Exploring JPEG Image Approximations and Outer Product Calculations
Dive into the world of JPEG image approximations with 8x8 pixel blocks and explore outer product calculations within the images for data analysis. Learn about different levels of approximation and how they affect the final image quality.
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Presentation Transcript
original image 20 Consider this 8 by 8 block 40 60 80 100 120 140 -20 0 20 40 60 80 100 120 140
The 8 by 8 block 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 9
1 outer product 1 2 Original 3 4 sum Outer product 5 6 7 8 1 0 1 2 3 4 5 6 7 8 9 1 2 2 3 3 4 4 5 5 6 6 7 7 8 0 1 2 3 4 5 6 7 8 9 8 0 1 2 3 4 5 6 7 8 9
2 outer products 1 2 Original 3 4 sum Outer product 5 6 7 8 1 0 1 2 3 4 5 6 7 8 9 1 2 2 3 3 4 4 5 5 6 6 7 7 8 0 1 2 3 4 5 6 7 8 9 8 0 1 2 3 4 5 6 7 8 9
3 outer products 1 2 Original 3 4 sum Outer product 5 6 7 8 1 0 1 2 3 4 5 6 7 8 9 1 2 2 3 3 4 4 5 5 6 6 7 7 8 0 1 2 3 4 5 6 7 8 9 8 0 1 2 3 4 5 6 7 8 9
4 outer products 1 2 Original 3 4 sum Outer product 5 6 7 8 1 0 1 2 3 4 5 6 7 8 9 1 2 2 3 3 4 4 5 5 6 6 7 7 8 0 1 2 3 4 5 6 7 8 9 8 0 1 2 3 4 5 6 7 8 9
5 outer products 1 2 Original 3 4 sum Outer product 5 6 7 8 1 0 1 2 3 4 5 6 7 8 9 1 2 2 3 3 4 4 5 5 6 6 7 7 8 0 1 2 3 4 5 6 7 8 9 8 0 1 2 3 4 5 6 7 8 9
6 outer products 1 2 Original 3 4 sum Outer product 5 6 7 8 1 0 1 2 3 4 5 6 7 8 9 1 2 2 3 3 4 4 5 5 6 6 7 7 8 0 1 2 3 4 5 6 7 8 9 8 0 1 2 3 4 5 6 7 8 9
7 outer products 1 2 Original 3 4 sum Outer product 5 6 7 8 1 0 1 2 3 4 5 6 7 8 9 1 2 2 3 3 4 4 5 5 6 6 7 7 8 0 1 2 3 4 5 6 7 8 9 8 0 1 2 3 4 5 6 7 8 9
8 outer products 1 2 Original 3 4 sum Outer product 5 6 7 8 1 0 1 2 3 4 5 6 7 8 9 1 2 2 3 3 4 4 5 5 6 6 7 7 8 0 1 2 3 4 5 6 7 8 9 8 0 1 2 3 4 5 6 7 8 9
9 outer products 1 2 Original 3 4 sum Outer product 5 6 7 8 1 0 1 2 3 4 5 6 7 8 9 1 2 2 3 3 4 4 5 5 6 6 7 7 8 0 1 2 3 4 5 6 7 8 9 8 0 1 2 3 4 5 6 7 8 9
10 outer products 1 2 Original 3 4 sum Outer product 5 6 7 8 1 0 1 2 3 4 5 6 7 8 9 1 2 2 3 3 4 4 5 5 6 6 7 7 8 0 1 2 3 4 5 6 7 8 9 8 0 1 2 3 4 5 6 7 8 9
11 outer products 1 2 Original 3 4 sum Outer product 5 6 7 8 1 0 1 2 3 4 5 6 7 8 9 1 2 2 3 3 4 4 5 5 6 6 7 7 8 0 1 2 3 4 5 6 7 8 9 8 0 1 2 3 4 5 6 7 8 9
12 outer products 1 2 Original 3 4 sum Outer product 5 6 7 8 1 0 1 2 3 4 5 6 7 8 9 2 1 3 2 4 3 5 4 6 5 7 6 8 7 0 1 2 3 4 5 6 7 8 9 8 0 1 2 3 4 5 6 7 8 9
