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A Theory of Specular Surface Geometry

11:43 PM ET (US)
Hello, nice site :)
09:45 AM ET (US)
Hi! Nice site!
John Doe
07:48 AM ET (US)
Deleted by topic administrator 07-21-2006 08:58 AM
Ted EriksonPerson was signed in when posted
01:30 PM ET (US)
What are you doing here!! Goodbye.
Neil Alldrin
06:53 AM ET (US)
Just a quick comment, it seems like the coordinate system they use (at least the 2D case) is the same as used in the Hough transform for finding lines in images. How and where they are used is definitely different though.
03:20 AM ET (US)
Hi Mike,
I think this is eminently doable in real time. The tracking used in the paper is pretty basic and can be improved upon by using something like the Kanade-Lucas-Tomasi tracker, beyond that there is some straight forward smoothing of data using quadratic polynomial fitting and detection of spread using pca for example.

Mike McCracken
03:11 AM ET (US)
I thought the feature classification part of this paper was really interesting. My question is that it seems like although they say that it would be a good preprocessing step for structure from motion and related techniques, it seems like they'd need a sequence of images to get their image trajectory for the classification - is it possible to do something like this in real time?
Matt Clothier
12:11 AM ET (US)
Thanks for the information Sameer. Looking forward to the presentation tomorrow!
11:24 PM ET (US)
While the paper talks about the Legendre Transform, the actual mathematical object that they end up using is a support function transform, which though similar is not exactly what Legendre had in mind.

While this paper was a substantial breakthrough, it is still nowhere near the solution to the problem of recovering the surface of a mirror.

In the years since the publication of this paper, there have been two more pieces of significant work on recovering specular geometry.

The first is the work by Silvio Savarese which we discussed earlier in the class. Besides this there has been work on using rotating an object under a light bean and observing the highlights so created (the exact reference escapes me at the moment, its cited in silvio's papers).
Matt Clothier
09:52 PM ET (US)
Cool! I'm reminded of ray tracing specular spheres in a Cornell Box. ;) Specular surfaces has always been a gotcha in computer vision applications, especially in regards to tracking and recovering 3D surfaces. Initially reading the paper, one of the coolest things was using the Legendre transform to represent a curve (I had never heard of it before now). As the paper suggests this greatly simplifies the description of the geometry of the specular reflection in the 2D case.

Unfortunately, the 3D case is not as trivial. They end up introducing a new, "moving" coordinate system attached to reflected rays. Unfortunately, I have a hard time visualizing what this coordinate system looks like (anyone willing to help explain this?). The coordinate system aside though, they are able to recover an large amount of information such as image trajectories and caustic curves. Pretty neat!

I know that using computer renders is a "sin" in computer vision papers, but wouldn't the use of a ray tracer help various aspects of their research? Even though the ray tracer would produce a perfectly specular object (which doesn't exist in real life), I would think that they could still produce some meaningful results since they wouldn't have to deal with as many unknowns. This was just a though that I had.

These results are impressive considering how difficult this problem is. I would be interested to see what research has been done since 1996. Does anyone know if there have been papers addressing the issue of moving specular objects?

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