Rows contained in other rows

I have a matrix such as A=[1 2 3;1 3 5] and I want to determine which row(s) is(are) totally contained in one (or more) single row(s) of another matrix such as B=[1 4 3 2 8;1 4 5 9;1 2 5 8 9]. In this example, row 1 of A is contained is the first row of B, but second row of A is NOT contained in a single row of B (elements 1 and 3 are in first row of B, and element 5 is in second). I know I could use ISMEMBER function for each row of A, but my matrices are too large, and a loop would take too long. Does anyone have a solution for that without a FOR-END or WHILE-END loop?

Answer 1

[Image Analyst]

How large? What are your actual, typical size dimensions for A and B? I just did a for loop with a million iterations and the for loop itself (not with ismember in it) took 0.002 seconds.

One way to do it with 2-D arrays is to use normalized cross correlation with normxcorr2(). See attached demo.

[Alberto Rocha]

A is 1365x11 and B is 26000x15. Do you know a way to do that faster? The lines of code that I wrote already took more than 4 hours.

PS: Let me explain better: I have more than 20000 matrices the same size as A, and, for each of them, I have to do what I explained above. The loop for EACH matrix like A is quick, but taking into account all of them, it takes too long.

[Image Analyst]

Did you even try normxcorr2() like I suggested? Your images aren't that big so for one pair, it shouldn't take that long. For my images, which are bigger than yours, it took 0.696949 seconds. So for 20,000 of them it would take 232 minutes, or almost 4 hours. You may be faster since your images are a lot smaller, but for 20,000 images, it will still take a long time. You may just have to live with it.

[Alberto Rocha]

I tried, but I couldn't understand what this function does. I'll keep trying. Would you have a link to a simpler example ? (the one in help file is too complicated for me). Thanks

[Image Analyst]

Does this help: https://en.wikipedia.org/wiki/Cross-correlation

https://en.wikipedia.org/wiki/Template_matching

You could use the moving SAD method - very accurate, but it might be slow.

[Alberto Rocha]

Thanks a lot. I'll try to learn how to use this function.