Module Contact: Dr Barry-John Theobald, CMP Copyright of the University of East Anglia Version 1

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1 UNIVERSITY OF EAST ANGLIA School of Computing Sciences Main Series UG Examination COMPUTER VISION (FOR DIGITAL PHOTOGRAPHY) CMPC3I16 Time allowed: 3 hours Answer THREE questions. All questions carry equal weight. Notes are not permitted in this examination. Do not turn over until you are told to do so by the Invigilator. CMPC3I16 Module Contact: Dr Barry-John Theobald, CMP Copyright of the University of East Anglia Version 1

2 Page 2 1. (a) Let R(λ), E(λ) and S(λ) respectively denote the sensitivity of a camera sensor, the spectral power distribution of light and a surface reflectance spectrum. (i) Write down an integral expression that describes the camera response. (ii) Under E 1 (λ) and E 2 (λ) the camera records the values p 1 and p 2 respectively. Using your answer to Question 1(a)i, prove that under E 3 (λ) =.4E 1 (λ)+.2e 1 (λ) the camera response is equal to.4p1 +.2p2 [7 marks] (iii) Lambert s law describes how the magnitude of the sensor response depends on the relative orientation of the imaged surface with the light source direction. Describe in detail Lambert s law. In your answer, include a diagram that shows how the same surface can induce exactly the responses p and 0.5p in a camera. (b) In the context of tone mapping and HDR imaging: (i) What is the difference between a HDR and a standard LDR image? (ii) How can you display an HDR image on a standard display. (iii) Explain the function of a projector-based HDR display. (iv) Discuss the relationship between the camera bit depth and its dynamic range. (v) Compare global and local tone mapping. Your answer should include a list of the advantages and disadvantages of both. [6 marks]

3 Page 3 2. (a) Filter the following monochromatic image, I, with the following mask, M. The output image, I O, should be the same size as I and the calculations should assume zero padding. I = ,M = 1 9 (b) What function does this filter perform? What is the name of this filter? (c) Contrast the filter from Question 2b with Gaussian and median filtering. Your answer should make clear how each method works and discuss their respective advantages and disadvantages. [16 marks] (d) Describe the Histogram Backprojection (hint: not Indexing) algorithm as described by Swain and Ballard. [12 marks] (e) Assume you are using an indexing algorithm that utilises 3-D histograms created from image R, G and B values. How would you modify these image features (histograms) to make them illumination intensity invariant. TURN OVER

4 Page 4 3. (a) An automated quality control system requires an object to be segmented from the background. Your job is to design a system to perform the segmentation using only the image histogram. A typical example of a histogram from an image captured by the imaging device is shown in Figure 1. Figure 1. An example image histogram. Describe a method for robustly segmenting the object from the background. You may assume that one of the peaks in the histogram corresponds to the region of interest in the image, whilst the second peak corresponds to the background. State all other assumptions. [15 marks] (b) A line measurement system outputs the following set of noisy coordinates: (0,1), (1,3.3), (1,4.1), (2,4.6), (3,6.9), (3,5.8), (4,9.2), (5,11.5). The expected gradient lies between Showing all of your working, use the Hough transform to find the parameters of the straight line. (c) Outline, using equations and diagrams where appropriate, the Canny edge detector. (d) What is RANSAC? Give an example of where it might be used.

5 Page 5 4. Statistical models of shape, such as point distribution models (PDMs), provide a powerful means for representing and locating objects in images. (a) To train a PDM it is important to first align all of the shapes into a common coordinate frame. Why is this so? [4 marks] (b) During the alignment process it is common to weight each landmark according to their significance in the alignment. Why is this so and how are the weights usually calculated? (c) What are good landmark positions for use in defining a PDM? [4 marks] (d) Explain the difference between primary and secondary landmarks in a PDM? [6 marks] (e) An active shape model (ASM) is an iterative fit of a PDM to an image. One option for performing this fit is to model the grey-level appearance local to each landmark using principal components analysis and then measure the error between the expected and the observed appearance at the current estimate. (i) The difference between the appearances can be written as e = g s ĝ s, where e is a vector of differences, g s is the expected appearance and ĝ s is the observed appearance. Show that the squared error between the observed appearance and the local appearance model can be written as: E 2 = (g s g) T (g s g) b T g b g where b g is the projection of ĝ s onto the appearance principal components. Note you may find following useful: (P T b) T = b T P. [15 marks] (ii) Outline an algorithm for using this error function to fit the model to the image. (iii) Explain why ASMs are generally more robust than more general Active Contour Models, such as Snakes. END OF PAPER