A novel algebraic method for kernel-based object tracking

Highlights

• We introduced an algebraic method for kernel based object tracking.

• A new method for background removing is proposed by dividing the candidate area in two parts.

• The effect of noise and background clutter is reduced by segmentation of object.

• We propose radial scanning of histogram for solving the problem of changes in scale and shape.

Abstract

In the present paper, a new tracking method based on kernel tracking is proposed. The proposed method employs a novel algebraic algorithm to get the kernel movement. In contrast to the mean-shift method which uses a weighted kernel to reduce the effect of the background, the algebraic algorithm of the proposed method allows dividing the candidate area into two parts in order to identify the object and background regions. To detect the object and background regions, we propose measuring the similarity of weighted histogram for each part. The experiments show the superiority of the proposed method for the removal of the background. The effect of noise and background clutter is reduced by segmentation of the object which produces the narrow histogram. In conclusion, the ability of the proposed method for tracking in crowded and cluttered scenes is demonstrated.

Introduction

Due to the simplicity and efficiency of mean-shift tracking, it is a common method for kernel object tracking. In the original mean-shift tracking, a symmetric weighted histogram kernel and a geometric shape are used for modeling the target [1]. The motion of the kernel from one video frame to the next is computed by iteratively estimating the color centeriod for reach to the best similarity between the candidate and the target models. Including the spatial information, predictive component, radial basis function network and multiple reference histograms to the mean-shift tracking are proposed for better performance [2], [3], [4], [5], [6]. Many efforts are made to solve the original mean-shift drawbacks related to its scale and orientation changes, symmetric kernel and isotropic shape. Because of change in object size, the fixed scale model is not appropriate for tracking. Using three different kernel bandwidths (scales) for algorithm and selecting the one which maximizes the appearance similarity is proposed by Comaniciu [7]. This method, named as ±10% method, is computationally expensive due to the brute-force nature. Using difference of Gaussian mean-shift kernel in scale to include scale as additional dimension has been proposed in [8]. This method performs well; but, it needs convolving the image with a set of Gaussian filters at various scales which is a computationally complex task. Using asymmetric kernel and considering the scale and orientation as additional dimensions to the spatial image in which the tracking algorithm is solved simultaneously in all coordinates can be seen in recent works [9], [10], [11], [12]. Paying attention to the moment features of the weight image of the target candidate region and the bhattachryya coefficients and also using the principal components of the variance matrix of the spatial-color distribution are proposed to solve the scale and orientation problems [13], [14]. Another limitation is related to the geometric region and its asymmetric kernel. In cases where the object does not have an isotropic shape, the symmetric kernel which is isotropic in shape cannot describe the object properly, and it can be contain the considerable background information. Using a Shape-adapted asymmetric kernel constructed based on the mask of the detected object can improve the tracking result [15], [16], [17]. Despite various efforts to improve the mean-shift algorithm, there is an intrinsic problem in all mean-shift methods. The problem is related to the iterative process of mean-shift tracker for finding the best similarity between the candidate and the target model. In the first iteration, the candidate and model regions are considerably inconsistent. Thus, the influence of background information can be significant, especially in objects which are undergoing rapid motions or are spatially adjacent objects. Of course, this is the problem of every tracker which finds the target by searching for the best match such as contour [18], [19], [20], [21] and template tracking [22], [23].

In this paper, we propose a new method for tracking the target area in which the displacement of the kernel is obtained using the previous object region as a starting point in the current frame. In contrast with the mean-shift tracking which finds the kernel location using an iterative technique to achieve the best histogram matching, the proposed method offers algebraic equations for the kernel displacement. Expressing the displacement kernel using algebraic equations is much more effective than the mean-shift way to remove the background. In order to eliminate the effect of background, we have defined two types of disconnected and connected background. Defining disconnected background allows the algorithm to consider the object and background areas as individual objects. We acquire the corresponding target area for each of these objects using tracking equations. The object and the background can be identified with the weighted histogram, which is defined as a metric to measure the similarity. The background which is connected to the object can be eliminated using the segmentation of object and also modified histogram. The experiments results depict the validity of the proposed tracking equations and its advantages over the mean-shift method to remove the effect of the background.

The paper is organized as follows. In Section 2, the target model is presented. Section 3 describes the proposed method for calculating the displacement of kernel and removing the background effect. Experimental results and conclusion are given in Sections 4 Results and discussion, 5 Conclusion.