# ECSE4540 Homework#1 solution

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1. (30 points.) Create the following 500×500 8-bit images in Matlab; include a picture and the Matlab commands you used in your writeup. Note that each of these only requires 1-3 lines of Matlab code, no for loops, and no if statements! Use the image (not Cartesian) coordinate system; that is, x indexes the rows from top to bottom and y the columns from left to right. Use imshow(im,[0 255]) for grayscale image display. Use uint8(im) for commands that don’t produce an integer output. You will be penalized if your codeistoocomplicated.
(a) Agrayscaleimageofconstantintensity60 (b) Agrayscaleimagewithalternatingblackandwhiteverticalstripes,eachofwhichis2pixelswide (c) Agrayscaleimagewherethelefthalfhasintensity32andtherighthalfhasintensity200 (d) Agrayscaleimagewitharampintensitydistribution,describedby I(x,y)=x/2 (e) AgrayscaleimagewithaGaussianintensitydistributioncenteredat(64,64),describedby I(x,y)=255exp−³(x−64)2+(y−64)2 2002 ´(f) A color image where the upper left quadrant is white, the lower left quadrant is magenta, the upper rightquadrantiscyan,andthelowerrightquadrantisblue
2. (20points.) (a) A 4K HDR Netﬂix video stream transmits frames of size 4096×2160 at 30 frames per second with 10 bits per color channel. Compute the number of bits it would take to stream the season premiere of StrangerThings2,a48-minuteepisode. (b) Suppose your internet provider caps your download rate at 30 Mbps. Based on your answer in part (a), compute a lower bound on the compression ratio that must be achieved by Netﬂix’s video compressionalgorithminordertodeliverthestream.
3. (20 points.) Consider the image in Problem 1e, which has 256 gray levels. Create quantized versions of this image with 128, 64, 32, and 16 gray levels (this involves the round command). At what point can you visuallydetectfalsecontouring?
4. (15 points.) We model the camera in the iPhone 8 as a pinhole placed at (0 m, 0 m, 0 m) in world coordinates. Suppose the focal length is 28mm and a 6.29×5.21 mm CCD array that has 4608 pixels in the x direction and 2592 pixels in the y direction is placed at the focal plane. What image pixel does the world coordinate (-0.05 m, 0.1 m, 2.5 m) project to, assuming (0,0) is at the upper left corner (not the center) of thearray?
5. (15points.) ThecolorofRey’slightsaberisgivenbytheHTMLRGBcode #A8D0E8. Representthiscoloras:
(a) AnRGBtripletwhereeachvalueisintherange[0,1]. (b) ACMYtripletwhereeachvalueisintherange[0,1]. (c) An HSI (hue-saturation-intensity) triplet where each value is in the range [0,1]. See Gonzalez and Woods (Section 6.2 3rd ed., Section 7.2 4th ed.) for how to do the conversion and show your work! Note that Gonzalez and Woods deﬁne the intensity component slightly differently than Photoshop andotherpaintprograms,andthatHSIisnotthesameasHSV! (d) aninterpretationoftheHSItripletinwords(e.g.,similarto“adeep,darkred”.)