Covariance Tracking Algorithm on Bilateral Filtering under Lie Group Structure Yinghong Xie 1,2,a Chengdong Wu 1,b

Transcription

1 Applied Mechanics and Materials Online: ISSN: , Vols , pp doi:10.408/ 014 Trans Tech Publications, Switzerland Covariance Tracking Algorithm on Bilateral Filtering under Lie Group Structure Yinghong Xie 1,,a Chengdong Wu 1,b 1 College of Information Science and Engineering, Northeastern University, Shenyang, ,China School of Information Engineering, Shenyang University, Shenyang,110044,China ieyinghong@163.com wuchengdong@ise.neu.edu.cn Keywords: object tracking, bilateral filtering, Log-Euclidean Abstract. The eisting object tracking method using covariance modeling is hard to reach the desired tracking performance when the deformation of moving target and illumination changes are drastic, we proposed a object tracking algorithm based on bilateral filtering. Firstly, the algorithm deals the image to be tracked with bilateral filtering, and etracts the needed features of filtered image to construct covariance matri as tracking model. Secondly, under log- Euclidean Riemannian metric, we construct similarity measure for object covariance matri and model updating strategy. Etensive eperiments show that the proposed method has better adaptability for object deformation and illumination changes. Introduction At present, many algorithms[1-] model the tracking objects using covariance matrices, which adopt either Riemannian metric or Log-Euclidean metric for calculating the similarity and distance between feature matrices. For covariance matrices are not so sensitive to the variations in illumination and appearance deformation. But the tracking results are not so accurate, when there is drastic change in deformation or illumination. There are many other algorithms [3-5] introducing structure tensor to object tracking or image matching domains, for structure tensor is also insensitive to the variations of illumination and deformation. The algorithms shows that realizing image tracking or matching by building structure tensor is essentially preprocessing the positive matrices by Gauss filtering firstly, and the positive matrices are built by some features of image. However, Gaussian filter is a linear filter. It has the characteristics of isotropic, which is easy to filter out the information of weak corners. Based on Gauss filter, bilateral filter and its improved algorithm are proposed [6-7]. The bilateral filter calculates the gray value of each piel in the image by nonlinear combination of the information of grayscale and space in the image, which makes the output image maintain the edges information well, while filtering out background noise. Currently, there is little literature that applies the bilateral filtering theory to the tracking algorithm for non-rigid image with illumination variation. We apply the bilateral filtering theory to the covariance model in the process of object tracking and propose object tracking algorithm based on bilateral filtering under Lie group structure, which deals the image with bilateral filtering firstly, and gains the information of grayscale and space of the image, and then building feature covariance matrices and tracking object. And the distance and similarity between feature covariance matrices are calculated under Log-Euclidean metric. The eperiments results under various conditions show that the proposed algorithm is robust when the object to track under drastic deformation and illumination changes. All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications, (# , Pennsylvania State University, University Park, USA-18/09/16,16:7:05)

2 Applied Mechanics and Materials Vols Bilateral filtering theory Bilateral filter is an improved Gauss filter, which uses Gauss Coefficient G σ as weight value for image filtering. Let I be the original image, and I be the filtered image, and I(0,y0) denotes the gray value of piel (0,y0), while the piel (,y) denotes a point in neighborhood w of (0,y0), the formula for Gauss filter is as following: 1 ( 0) + ( y y0) G = ep( ) σ πσ σ (1) Gauss filter only considered the space information of image, however, the bilateral filter combines the gray information of image, while calculating the weight value. It can maintain the information of image edge well, through the combination of the information of grayscale and space in the image. Any N, weight value ρ δ of (,y) w is defined as: 1 ( - 0) + ( y y ( ) ( ) 0) I + I ep( 0 y y0 N = ) ep( ) ρ, δ C ρ, δ ρ δ () Where ρ and δ are the parameters to control the decaying speeds over spatial and gradient distances, and ( - ( ) ( ) 0) + ( y y0) I + I 0 y y0 Cρ, δ = ep( ) ep( ) (, y) w ρ δ (3) The formula of bilateral filtering is defined as: I ( 0, y0 ) = N, * I(, y) (, y) w ρ δ (4) Distance under Log-Euclidean metric The similarity metric of feature matrices between the model and which in the search window is typically be measured by the corresponding distance between them. And the region with the minimum distance is the tracked object. Covariance matri does not obey European vector space,so the arithmetic algorithms for Euclidean space are not suitable for the covariance matri. In order to calculate the distance between the covariance matrices, we first briefly review Riemannian geometry and the distance metric based on the Log-Euclidean [1][8]. Under the Log-Euclidean metric, SPD matri obeys Lie group G. Tangent space at the unit element N of group G constitutes Lie algebra H, which is vector space. Given SPD matrices{ X } i i= 1, in order to calculating the Log-Euclidean mean value, firstly, mapping them to vector space: {log( X ) N i } i= 1, then, 1 N computing their algebra mean: µ = log( X i ), lastly, mapping the algebra back to Lie group G: 1 N * µ = ep( log( X )). And N i= 1 i N i= 1 * µ is the Log-Euclidean mean. Under the Log-Euclidean metric, the distance between any points X and Y on Sym + (n) is defined as: d ( X, Y ) = log( Y ) log( X ) (5) Obviously, the distance formula based on Log-Euclidean metric is much easier than which is based on Riemannian metric.

