A Trainable Object-Tracking Method using Equivalent Retinotopical Sampling and Fisher Kernel

In this paper, two object detection techniques in computer vision are proposed. The first method is a trainable objecttracking method, based on maximum likelihood. The second method is an extension of support vector machines (SVMs). The first method is an extension of Retinotopical Sampling (RS). RS is a Gaussian filter with object detection mechanism. The concept of RS was inspired by human saccadic eye movements. However, when the object size is inferred by RS the result tends to gravitate towards zero. In this paper, Equivalent Retinotopical Sampling(ERS), which is an extension of RS, is proposed. ERS is reformulated RS by introducing an amount of information from each sampled point. The second method is an extension of discriminant function trained by SVMs for object recognition in an image. The discriminant function is formulated as an analytical function of the object position and the object size in an image. The extension is introducing ERS to SVMs. Introduction Support vector machines (SVMs) have yielded good generalization performance on wide range of problems. In the pattern recognition field, SVMs have been applied to isolated handwritten digit recognition, object recognition, speaker identification, charmed quark detection, face detection in images, and text categorization. In most of the applications, SVM’s generalization performance either matches or is significantly better than that of competing methods. In this paper, an extension of a discriminant function trained by SVM for object recognition in an image is suggested. By this extension, the discriminant function is formulated as an analytical function of the object position and the object size in an image. This extension realizes a trainable object-tracking method as gradient decent method for the discriminant function like figure 8. The extension is introducing a concept of Retinotopical Sampling (RS)(Smeraldi & Bigun 2002) to SVMs. The concept of RS was inspired by human eye mechanism(Smeraldi & Bigun 2002). Using the concept of RS, a statistical object model is defined. Then, Fisher Kernel(Jaakkola & Haussler 1999) using this statistical model is defined. This kernel function is an analytical function of the object position and Copyright c © 2003, American Association for Artificial Intelligence (www.aaai.org). All rights reserved. the object size. Then, the discriminant function becomes an analytical function of the object position and the object size. Statistical Object Model In this section, the statistical object model is described. And, a maximum likelihood based trainable object-tracking method is discussed. The concept of RS was inspired by human saccadic eye movements and enables a quick recognition of eyes, mouth in static images(Smeraldi & Bigun 2002). RS is a Gaussian filter with object detection mechanism. Tao et al. formulated object-tracking as a similar model (Tao, Sawhney, & Kumar 2002), with the object position represented by Gaussian prior distribution. This model enables estimation in a maximum a posteriori (MAP) framework using a generalized expectation-maximization (EM) algorithm. Moreover, RS has a high calculation speed. In this paper, instead of Gaussian prior distribution, RS is used. When the object size is inferred by RS the result tends to gravitate towards zero. To avoid this difficulty, Equivalent Retinotopical Sampling(ERS), which is an extension of RS, is proposed. ERS can infer the size of objects more accurately. Using ERS, a trainable static object-tracking method, with essentially only two parameters, has been formulated. Notation and Model In this paper, an image is represented as a following set. I = { (x1, y1, i1, ∂i1 ∂x ), (x2, y2, i2, ∂i2 ∂x ), ... } = {X1,X2, ...} (1) Xn = X(xn) = (xn, in, ∂in ∂x ) X(x) = (x, i(x), ∂i ∂x (x)) Here, xn = (xn, yn) denotes the coordinates of the nth pixel, in = i(xn) denotes intensity of the nth pixel. ∂in ∂x = ∂i ∂x (xn) is the intensity gradient at xn. X denotes a state of a pixel at x. Xn denotes the state of nth pixel. The designated objects (for training) are represented by the following Gaussian mixture distribution for the state of a pixel p(X|Θ). p(X|Θ) = M ∑ k=1 pkN5 (X; ςk,Σk) (2) Θ = (ς1,Σ1, ...ςM ,ΣM ) Nl (x; ς,Σ) = l dimensional normal distribution Nl (x; ς,Σ) = 1 √ (2π) |Σ| exp (− (x− ς)Σ−1 (x− ς) /2) Here, parameter Θ is determined to give the maximum likelihood for all pixels in the designated images for training. Θ is determined by the method Verbeek et al.(Verbeek, Vlassis, & Krose ) proposed. In the model Tao et al.(Tao, Sawhney, & Kumar 2002) proposed, an appearance model as p(i|n : pixel number) is used. Because, a simple Gaussion mixture model