<p>For a naive feature detection algorithm, I'll divide the image in 8x8 grayscale tiles. I want to be able to represent the 64 pixels of each tile in a lower dimensional form. Each tile should be an approximation of a linear combination of less than 64 tiles. What is the name for what I am trying to do? Could you point out some references to this?<br>
I hope this is the appropriate site to ask this question.
Thanks</p>

CC BY-SA 3.0
2011-10-07T15:54:52.063Z
By the way, why was this off-topic?
Jukka Suomela
CC BY-SA 3.0
2011-10-07T16:34:14.997Z
on second reading, I'm not entirely sure myself. I'm guessing the OP wants some kind of dimensionality reduction method ?
Suresh Venkat
CC BY-SA 3.0
2011-10-07T18:00:31.070Z
@Suresh: Why was my close vote removed?  And why cannot I vote to close any longer?  I fail to see any question in theoretical computer science in this post.
Tsuyoshi Ito
CC BY-SA 3.0
2011-10-07T18:02:24.087Z
I asked here, http://mathoverflow.net/questions/77465/hyperplane-least-square-through-points , Gottfried suggested PCA, I think it will help me. Any related ideas to this? Thanks
titus
CC BY-SA 3.0
2011-10-07T18:29:36.223Z
@TsuyoshiIto: I think there might be some *theoretical* reasons why, e.g., PCA is "better" than ICA or vice versa in this kind of application (for some definition of "better", subject to some assumptions about the inputs).
Jukka Suomela
CC BY-SA 3.0
2011-10-08T04:12:14.713Z
I think what happened is that when I reopened, your close vote was wiped out.
Suresh Venkat
CC BY-SA 3.0
2011-10-08T12:18:07.837Z
For the record, I am still not convinced that this question is in scope, although I cannot vote to close it because of a bug in the system.
Tsuyoshi Ito
CC BY-SA 3.0
2011-10-10T14:16:18.330Z
Replace "8x8" and "64" with "kxk" and "k^2", and it becomes an interesting theoretical question (about dimensionality reduction).  So the question *as written* may not be within scope, but it has small edit distance to a question that is in scope.
Jeffε
CC BY-SA 3.0
2011-10-10T21:41:48.710Z
Maybe this question should be closed because it is too vague, not because it is off-topic. Are you trying to a take $64 \times n$ matrix, and approximate it by a matrix of relatively low rank? Is *principal component analysis* the term you're looking for? Or did I totally misunderstand your question?
Peter Shor 
CC BY-SA 3.0
2011-10-11T02:50:44.383Z
@Peter Shor: Yes that is what I want to do, but also find a basis for the columns in the approximated matrix and the coefficients for representing each of those columns in the basis. From what I have read so far PCA finds the basis. By projecting the initial columns on the basis I think I can find the coefficients.
titus
CC BY-SA 3.0
2011-10-11T15:49:56.803Z
Projection should indeed find the coefficients.
Peter Shor 
<cv.computer-vision>
represent tiles in lower dimensionality
titus
# represent tiles in lower dimensionality

(Asked by: username_0 on 2011-10-07)

For a naive feature detection algorithm, I'll divide the image in 8x8 grayscale tiles. I want to be able to represent the 64 pixels of each tile in a lower dimensional form. Each tile should be an approximation of a linear combination of less than 64 tiles. What is the name for what I am trying to do? Could you point out some references to this?  
I hope this is the appropriate site to ask this question.
Thanks

**Tags:** cv.computer-vision

> **Comments:**
> **username_1**: By the way, why was this off-topic?  
> **username_2**: on second reading, I'm not entirely sure myself. I'm guessing the OP wants some kind of dimensionality reduction method ?  
> **username_3**: @Suresh: Why was my close vote removed?  And why cannot I vote to close any longer?  I fail to see any question in theoretical computer science in this post.  
> **username_0**: I asked here, http://mathoverflow.net/questions/77465/hyperplane-least-square-through-points , Gottfried suggested PCA, I think it will help me. Any related ideas to this? Thanks  
> **username_1**: @TsuyoshiIto: I think there might be some *theoretical* reasons why, e.g., PCA is "better" than ICA or vice versa in this kind of application (for some definition of "better", subject to some assumptions about the inputs).  
> **username_2**: I think what happened is that when I reopened, your close vote was wiped out.  
> **username_3**: For the record, I am still not convinced that this question is in scope, although I cannot vote to close it because of a bug in the system.  
> **username_4**: Replace "8x8" and "64" with "kxk" and "k^2", and it becomes an interesting theoretical question (about dimensionality reduction).  So the question *as written* may not be within scope, but it has small edit distance to a question that is in scope.  
> **username_5**: Maybe this question should be closed because it is too vague, not because it is off-topic. Are you trying to a take $64 \times n$ matrix, and approximate it by a matrix of relatively low rank? Is *principal component analysis* the term you're looking for? Or did I totally misunderstand your question?  
> **username_0**: @Peter Shor: Yes that is what I want to do, but also find a basis for the columns in the approximated matrix and the coefficients for representing each of those columns in the basis. From what I have read so far PCA finds the basis. By projecting the initial columns on the basis I think I can find the coefficients.  
> **username_5**: Projection should indeed find the coefficients.  

---

## 0 answers