3 686 Computer and Information Technology Tracking method and update strategy 4.1 Tracking method Given piel (,y), we define the following feature vector: f = (, y, I, I k y, I y ). Where (,y) is the coordinate of image I, I and I y denotes gradient value on -direction and y-direction of image I respectively. I y denotes the convolution of I and I y. For efficient tracking, we propose the following tracking method: Input the first frame of the video, determining model manually, and bilateral filtering, according to formula (4), and calculating I and I of the filtered image I. Then, calculating the feature y covariance matri C0 of the template. Let i=0, which is the number of the total frames input. Inputting net frame of the video, for each window in searching region, calculates the corresponding matrices {Ci}i=1,,...,m, m is the number of window in searching region; Calculate the distance between current model C0 and {Ci}, making use of formula (5). From step 3, we can gain a minimal distance. And the corresponding window is the tracking target. According to the following model update strategy, estimating whether the model needs to be updated. If needing, update the model; If there are frames to be tracked, turning to step. Otherwise, coming to the end. For non-grid object may eperience shape, scale and appearance deformation, in order to realize stable tracking result, model updating strategy must be built to adapt to these changes. The proposed method updates model every m frame. Let {T1,T,,Tm } denotes the covariance matrices of the tracking objects in the latest m frames, where the value of m is determined according to practical application. The Log-Euclidean mean of {T1,T,,Tm } is taken as the current tracking model. Eperiments and results To verify the validity of our proposed algorithm, we compare the tracking effect of the proposed bilateral filtering algorithm (BFT) with Gauss filtering tracking algorithm (GFT). Firstly, eperiments are preformed on rigid object sequences. Figure1and Figure are the tracking results of car on GFT and BFT, respectively. Where the size of neighborhood region is 1*1 (piel) and smooth scale is 0.4. The model update frequency is 10. The eperiments results show that both GFT and BFT algorithm can realize efficient tracking, but for each frame, compared with GFT, BFT algorithm has higher tracking accuracy. Finally, eperiments are preformed on object eperiencing illumination variation. Figure 3shows the tracking result on GFT algorithm. Figure 4 shows the tracking results on BFT, respectively. Where the size of neighborhood region is * (piel) and smooth scale is 0.8. The model update frequency is 8. IN this group of eperiments, the comparison of the two methods of tracking effect is obvious. With the increasing of the number of frames, the illumination changes largely, the tracking of GFT is almost failed. While using BFT algorithm, it can reach more stable tracking. (a)frame 1 (b) frame 80 (c) frame 160 (d)frame 04 Figure1 Rigid object tracking results on GFT algorithm

4 Applied Mechanics and Materials Vols (a) frame 1 (b) frame 80 (c) frame 160 (d)frame 04 Figure. Rigid object tracking results on BFT algorithm (a) frame 1 (b)frame 60 (c)frame 390 (d)frame 45 Figure 3. Illumination variation object tracking results on GFT algorithm (a) frame 1 (c)frame 60 (d)frame 390 (f)frame 45 Figure 4. Illumination variation object tracking results on BFT algorithm When processing of the adjacent piel gray value, Bilateral filtering not only takes into account the adjacent relation between geometric space, but also takes into account the similarity of brightness, which makes the bilateral filtering has the characteristic of anisotropic. Through the nonlinear combination of the two, the information of edges of image is well preserved while processing the noise of background. At the same time, the filtered image is insensitive for illumination variation. Conclusions Applying the bilateral filtering theory to the field of target tracking, the paper proposes the covariance image tracking algorithm based on of bilateral filtering, which processes image with bilateral filtering firstly, to gain gray and gradient information of image. Then, the covariance matrices of tracking region are built. For non-grid object may eperience shape, scale and appearance deformation, in order to achieve stable tracking result, model updating strategy is built to adapt to these changes, in this paper, the tracking model is update every some frames. The eperimental results show that the proposed method has good validity and robustness. References [1] LI G W, LIU Y P, YIN J, Target tracking with feature covariance based on an improved Lie group structure. Chinese Journal of Scientific Instrument, vol. 31, no. 1, pp , 010. [] WU Y, WANG J Q, Real-time visual tracking via incremental covariance model update on Log-Euclidean Riemannian manifold, Chinese Conference on Pattern Recognition, pp. 1-5, 009. [3] GU Q Q, ZHOU J, A similarity measure under Log-euclidean metric for stereo matching, 19th International Conference on Pattern Recognition, pp. 1-4, 008. [4] DONOSER M, KLUCKNER S, Object tracking by structure tensor analysis, 0th International Conference on Pattern Recognition, pp , 010.

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