6 098 6 882 Computational Photography 1 Problem Set 1 Assigned Feb 9 2006 Due Feb 23 2006 Note The problems marked with 6 882 only are for the students who register for 6 882 Of course students registering for 6 098 may do these problems according to their interests but they will not be graded The problems marked extra credit are for both 6 882 and 6 098 students For those who are not familiar with image processing manupulation in MATLAB please see the appendix to this problem set for a brief introduction Students are encouraged to collaborate on the assignments However each student should individually do the coding and the write up Please hand in solutions on the due date and email the code and results in a zipped file to TA In the email please also indicate how much time you took on this problem set Please go to webpage http groups csail mit edu graphics classes CompPhoto06 download and unzip file ps1 zip under the link problem sets and solutions Problem 1 Pinhole Camera a With a pinhole camera if you photograph a brick wall with the sensor plane parallel to the brick wall will the lines of the bricks be parallel or converging in the resulting photograph b Suppose you move the camera during an exposure Under each of the following types of camera motion will the amount that an object is blurred depend on its distance away from the camera and why i rotation about a vertical axis through the pinhole vertical axis assumed to be parallel to the sensor plane ii rotation about the optical axis iii translation in a direction parallel to the sensor plane 6 098 6 882 Computational Photography 2 Vertical axis Sensor plane Pinhole Optical axis Figure 1 Pinhole camera schematic defining the vertical and optical axes iv translation perpendicular to the sensor plane c For a pinhole camera how will the image change from one obtained using a small circular aperture ignoring diffraction effects i if you double the size of the aperture ii if you change the aperture to a thin vertical slit Problem 2 Warm up Matlab Assignment Unzip file ps1 zip Load image street jpg into Matlab This is the output data taken by a CCD color camera before tonescale adjustment Apply a gamma tonescale correction of Iout Iin where 0 5 Display the two images side by side in your answer document Problem 3 Color Load image desk orange jpg into MATLAB The image is from web http www scifun ed ac uk card images left desk orange jpg This is a photograph taken under Tungsten illumination Usually color correction is done before the tonescale adjustment but for convenience in viewing the images we will apply it after tonescale adjustment here Von kries adaptation refers to restricting the 3x3 color transformation matrix to have zeros on all off diagonal terms What 3 entries for von kries 6 098 6 882 Computational Photography 3 adaptation color scaling is needed to provide proper color balance to this image under the assumption of a gray world the average pixel intensity for each color channel is the same for all 3 color channels To minimize the overall brightness change assume that the average pixel value of the color balanced image is c c c where c is the maximum of the mean value per each uncorrected RGB channel Show side by side the uncorrected and color corrected images b the brightest pixel value in each color channel in the image is white Show side by side the uncorrected and color corrected images c 6 882 only For a generic color balanced image not specific to the image above what 3x3 matrix applied to every pixel will increase the color saturation of the image Your answer should be a formula for the matrix parameterized by the amount of color saturation desired Load image harbor bmp into Matlab apply the transform and display the two images side by side Problem 4 Demosaicing Given image watchtower jpg a synthesize the image observed through YGC striped sampling pattern b form the RGB demosaiced image using a linear interpolation algorithm for demosaicing c form the RGB demosaiced image using the median filter interpolation algorithm Assume 0 5 0 5 0 R Y G 0 1 0 G B C 0 0 5 0 5 d extra credit Put yourself in the shoes of an image demosaicing algorithm Guess by any means eyeballing it by plotting color values by using a color interpolation algorithm what the true values are for the missing color samples in waterfall bmp Assume that an initial color interpolation has been performed for the surrounding pixels and that we only have to infer the missing color values for the 4 central pixels of the image patch which lies at the center of the image or im 64 65 64 65 in MATLAB notation 6 098 6 882 Computational Photography 4 Your answer to this problem should be 8 numbers the 2 missing colors in each of the 4 pixels that are missing color samples in the image patch The color sampling was made using a Bayer sampling pattern Scoring for this extra credit problem will be a function of the squared error distance between your estimated values and the actual pixel values that were present in the original image Problem 5 Color Metamerism Not required Extra Credit The Matlab file CIE mat contains the spectra which will be needed for this problem The vectors cx cy and cz give the CIE color matching functions for the X Y and Z coordinates respectively These functions are sampled at 5nm intervals for wavelengths from 400 through 700 nm Suppose you have a test color specified as a linear combination of three spectral primaries at 420 520 and 620 nm given by a b c T respectively In terms of a b and c what linear combination of light sources at 460 510 and 590 nm is needed to give a perceptual match to the test color Appendix Image Operation in MATLAB MATLAB is a great tool for scientific computation There are three reasons we choose it as the programming language for the class MATLAB code is very compact The learning curve is very short Because matrix operation is embedded it is straightforward to code and easy to debug There are academic papers coded in only a few lines ICCV or less than a hundred lines Siggraph It is cross platform for Windows Linux and Mac OS For most of the code it requires no change to be transplanted from one operating system to another MATLAB provides a rich library of toolboxes which covers a broad range of scientific computation Besides there are many public MATLAB code downloadable from the internet But MATLAB is also notorious for loops If you are a Pascal C or C coder you may find it a little difficult to get used