#### Quadratic denoising - House with hole (inpainting)

Image size: 256 x 256, labels: 256
Data term: squared differences, except in hole where data costs = 0 for all labels
Smoothness term: squared differences (L2 norm), lambda=5

BP-P: Pedro Felzenszwalb's BP implementation
[P. Felzenszwalb and D. Huttenlocher, Efficient belief propagation for early vision, IJCV 70(1), 2006].

HBF: Rick Szeliski's fast quadratic solver using hierarchical basis functions
[R. Szeliski, Locally
adapted hierarchical basis preconditioning, SIGGRPAH 2006].

Since this is a quadratic problem, there is a single (real-valued)
global minimum, which can be found with a quadratic solver. If ICM
was run with real-valued variables, it would converge to this
solution. For comparison, the plots contain the solution obtained
after 5 iterations of the (HBF) solver, which takes less than 0.5
seconds. The solution, when rounded to the nearest integers, has an
energy about 0.1% higher than the best integer solution found by
TRW-S.

Spreadsheet

Program log

Input image (noise contaminated), and the original image ("ground truth"):

(The black areas have data costs = 0 for all labels.)

All algorithms use the input intensities as start values.

Result images and their energies: