• Use Matlab or Python for your implementation. Do not use pre-defined functions. For Python users, you may use libraries minimally to load data or perform basic operations such as matrix multiplications. • • Use either Matlab or Python. Problem descriptions are based on Matlab codes, but you may convert them to equivalent functions in Python. Problem 1 (Edge detector, Edge linking, 30pts)

1. Write a gradient based edge detector. Your code should load in a gray-scale image (use imread and convert to a double array using im2double). You can display the image using functionality like imagesc. Once you have loaded in the image, you should smooth the image with a Gaussian filter and then compute horizontal and vertical derivatives using a derivative filter. The amount of smoothing is determined by the parameter σ of the Gaussian (which should be a parameter in your code). You can use conv2 to perform the required convolutions. Once you have computed the derivatives in the x and y directions, compute the gradient magnitude and orientation. Display the gradient magnitude as a image and the orientation using quiver functionality.
2. We want to extract the outer boundary of each object contained in one image. First, use edge() function (pre-defined or your own edge detector) to obtain the edge map. Then use imview() function to manually locate one pixel located on the outer boundary of each object. Next, apply any technique you can come up with to trace the boundary edge pixels. Try to get a boundary as complete and accurate as possible: it is OK if your results are not perfect (see below). Plot the final boundary you are able to detect and trace for each object. Discuss the success, failure, and possible ways for improvement in the report. Note that boundary tracing is a non-trivial problem, involving many complicated issues such as noise, broken boundaries, ambiguous locations and directions, among others. Thus, do not worry if you are not able to get a ‘perfect’ result — we just want to see how hard you tried. Do not use built-in functions such as ‘bwtraceboundary()’ provided by Matlab image processing library. The idea is for you to gain familiarity with the algorithm through the experiments in this task. Problem 2 (Corner Point Detection) Implement your own Harris corner detector to automatically identify corner points in an image. Your implementation should take an 2D image I as an input and compute corner responses for each pixel. Take the points of local maxima (within a radius r) of the response. Problem 3 (Hough Transform) The purpose of this component is to get familiar with the Hough transform for shape detection. You will need to implement the Hough transform on your own. The built-in functions such as hough() in Matlab are not allowed.
3. Write a program to automatically identify straight lines in an image: lines = myHoughLine (imBW, n), where imBW is a binary image and n is the desired number of lines (in order of voting importance). If there are not enough n lines in an image, return as many as your implementation detected. Test with n = 5, and plot your lines along with a few images in your report.
4. If you haven’t already, read “Generalizing the Hough transform to detect arbitrary shapes (Ballard, 1981)” and review for Hough transform. Write a program to find (roughly) circular objects of a specific radius in a binary image. You should write two functions, yourcellvar = myHoughCircleTrain(imBW, c, ptlist), and myHoughCircleTest(imBWnew, yourcellvar). The binary image imBW supplied to the first function will have a single circular object. Further, c will be the (given) reference point, and for convenience we will also provide you an ordered list of boundary points in ptlist. Use this information to construct whatever data structure you want (and save all tabular data necessary for the subsequent step), and return it as a cell array variable, yourcellvar. That is, yourcellvar is the object myHoughCircleTrain should return. Next, this will be passed directly to myHoughCircleTest where you will identify circular objects in a novel image, imBWnew. Your function should report the reference points for the top two circles identified. You will receive full credit if your reference point is close enough. Test with your own images and discuss your results with these images in your report.