Separation of Semireflective Layers

Abstract
The situation in which when looking out of a window we see both the view outside and the semireflection of the objects inside is common. Developing techniques that would enable us to separate this mixture to its components is important when, for example, the semireflected redundant scene is captured with an optical device such as camera.
This project suggests two methods for separation of mixtures to their semireflected layer and their original one.

The problem
A transparent surface is localized between a camera and the view it should capture. In addition, a polarizer is attached in front of the camera. Two pictures are taken for two different angles of the polarizer.
The surface’s index of refraction and its orientation in space are unknown. These two mentioned characteristics determine the reflectivity and the transmissivity for each polarization component. Two images are received in this process, each one is a linear mixture of independent sources – the reflected image and the trasmitted one.
Finally, as a result of the process, noise might also be added to the two raw images.
Separation of the described mixtures to their components can be considered as “Blind Source Separation” – BSS, and the problem can be solved by implementing BSS methods.

The solution
Two BSS methods are implemented for solving the problem. Both of them suggest geometric techniques for estimating the contribution of each source component in each mixture.
the methods would be:
1) Angular histogram
2) Clustering

An important preprocessing stage for both methods is performed in order to achieve sparse representation of the mixtures.

Applying each of the two methods requires vectoric representation of the preprocessed mixtures, and a scatter plot of the vectors to project to hyper sphere.

From this point each method implements a different algorithm:
1) Angular histogram – each one of the projected points on the sphere represents an angle. Building an angular histogram enables us to find the two most likely angles which correspond with the contribution of each source component in each mixture.
2) Clustering – projection on half sphere creates clusters of points. The angles in which are located the centers of mass of two clusters, correspond with the contribution of each source component in each mixture.

Eventually, a comparison with an existing method should be performed by implementing ICA method for BSS.

ICA – Independent Component Analysis.This is a statistical and computational technique for separating N statistically independent and linearly mixed sources, without further knowledge about the mixing hidden factors.
The Bell-Sejnowski Infomax algorithm, based on neural network, is a method that can approximate the solution to the ICA problem in many cases.

Implementing the suggested solution requires mixtures to be separated.
The mixtuturs that are being obtained in this project are created with an optical simulator.

Tools
The project was programmed in Matlab 6, on PC platform.

Results

Figure 1 – An example for separation of semireflective layers. The 2 mixtures are given for polarizer angles – 0 deg , 90 deg . The separation results yield 2 well reconstructed images

Conclusions
Examination of the suggested methods showd that in many cases both of them are efficient and suitable for dealing with the presented BSS problem.
I also learned the high importance of the sparse representation. A successful preprocessing stage yields good separation results.
Influence of noise has also been detected. The level of performance, for all the three mentioned algorithms, decreases when the level of noise increases.
Without noise, using angular histogram gives, in most cases, better results, in terms of SNR, than using clustering.
Noise affects the most on the results of separation with the angular histogram. At noise level of 30 dB, clustering is already the better algorithm. At noise level of 20 dB the angular histogram method, in most cases, can’t separate the mixtures successfully while clustering can still yield satisfactory results.
Comparison to separation with the ICA method leads to the conclusion that the two examined methods are considerable tools for BSS. The ICA method sometimes yields results that are better than those of the two other methods. In other cases the results where bad while the two other methods provided a very accurate separation.

Acknowledgment
I would like to thank my project supervisors, Alex Bronstein, Michael Bronstein and Dr. Michael Zibulevsky, for their guidance.
I am also grateful to the Ollendorff Minerva Center Fund for supporting this project.