Pattern matching vs probabilities

Hi,

I would like to ask if it can be assumed that the result of a pattern matching technique represents a probability density function.

To be a little bit more specific let's assume that I have a function f(x,y) with x,y having a specific value, which is being compared with the same function f(x,y) for all possible x,y. The resulting function is let's say g(x,y). Is it possible to assume that the g(x,y) represents a probability density function so that for a specific x,y it gives me the probability that x=x0 and y=y0?

Thanks in advance

Answer 1

[Image Analyst]

No, I would not say that. For example normalized cross correlation, like the demo I've attached, is a kind of pattern recognition. See the image below.

But I wouldn't say that the image in the lower left is a kind of PDF.

[Image Analyst]

Regarding your answer. You can see from the picture that the garlic looks a lot like the onion but the response was not all that high. In fact the similarity of the garlic is about the same as other vegetables even ones of different colors. Maybe that's what is wanted, but maybe not. There is a field called CBIR (Content Based Image Retrieval) that can be used to identify such similar-but-not-exact regions. For example it can find all images that have babies or buildings in them. That's out of my area of expertise. Maybe you might want to look into cbir.

For the case you gave in your answer, I guess you could call the distribution of reported locations a PDF if you want to.

Answer 2

[Symeon Mattes]

Image Analyst thank you very much for your response.

I'll try to put it in a different way based on the example you've gave me. Imagine you have one more onion somewhere in the picture. However instead of having so high correlation as in the first onion the correlation is less high. Let's say that in the first onion is 1 (high similarity) and in the second 0.8 (low similarity) or even lower. The reason for that might be because the 2nd onion is a little bit more blurred, or a little bit changed. However recognition should give me both onions as possible candidate.

How would you describe something like that? I understand from your picture that this is not a known pdf, but how could it be described mathematically or in another way?

Furthermore, imagine you're doing a hypothetical visual test in order to check the performance of humans in different things, e.g. in parallax effect, or Farsightedness. If the exact location of the 1st onion is lets say (100px,400px) and the 2nd (300px, 400px) (top,left) in an image of 600x600px, then the person might say that the object is at (95px, 380px) or somewhere around the location of the 1st onion, but also because the person might have some visual problems, he might say somewhere around the 2nd onion, e.g. (310px,410px). By doing that experiment you will get many points around the location of the 1st onion and some others around 2nd onion which is similar. Collecting all these points for sure you have a pdf, which is bimodal and I would say not a known pdf.

So having said something like that for the experiment you have a pdf, but in the first case you have a similarity metric which describe the same thing. So if the similarity metric is not a pdf what's that?

Although the above might be somehow hypothetical, it's quite true in audio. Instead of having visual objects you have an audio object coming from a specific location and the 1st onion is the true location of the sound the 2nd onion is a location that the sound is not coming from but it might be perceived as if it was.

Hope it makes sense.

Thanks anyway for your response.