13 outer products 1 2 Original 3 4 sum Outer product 5 6 7 8 1 0 1 2 3 4 5 6 7 8 9 2 1 3 2 4 3 5 4 6 5 7 6 8 7 0 1 2 3 4 5 6 7 8 9 8 0 1 2 3 4 5 6 7 8 9
14 outer products 1 2 Original 3 4 sum Outer product 5 6 7 8 1 0 1 2 3 4 5 6 7 8 9 1 2 3 2 3 4 4 5 5 6 7 6 7 8 0 1 2 3 4 5 6 7 8 9 8 0 1 2 3 4 5 6 7 8 9
15 outer products 1 2 Original 3 4 sum Outer product 5 6 7 8 1 0 1 2 3 4 5 6 7 8 9 1 2 2 3 3 4 4 5 5 6 6 7 7 8 0 1 2 3 4 5 6 7 8 9 8 0 1 2 3 4 5 6 7 8 9
16 outer products 1 2 Original 3 4 sum Outer product 5 6 7 8 1 0 1 2 3 4 5 6 7 8 9 1 2 2 3 3 4 4 5 5 6 6 7 7 8 0 1 2 3 4 5 6 7 8 9 8 0 1 2 3 4 5 6 7 8 9
17 outer products 1 2 Original 3 4 sum Outer product 5 6 7 8 1 0 1 2 3 4 5 6 7 8 9 1 2 2 3 3 4 4 5 5 6 6 7 7 8 0 1 2 3 4 5 6 7 8 9 8 0 1 2 3 4 5 6 7 8 9
18 outer products 1 2 Original 3 4 sum Outer product 5 6 7 8 1 0 1 2 3 4 5 6 7 8 9 1 2 2 3 3 4 4 5 5 6 6 7 7 8 0 1 2 3 4 5 6 7 8 9 8 0 1 2 3 4 5 6 7 8 9
19 outer products 1 2 Original 3 4 sum Outer product 5 6 7 8 1 0 1 2 3 4 5 6 7 8 9 1 2 2 3 3 4 4 5 5 6 6 7 7 8 0 1 2 3 4 5 6 7 8 9 8 0 1 2 3 4 5 6 7 8 9
20 outer products 1 2 Original 3 4 sum Outer product 5 6 7 8 1 0 1 2 3 4 5 6 7 8 9 1 2 2 3 3 4 4 5 5 6 6 7 7 8 0 1 2 3 4 5 6 7 8 9 8 0 1 2 3 4 5 6 7 8 9
Best Outer Product Approximations of Images (which require saving the outer products)
1 outer product 1 2 Original 3 4 sum Outer product 5 6 7 8 1 0 1 2 3 4 5 6 7 8 9 1 2 2 3 3 4 4 5 5 6 6 7 7 8 0 1 2 3 4 5 6 7 8 9 8 0 1 2 3 4 5 6 7 8 9
2 outer products 1 2 Original 3 4 sum Outer product 5 6 7 8 1 0 1 2 3 4 5 6 7 8 9 1 2 2 3 3 4 4 5 5 6 6 7 7 8 0 1 2 3 4 5 6 7 8 9 8 0 1 2 3 4 5 6 7 8 9
3 outer products 1 2 Original 3 4 sum Outer product 5 6 7 8 1 0 1 2 3 4 5 6 7 8 9 1 2 2 3 3 4 4 5 5 6 6 7 7 8 0 1 2 3 4 5 6 7 8 9 8 0 1 2 3 4 5 6 7 8 9
4 outer products 1 2 Original 3 4 sum Outer product 5 6 7 8 1 0 1 2 3 4 5 6 7 8 9 1 2 2 3 3 4 4 5 5 6 6 7 7 8 0 1 2 3 4 5 6 7 8 9 8 0 1 2 3 4 5 6 7 8 9
5 outer products 1 2 Original 3 4 sum Outer product 5 6 7 8 1 0 1 2 3 4 5 6 7 8 9 1 2 2 3 3 4 4 5 5 6 6 7 7 8 0 1 2 3 4 5 6 7 8 9 8 0 1 2 3 4 5 6 7 8 9
6 outer products 1 2 Original 3 4 sum Outer product 5 6 7 8 1 0 1 2 3 4 5 6 7 8 9 1 2 2 3 3 4 4 5 5 6 6 7 7 8 0 1 2 3 4 5 6 7 8 9 8 0 1 2 3 4 5 6 7 8 9
7 outer products 1 2 Original 3 4 sum Outer product 5 6 7 8 1 0 1 2 3 4 5 6 7 8 9 1 2 2 3 3 4 4 5 5 6 6 7 7 8 0 1 2 3 4 5 6 7 8 9 8 0 1 2 3 4 5 6 7 8 9
8 outer products 1 2 Original 3 4 sum Outer product 5 6 7 8 1 0 1 2 3 4 5 6 7 8 9 1 2 2 3 3 4 4 5 5 6 6 7 7 8 0 1 2 3 4 5 6 7 8 9 8 0 1 2 3 4 5 6 7 8 9
