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Detecting Regions of Interest in Dynamic Scenes with Camera Motions. OUTLINE. Introduction Related Work Detecting Regions of Interest Evaluation and Results Conclusion. Introduction.
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Detecting Regions of Interest in Dynamic Scenes with Camera Motions
OUTLINE • Introduction • Related Work • Detecting Regions of Interest • Evaluation and Results • Conclusion
Introduction • Automation of where to move the camera, which is driven by activities and events in the scene ,requires • knowledge of how the objects move in the scene • affordances related to how a camera can move to best capture these movements • ability to predict from motions of the camera and the dynamics of the scene where regions of interest are in the scene
Introduction • Our contributions in this paper are: • A method to generate a stochastic motion field that represents a global motion tendency using Gaussian process regression (GPR). • Techniques for predicting important future locations from mean and variance fields computed from the stochastic vector field. • An evaluation method for measuring the goodness of predicted important regions.
Related Work • Kim et al [6] introduced an approach to measure global • tendencies from sparse set of motion with radial basis • function (RBF) interpolation. • This approach is used to predict the regions of • importance in the scene of the soccer videos captured • from multiple-static cameras
Covariance • 共變異數(Covariance)在機率論和統計學中用於衡量兩個變量的總體誤差。 • 如果兩個變數的變化趨勢一致,也就是說如果其中一個大於自身的期望值,另外一個也大於自身的期望值,那麼兩個變數之間的共變異數就是正值。 如果兩個變數的變化趨勢相反,那麼兩個變數之間的共變異數就是負值。
Covariance • Covariance Function : • Specifies the covariance between pairs of random variables. • Covariance Matrix: • In probability theory and statistics, a covariance matrixis a matrix whose element in the i, j position is the covariance between the ith and jth elements of a random vector.
Stochastic Motion Field • Let be a set of locations of extracted motion • Each location x has a set of noisy observed velocity vector • components: • yu(the velocity component in the u-axis), • yv(the velocity component in the v-axis), • (and optionally yt for modeling the component in the time-axis). • We assume that each velocity component at the location • follows the regression model • i.e., Normal distribution.
Gaussian Process Regression • We propose using the Gaussian process regression model, where • f(x) is a zero-mean Gaussian process with covariance function • It is completely specified by a mean function • (typically assumed to be 0) • and a covariance function
Gaussian Process Regression • If we have training data • The N x N covariance matrix K is now defined as • We then define the observation vector y = • y can be shown as a zero mean Gaussian process • with a covariance matrix • The posterior density for a test point is • a normal distribution with the mean y and the • variance var(y):
Gaussian Process Regression • We can then express the mean flow as a vector field for • two dimensional motions, • and for three dimensional motions as • with a variance for each velocity component • respectively.
Detecting Locations of Convergence • Two problems. • Propagating every vector in the field has been shown to be computationally intensive. • extrapolated velocity vectors with large magnitudes can seriously bias accumulation and yield an unstable localization of converging points.
Detecting Locations of Convergence • Instead of propagating a magnitude of velocity, we transport certainty levels computed from GPR. • We transport the certainties only for the locations with high certainty levels. • Transporting the certainty level requires updating only the last destination point and is computationally more efficient.
Detecting Locations of Convergence • We first define an evaluating function • ,where is a motion field (mean field) • For example, if we denote the location of a motion as • the evaluating function iterates the locations by • ,where is computed from
Conclusion • We have shown that the prediction of the region of interests from • stochastic field using Gaussian Process Regression provides • robust results even with noisy motions from moving cameras. • In our future work, we will work on • Improving the scalability of the code-base acceleration since most computations consist of matrix-matrix products • Applying our approach for controlling actual robotic cameras in real-time.