Really neat! Mirrored objects have been a thorn in computer vision as there have been algorithms that will see the reflected objects as independent objects. Certainly this may help if it is known that a specular object is visible. They do make their job easier however by assuming that the camera and pattern are calibrated. In real life it may be easy to know the camera parameters but the "pattern" may be more difficult especially if all you have is just a single image (of course they make note of this in their conclusion).

I do wonder how far they can take their reconstruction procedure for a generic smooth surface. If the object has a lot of inner-reflections, this will be a lot harder to gain the shape from. For instance, if you have 2 flat mirrors 90 degrees from one another, the extracted shape may end up in the shape of a cross (the relections make it look like you have 4 mirrors instead of two). Anyone have any thoughts as to how they could solve this?

This paper reminds me of the literature for intrinsic and extrinsic camera calibration and the journey to making camera calibration a known thing, as it is today. This paper makes known one way to estimate generic specular surface geometry using patterns, and I'm sure transparent surfaces as a known thing are forthcoming as well, if not already. I felt this was one of those "Oh, why didn't i think of that" kind of papers.

I like the idea introduced in the beginning saying that the same math can be applied towards a situation where a LCD projector projects a calibrated pattern onto the specular surface and reflecting it onto a reference plane. I otherwise think that this algorithm is kinda weak since it requires knowing x_i (the imaged of the reflected pattern point). What if the specular surface were really small?

The monge representation and some of the symbols used in the paper are a bit confusing for me on one sitting with this paper. I'm looking forward to hearing about this on tuesday for sure.

So the basic idea is to find a bunch of tangent planes to the specular surface, based on pairs of lines that have known world location right? In their examples they use a tile pattern for the lines, but I'm wondering how they find the correct correspondences between reflected points and physical points. Seems like there could be any number of possible correspondences. I guess you could easily get around this by marking one of the tiles specially...

This paper goes into very detail about the principal reference system, which is introduced as their geometric coordinate, and the relationship of the surface parameters with the coordinate. They solved the surface parameters point by point instead of using a global estimated function. This is a very good approximation to get the real surface, since if we get more reconstructed points, we could have more information to formulate the actual surface. The problem here is that this method only works on specular surfaces. When the surfaces are not ideally reflective or the angle of reflection is distorted, the surface would not be correctly reconstructed. I'm just thinking of that can this method reconstruct the surface of a distorting mirror.

This paper is neat, but I can't see much application to the world of computer vision. The authors also said that their findings will be useful for calibration of amniview cameras with curved surfaces mirrors.
Still looking forward to the presentation tomorrow. The paper reminded me of the time in CSE250... learning about epipoles, etc.

I was curious about how important it was that they had a particular known pattern to work with. It sounds like they could do the same technique with any reflected image, as long as it had a line and a point in a known world position - so if there was a well-matched model of the scene, that should do just as well as a calibrated reference pattern, right?

I suspect that this is true, but that it just wasn't the focus of the paper to extend it in that way, but I'd be interested to hear if anyone thinks it's due to a limitation in the technique.

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