Computational Photography

World Coordinates and Image coordinates Pinhole Camera Model $$ x = K \left[ \begin{array}{ll} R & t \end{array} \right] x $$ x: Image Coordinates: $(u, v, 1)$ K: Intrinsic Matrix $(3 \times 3)$ R: Rotation $(3 \times 3)$ t: Translation $(3 \times 1)$ X: World Coordinates: $(X, Y, Z, 1)$ Basically, from the right side to the leftside, it is transforming a point (1) from the world coordinates to camera coordinates, and then project the point (2) from camera coordinates down to the image plane. ...

Pasting Images Method 1 — Cut and paste the images. Feathering Gives a smoother transition. But that’s all… Alpha composting Output = foreground $\times$ mask + background $\times$ (1 $-$ mask). We can also use alpha compositing together with the feathering — simply bluring the mask will give us a good feathering. This method is also good for multilayer processing, which allwos the compositing to be more complicated. Method 2 — Pyramid Blending At low frequencies, blend slowly At high frequencies, blend quickly Burt and Adelson 1983 Implementation: Build Laplacian pyramids for each image Build a Gaussian pyramid of region mask Blend each level of pyramid using region mask from the same level $$ L_{12}^i=L_1^i \cdot R^i+L_2^i \cdot\left(1-R^i\right) $$ ...

Texture Synthesis and Hole-Filling How do we cut something out of an image, and fill the hole naturally? Definition Texture depicts spacially repeating patterns. Texture Synthesis Create new samples of a given texture. Many applications: virtual environments, hole-filling, texturing surfaces. The challenge: Need to model the whole spectrum: from repeated to stochastic texture. One idea: Compute statistics of input texture Generate a new texture that keeps those same statistics. But it is hard to model those probabilities distributions. ...

How do you view the world Cones: cone-shaped, less sensitive, operate in high light, color vision Rods: rod-shaped, highly sensitive, operate at night, gray-scale vision, slower to respond Observation In a clear night, there are more stars off-center. This is because you have more rods in the middle, while more cones elsewhere. How to express colors? Basically, the most intuitive expression is the RGB color space. But it is not a linear color space. We perfer expressing using CIE-XYZ color space, which makes the calculation much easier. ...

Texture Synthesis & Hole Filling Texture Texture depicts spacially repeating patterns. Texture Synthesis Create new samples of a given texture. Many applications: virtual environments, hole-filling, texturing surfaces. The challenge: Need to model the whole spectrum: from repeated to stochastic texture. One idea: Compute statistics of input texture Generate a new texture that keeps those same statistics. But it is hard to model those probabilities distributions. Another idea: ==Efros & Leung algorithm== ...