Questions about Lecture Shape from Texture

Questions about Lecture Shape from Texture

by Ruihang Jiang -
Number of replies: 2

Hello, 

I have some questions toward the lecture Shape from Texture.

1) P10-11. About tilt and slant. I am a bit confusing about the definition of tilt and slant. It seems that what I find in paper is contradict with what the professor says in the lecture. I find the definition online as following:


It seems that the tilt means the orientation of the surface normal projected into the image plane, while slant means the angle between the object plane and the image plane. However, I remember that the definitions of "tilt" and "slant" provided by the professor in class are opposite to the information mentioned above. I would like to confirm what is the correct definition of tilt and slant?

2) P15. I do not understand the equation:

 

What is the vector [x0, y0, z0] refer to in the equation? Does it mean the normal at location (x0, y0, z0)?

Thanks in advance!

In reply to Ruihang Jiang

Re: Questions about Lecture Shape from Texture

by Corentin Dumery -


Hi Ruihang,

1) Yes, these definitions do not conflict. In the lecture, it is defined with the axes of the ellipse, because this is what can be measured directly.

* By looking at the two axes of the ellipse, you get the direction of compression, which is the definition of tilt. This corresponds to the direction of the surface normal projected into the image plane.

* And from the extent of this compression, you get slant. This indeed corresponds to the angle between the object plane and the image plane.


2) This notation means the dot product between the normal, which you are trying to estimate, and the vector [x0, y0, z0], which refers to the direction of the parallel projection. Intuitively, if the first parallel projection is poorly aligned with the normal of the surface, the projected area will be very small. See the image at the end, in the slide it's a bit harder to visualize because the parallel projection has almost the same direction.


Hope that helps!

Corentin


The paraperspective projection (a side view). The reference point is... | Download Scientific Diagram