For each one of the subspaces can be obtained a complementary subspace Wj with a basis given by the dilation and transla
E NHANCING EYE MOVEMENTS DATA FROM EYE - TRACKING SYSTEMS : PRELIMINARY RESULTS L. Dimieri† , L. R. Castro†‡ and O. E. Agamennoni†∗ †
Instituto de Investigaciones en Ingenier´ıa El´ectrica (IIIE), Universidad Nacional del Sur (UNS)-CONICET, Bah´ıa Blanca, Argentina,
[email protected] ‡ Depto. de Matemtica, Universidad Nacional del Sur (UNS), Bah´ıa Blanca, Argentina, ∗ Depto. de Ing. El´ectrica y de Computadoras, Universidad Nacional del Sur (UNS), Bah´ıa Blanca, Argentina,
Abstract: During the last two decades, many eye-tracking systems have emerged with different methods and performance features. The most comfortable and cheaper ones are generally those having the poorest measuring characteristics, reaching to maximum framerates below 250fps. The best systems, in terms of accuracy and high framerates, are very expensive apparatus and very often complicated to assembly. Also, they tend to work in fixed setups and it is hard to perform outdoor experiments, like driving a real car or walking long distances. The main advantages of modern remote eye-tracking systems are that, in general, they allow small head movements and the subject has not wear any kind of hardware. This feature is especially important when working with children or people with some kind of physical impairment. These modern eye-trackers are independent, small and one-piece hardware ready to plug into a mobile computer or laptop, allowing for doing any variety of experiments. In this work, we propose a wavelets based method for upsampling eye movements measures of very low framerates, that allows to improve and reconstruct the original signal by obtaining a signal with around five times the original measuring framerate. Although a more complete analysis and tests are required, results obtained with the method presented here are encouraging.
Keywords: eye movements, eye-tracking, wavelets 2000 AMS Subject Classification: 21A54 - 55P54
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I NTRODUCTION
Eye movements have been largely studied in the last century and more intensively in the last twenty years with the discovery of a strong relationship of these movements with some neuropathologies and the possibility of early detections and diagnosis of cognitive impairment (e.g. Alzheimer’s disease [1][2]). The advances in the development of better devices for measuring eye movements has necessarily become a priority and many techniques appeared through time, although some of them were very invasive methods and required the observer’s head to be still and fixed. Fortunately, advances in technology have been really fast and have allowed eye-tracking via digital video analysis of eye movements, opening a new door for a broad variety of detection techniques. The best commercial eye-tracking equipments have then became popular, yet very expensive. In order to have high performance and good accuracy, the video camera used in these devices need to be of large framerate and the setup of the system requires very particular software specification and architecture. With the development of technology today it is possible to have high-quality cameras and fast enough computers to process video in real time for performing eye-tracking. Even small and dedicated hardware have been developed to achieve these tasks (e.g. Tobii eyeX, SMI Eye Tracking). These modern devices are good enough to make reliable measurements, but still are expensive products. With the posibility of accesing to open source software (e.g. PyGaze, OpenCV) it is possible to build home and cheap eye-tracking systems and the results can be considered acceptable, but they are poorly accurate for some precise applications. Although it is possible to have good spatial accuracy (say 1◦ ) with commercial webcams, the framerate is only 30fps or 60fps in best case. For many cases, these measurements are enough but to study in more detail the fine eye dynamics and its information stored, we require more accurate and dense data. It is hard to get today, faster home cameras that can perform live capure at a higher framerate, that’s why we are focoused on solving the problem by looking the data from the analysis side. Also, with the development of high quality video code and decode for transmition, it has been studied the problem of restoration of images by reconstructing its coded lost information, with excellent results. From the literature, one can observe that the major applications of wavelets as a tool for data restoration is in the field of 2D images. So, taking into account methods for fast image restoration based on wavelet analysis
(for example, [3]), in this work we propose considering that a signal measured with a low and non-constant samplerate can be seen as an image with missing blocks and regions. Using a similar technique but for 1D signals, we propose to upsample an eye-tracking dataset obtained by a poor performance device with low framerate data capture, in order to gain resolution by reconstructing it with more accuracy.
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T HEORETICAL F RAMEWORK : WAVELETS
Wavelets are very well known functions that gave origin to Continuous and Discrete Wavelet Transform and were defined indepently by mathematicians and physicists. Its theory has been developed during the last century and they have been implemented in a great number of applications, including signal and image processing and analysis. Briefly, wavelets can be thought as basis functions used to represent signals. They have the special feature of being well localized in both spatial and frequency domains. This property can be thought as having a finite and adaptive sliding window in time domain that determines a sliding window in the frequency domain, which allows to select only a frequency band. Another important feature of discrete wavelets is the multiresolution analysis. Basically, this analysis can be thought as an infinite sets of nested subspaces {Vj }1≤j
