Edge-Detection-and-Noise-Removal

Implementation of standard filtering techniques for image enhancement, edge detection and noise removal

1. [5 points] Implement an AverageFiltering function to perform a filtering operation (i.e., convolution operation), as explained in class, on the input image. The prototype of this function should be: function [filteredIm] = AverageFiltering (im, mask) where im is the original grayscale image and mask is the square filter with an odd number of rows and columns. Make sure that your function shows appropriate error messages when the mask’s dimension is not an odd number, the mask is not a square (i.e., the number of rows and the number of columns are not the same), and the mask does not possess the three properties of the low-pass filter (i.e., all the elements in the mask are positive, the total of all the element is 1, and the elements are symmetric around the center). Note: Both input and output images of the AverageFiltering function should be an array with the same size and the same data type uint8. You are not allowed to simply use the Matlab “filter2” or “conv2” or “fspecial” or “imfilter” or other built-in functions in your implementation. Call AverageFiltering function to process the noisy image Circuit using a weighted 3×3 averaging filter and a standard 5×5 averaging filter, respectively. Display the original image and two processed images in figure 1 with appropriate titles.

2. [5 points] Implement a MedianFiltering function to perform a filtering operation, as explained in class, on the input image. The prototype of this function should be: function filteredIm = MedianFiltering(im, mask) where im is the original grayscale image and mask is the square filter with an odd number of rows and columns. Make sure that your function shows appropriate error messages when the mask’s dimension is not an odd number, the mask is not a square, and all the elements in the mask are positive integers. Note: Both input and output images of the MedianFiltering function should be an array with the same size and the same data type uint8. You are not allowed to simply use the Matlab “medfilt2” or other built-in functions in your implementation. However, you can use the built-in functions to sort a sequence of numbers or find the median value of a sequence of numbers.Call this function to process the same noisy image Circuit using a weighted 3×3 median filter M = [1 2 1 ; 2 4 2; 1 2 1] and a standard 5×5 median filter, respectively. Display the original image and two processed images in figure 2 with appropriate titles. Note: The standard median filter explained in the class isvalue in the median filter indicates the number of copiesimage involved in the standard median filtering. a special kind of the weighted median filter. Each of the corresponding masked value in the original

3. [5 points] Use the strong 3×3 Laplacian mask to filter the image Moon by calling an appropriate Matlab built-in function. Use the formula Enhanced Image = Original Image - Filtered Image to get the final enhanced image (Hint: This formula indicates that one of the two strong Laplacian masks should be used). Use imshow to display four images including the original image, the filtered image (display it by setting the values larger than 255 as 255 and setting the values smaller than 0 as 0), the scaled filtered image whose intensities fall in the range of [0, 255], and the enhanced image, in figure 3 with appropriate titles.

Problem II: Exercises on Edge Detectors in the Spatial Domain [Total: 10 points]

1. [5 points] Apply the Sobel edge detector, as explained in class, to find the important edges in the image Rice. Refer to slides 61 and 63 of my notes. On the Matlab console, explain your strategy to choose the appropriate threshold to locate the important edges in Rice.

2. [5 points] Implement a CalEdgeHist function to compute the edge histogram of the input image. The prototype of this function should be: function edgeHist = CalEdgeHist(im, bin) where im is the original grayscale image and bin is the number of bins. Edge histogram contains the counts of the angle of orientation of the edge, which can be computed by:   arctan G / G  , where Gx is the x ygradient component produced by the horizontal edge detector and Gy is the gradient component produced by the vertical edge detector (Refer to slide 63 of my notes. Gx is the left-side filter and Gy is the right-side filter). Call this function to compute the 18-bin edge histogram (e.g., dividing the entire range of angles of orientation of the edges into 18 equal intervals and get the counts of the number of angles falling in each interval) of the image Rice. Display the original image, the image with the important edges, and the edge histogram in figure 4 with appropriate titles. Note: The entire range of angles of orientation of the edge should cover 360 degrees.

Problem III: A Practical Problem [10 points] Use the techniques explained in class to get rid of the streaks (stripes) in the image “Text.gif”. Please write a function with the original grayscale image as the input and the cleaned grayscale image as the output. Summarize the basic idea of your solution on the Matlab console. Display the original, some important intermediate images (plots), and the enhanced image in a few figures with appropriate titles. [8 points] You may test the effectiveness of your solution on two additional images (e.g., Text1.gif and Text2.jpg) by calling your implemented function to see whether it can get rid of the stripes in these two images. [2 points] In order to get the full credit for this problem, your main function should be able to remove the stripes in all three images without changing the implementation. Note: The student who comes up with the best solution will earn a 2-point extra credit!