【数字图像处理】期末复习资料及期末模拟试卷(含答案)doc

Digital Image Processing Examination

1. Fourier Transform problem.

1） F or 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),where δ is the Dorac Delta function.

2） F or 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

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 is

⎪⎩⎪⎨⎧≥≤≤=222

0log 21)(σσσD D for D D R

a) Plot this function

b) What is D max c) 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 to

convert 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 con-veyor 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 where each image pixel is located on the conveyor belt at every point in time.

Provide an annotated flow chart of the algorithm you propose.

5.In a given application, an averaging mask is applied to input images to reduce noise and then a

Laplacian mask is applied to enhance small details. Would mathematics predict that the result should be the same if the order of the operations were reversed? What practical issues would be encountered in computer implementation?

Digital Image Processing Examination

1. A preprocessing step in an application of microscopy is concerned with the issue of

isolating individual round particles from similar particles that overlap in groups of two or more.

Assuming that all particles are of the same size, propose a morphological algorithm that will produce an image that contains only the isolated (non-overlapping) particles that are not in contact with the boundary of the image.