13 01 2023 E TS

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Algorithms and Parallel Computing Course 052496 Prof. Danilo Ardagna Date: 13-01-2023 Last Name: ............................................................. First Name: ............................................................. Student ID: ............................................................. Signature: ............................................................... Exam duration: 2 hours and 15 minutes Students can use a pen or a pencil for answering questions. Students are NOT permitted to use books, course notes, calculators, mobile phones, and similar connected devices. Students are NOT permitted to copy anyone else’s answers, pass notes amongst themselves, or engage in other forms of misconduct at any time during the exam. Writing on the cheat sheet is NOT allowed. Exercise 1: Exercise 2: Exercise 3: Exercise 1 (14 points) A digital image is displayed as a 2-dimensional grid of points, called pixels, of different colors. This is often achieved by splitting the image into components, each representing one single primary color (with its varying degree of intensity) and whose superposition gives the full-color representation of the image. These components are called channels, and are basically a single-color replica of the original image, as shown in Figure 1. Figure 1: Example of decomposition of an image (height=198, width=319) into 3 channels (Red, Green, Blue). In our case, an image is represented by anstd::vector of channels (which will be stored in thechannels class data member), which in turn are each represented by an instance of theDenseMatrix class (whose header file is reported below). All num_chan channels in an image must have the same dimensions (height rows by width columns). Entries of the matrices aredoubles in the[0,1] interval, and…