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# Mathematical model of autofocus function in the human eye

Scientists still have not known how the autofocus functions in the human eye and other animals. We know that it functions extremely fast and accurately. When the brain gets blurred image it instantly measures the distance to the object and changes the focal length, the curvature of crystalline lens to get a clear image on the retina.

There is a question, how does a focusing mechanism function in the human visual system? Now, the biologists have come close to answering this question. Experts from the Center of Perceptual Systems, University of Texas at Austin (USA) have developed a self-learning statistical algorithm, which eventually learned quickly and accurately to calculate the defocusing degree of any fragment of the blurred image.

The algorithm is a computer model of the biological system of human vision, which was "tested" with 400 fragments of digital photographs of natural scenes in the size of 128x128 pixels. First, the data was collected, in other words as the frequency-contrast characteristic looks like, namely MTF curves for the images of various degrees of defocusing (in diopters, ΔD). It has been known that the blurriness of image directly affects on this characteristic.

After that, the algorithm was run through the pictures that based on the method of accuracy maximization analysis (AMA, accuracy maximization analysis, AMA code for Matlab) in increments of 0.25 diopters. The optimal filters were obtained that at most approximate a graph of MTF of blurred image to the ideal.

In order to test the researchers took a new data set (400 more images), which was run through the filters. If each filter is used for the same object, then we can compare their results and see which filter is best, namely what is a degree of the image blurriness. The graph shows the results of the algorithm to determine the degree of defocusing in diopters with a probability of 68% (thick vertical strips) and 90% (thin strips).

The researchers decided to add a model of monochromatic aberrations of the human eye - essentially unavoidable errors of optical systems in order to improve the accuracy of the system. The eye of every person does not function perfectly; it has some inaccuracies concerning the focus and astigmatism. These inaccuracies (the card of aberrations) can be measured on special ophthalmic equipment.

The scientists have changed the working algorithm of the filters taking into account the card of aberrations of the human eye and the corresponding frequency-contrast characteristics. Ironically, the accuracy focus of blurred images has increased significantly. It turned out that to determine the focus of the image in the human eye plays important role astigmatism; it is one of aberration types in the human eye. The image dot that is outside the axis and it is formed by a narrow beam of light, which consists of two straight pieces that are perpendicular to one another at different distances from the plane of aberration-free focus (Gauss Plane).

Now, it became clear, why many patients lose temporarily the ability to see sharp images, when they undergo the treatment of astigmatism.

New filters could recognize the image blurriness with much greater accuracy after taking into account the chromatic aberrations and diffraction in the human eye.

Published work may form the basis of fundamentally new systems of autofocus, which will be used in the image processing programs for filter sharpening, as well as in digital cameras and camcorders. Here, they can replace the multipoint AF, which works less efficiently.

Optimal defocus estimation in individual natural images. Johannes Burge, Wilson S.Geisler. Proceedings of the National Academy of Sciences, October 4th, 2011, vol. 108 no. 40, doi: 10.1073/pnas.1108491108, PDF
Skull 16 december 2011, 12:54
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