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1Project 3Allan Reyes[email protected]Project’s ApproachFor this project I decided to take the lessons learned from Project2 (where I wasted a whole week trying to implement a fractal-based algorithm with mediocre results) and stick to my originalapproach which had great success on the past two projects.Furthermore, in Project 2 I had already worked on extending it tohandle 3x3 problems, so applying it to this last project wasstraightforward. At a high-level my approach involves usingvisual transformations to manipulate images, as well as,semantic relationships whenever image transformations are notenough to solve the problems.Once I started following the approach mentioned above, I hadtwo key realizations based on the problems in each of the twosets. First, for set D, I realized that almost all the problemsinvolved finding a missingelement of the matrix: shapes orpatterns or both. For example, Basic Problem D-02 (Figure 1.A)involves finding the missing shape, while Basic Problem D-07(Figure 1.B) involves finding the missing shape and the missingpattern around that shape. This allowed me to focus most of myefforts efficiently in developing common heuristics for findingshapes and patterns, and then simply adapting them to each oftheproblems’particularcharacteristics.Figure 1. A. Basic Problem D-02 where a shape is missing. B. Basic ProblemD-07 where a shape and a pattern are missingFigure 2.A. Basic Problem E-07 solved by using XOR. B. Basic Problem E-11 solved by using intersection.
2On the other hand, for set E, I realized that the vast majority ofthe problems could be solved by simple purely-visualtransformations. I thought this was interesting because, beingthe last set, I had imagined the problems in set E would be thehardest ones to solve; however, my agent was able to performreally well on this set because the transformations were fairlysimple. As an example, look at Basic Problem E-07 (Figure 2.A),at first sight it seems this problem is quite complicated withseveral different shapes being transformed; however, it can beeasily solved by taking the pixel-wise difference between theimages in the first two frames (something known as the XORoperator). Likewise, Basic Problem E-11 (Figure 2.B), despitehaving different patterns based on filled vs. empty squares, canbe solved by finding the commonpixels between the images in thefirst two frames, i.e. theintersection.One of the other things that Inoticed while working on theproblems was that the existingtransformations and semanticrelationships, which were implemented as part of Project 2 forthe set C, were causing a lot of false positives when they wererunning against the new sets D and E. One way of solving thiswould have been to simply separate the problem sets; however,to me it seemed like a band-aid instead of a solution to theactual problem. After some debugging, I came to the conclusionthat the root cause was the fact that existing heuristics werealwaystrying to find an answer for the problem even if theproblem did not really meet the conditions. So, one of the