Learning Support Correlation Filters for Visual Tracking

For visual tracking methods based on kernel support vector machines (SVMs), data sampling is usually adopted to reduce the computational cost in training. In addition, budgeting of support vectors is required for computational efficiency. Instead of sampling and budgeting, recently the circulant matrix formed by dense sampling of translated image patches has been utilized in kernel correlation filters for fast tracking. In this paper, we derive an equivalent formulation of a SVM model with the circulant matrix expression and present an efficient alternating optimization method for visual tracking. We incorporate the discrete Fourier transform with the proposed alternating optimization process, and pose the tracking problem as an iterative learning of support correlation filters (SCFs). In the fully-supervision setting, our SCF can find the globally optimal solution with real-time performance. For a given circulant data matrix with <inline-formula><tex-math notation="LaTeX">$n^2$</tex-math><alternatives><mml:math><mml:msup><mml:mi>n</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:math><inline-graphic xlink:href="yang-ieq1-2829180.gif"/></alternatives></inline-formula> samples of <inline-formula><tex-math notation="LaTeX">$n \times n$</tex-math><alternatives><mml:math><mml:mrow><mml:mi>n</mml:mi><mml:mo>×</mml:mo><mml:mi>n</mml:mi></mml:mrow></mml:math><inline-graphic xlink:href="yang-ieq2-2829180.gif"/></alternatives></inline-formula> pixels, the computational complexity of the proposed algorithm is <inline-formula><tex-math notation="LaTeX">$O(n^2\; \log n)$</tex-math><alternatives><mml:math><mml:mrow><mml:mi>O</mml:mi><mml:mo>(</mml:mo><mml:msup><mml:mi>n</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mspace width="0.277778em"/><mml:mo form="prefix">log</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href="yang-ieq3-2829180.gif"/></alternatives></inline-formula> whereas that of the standard SVM-based approaches is at least <inline-formula><tex-math notation="LaTeX">$O(n^4)$</tex-math><alternatives><mml:math><mml:mrow><mml:mi>O</mml:mi><mml:mo>(</mml:mo><mml:msup><mml:mi>n</mml:mi><mml:mn>4</mml:mn></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href="yang-ieq4-2829180.gif"/></alternatives></inline-formula>. In addition, we extend the SCF-based tracking algorithm with multi-channel features, kernel functions, and scale-adaptive approaches to further improve the tracking performance. Experimental results on a large benchmark dataset show that the proposed SCF-based algorithms perform favorably against the state-of-the-art tracking methods in terms of accuracy and speed.