FFg(x,y)_3) three binary images (with value 1 on black areas and value 0 elsewhere) are shown below. Sketch the continuous 2D FT of these images(don’t do this mathematically, try to use instead the convolution theorem and knowledge of FTs of common functions)2. The rate distortion function of a zero memory Gaussian source of arbitary mean and variance σ2 with respect to the mean-square error criterion isa)Plot this functionb)What is Dmaxc)If a distortion of no mor than 75% of the source’s variance is allowed, what is the maximum compression that can be achieved?3.The PDF of an image is given by Pr(r) as shown below. Find the transform toconvert the image's PDF to Pr(z). Assume continuity, and find the transform in terms of r and z. Explain the transformation.4. A certain inspection application gathers black & white images of parts as they travel along a conveyor belt. It is necessary to sort the parts into two categories: parts with holes and parts with-out holes. An example of an image that might be taken by the inspection camera is shown at the right.Propose a method to identify and locate the objects of each category in the image so that they can be picked up by a robotic system and placed in different bins. Assume that the imaging system knows ...
