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PiLab-CAU / ComputerVision-2401

Computer Vision Course 2024-01
Apache License 2.0
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[Lecture2][0415] About Filters and Convolution self study 2 #16

Closed kimjyan20221186 closed 3 months ago

kimjyan20221186 commented 5 months ago

@yjyoo3312, when I'm attempting to solve the self-study materials, specifically on problem 2, I have concerns that the proof regarding shift invariance may not be properly constructed. Could you please advise if the proof I have formulated is sufficient? If not, could you suggest which properties should be utilized? photo_2024-04-15_22-45-08

yjyoo3312 commented 5 months ago

@kimjyan20221186 Ah, I just saw this now. I will answer it after the class:)

yjyoo3312 commented 5 months ago

@kimjyan20221186 Sorry for the late reply!

I've attached a sample solution to your question. While it may not meet the strictest standards required in a math class, this answer would still earn a perfect score in my computer vision class (The gray terms would be bit redundant).

image

The overall derivation in this solution is similar to yours, but it uses a more traditional format for clearer mathematical explanation. Typically, especially in math classes, it's advisable to start with a definition and then solve the problem based on that definition. However, I don't view this computer vision course as strictly mathematical, and your answer captures the essential concept needed for the derivation, so I find it acceptable. I will award full marks for the quality of your answer:)

P.S. Could you possibly send your name to my email (yjyoo3312@cau.ac.kr)? It's for the e-class record.

kimjyan20221186 commented 5 months ago

@yjyoo3312 Thank you for the clear proof! I will send an email soon :)