EEL 6562 Image Processing and Computer Vision Image Restoration

Transcription

1 DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING EEL 6562 Image Processing and Computer Vision Image Restoration Rajesh Pydipati

2 Introduction Image Processing is defined as the analysis, manipulation, storage, and display of graphical images from sources such as photographs, drawings, and video. Image processing spans a sequence of three steps. The input step (image capture and digitizing) converts the differences in coloring and shading in the picture into binary values that a computer can process. The processing step can include image enhancement and data compression. The output step consists of the display or printing of the processed image. Image processing is used in such applications as television and film, medicine, satellite weather mapping, machine vision, and computer based pattern recognition [1]. Problem statement: Perform Image restoration of a noisy image Approach: Image Restoration Sometimes an image is blurred or degraded by an optical system, motion, defects, etc. If the transfer function of the degradation is known (this is a big if) then a process of inverse filtering can restore the original image. Assuming little or no noise, G = HF so F = G/H This works if there is little noise and the transfer function H is known. If there is noise, the process falls apart. Even then, a more sophisticated method using the so-called Weiner filter can sometimes give back a fairly well restored image. However, the real limitation of such methods is the need to know H. Procedure The following steps were performed in sequence: 1) The Lena image was centered in a 524x524 image with background pixels set to zero. 2) The image was now blurred using an 11x11 Box filter. 3) The resulting image was trimmed to fit in a 512x512 image 4) Now DFT of the blurred image was calculated using the routines provided. 5) The DFT of the Pseudo inverse filter function was already calculated in the code given to the class. 6) Now the DFT s of both the blurred 512x512 image and the pseudo inverse filter were multiplied. Here, it should be noted that since both the DFT samples are complex, the multiplication is actually complex multiplication. 7) Now an inverse FFT was performed on the resulting matrix which gives the 512x512 restored image 8) The unnecessary border was cut off and the 256x256 restored Lena image was written out into a file in the final step Rajesh Pydipati 4 Spring 2003

3 Software Used: C programming language was used for performing Image restoration. The utilities fft.c, fft.h, tiff_util.c and tiff_util.h were used as is from the class website. Changes were made in the main program. Results: Original 256x256 Image Lena centered in a 524x 524 image The 512x512 blurred image DFT of the blurred 512x512 image 2003 Rajesh Pydipati 5 Spring 2003

4 DFT of the averaging filter Pseudo inverse filter frequency response The final 256x256 restored Lena Image Questions: 1) What is the dominant noise source in this lab? Calculate its mean and variance. The dominant noise source in this particular problem is the averaging filter which is used to blur the image. It is actually an 11x11 Box filter. Its mean is and variance is e-034.It is easily seen that the noise in this particular problem is very low. 2) What other limitation, other than the noise source above, prevents a perfect reconstruction of the image? We know that f (u, v) = F(u,v) + N(u,v) / H(u,v) 2003 Rajesh Pydipati 6 Spring 2003

5 Where f (u, v) is the estimate of the transform of the original image The expression tells us that even though we know the degradation function we cannot recover the undegraded image exactly because N (u,v) is a random function whose Fourier transform is not known. Another problem is that if the degradation has zero or very small values, then the ratio N (u, v) / H(u,v) could easily dominate the estimate f (u,v). This may be the other limitation which prevents a perfect reconstruction of the image. One approach to get around the zero or small value problem is to limit the filter frequencies to values near the origin. We know that H (0,0) is equal to the average value of h(x,y) and that it is usually the highest value of H(u,v) in the frequency domain. Thus by limiting the analysis to frequencies near the origin, we reduce the probability of encountering zero values. This fact is easily observed in the pseudo inverse filter frequency spectrum. References: [1]. Microsoft Computer Dictionary: [2]. Digital Image processing by Rafael.C. Gonzalez [3] Rajesh Pydipati 7 Spring 2003