Training Effective Node Classifiers for Cascade Classification

authors: Chunhua Shen, Peng Wang, Sakrapee Paisitkriangkrai, Anton van den Hengel
Abstract

Object detection is one of the key tasks in computer vision. The cascade framework of Viola and Jones has become the de facto standard. A classifier in each node of the cascade is required to achieve extremely high detection rates, instead of low overall classification error. Although there are a few reported methods addressing this requirement in the context of object detection, there is no a principled feature selection method that explicitly takes into account this asymmetric node learning objective. We provide such a boosting algorithm in this work. It is inspired by the linear asymmetric classifier (LAC) of Wu et al. in that our boosting algorithm optimizes a similar cost function. The new totally-corrective boosting algorithm is implemented by the column generation technique in convex optimization. Experimental results on face detection suggest that our proposed boosting algorithms can improve the state-of-the-art methods in detection performance.

Main results
  • We develop new boosting-like algorithms via directly minimizing the objective function of linear asymmetric classifier, which is termed as LACBoost (and FisherBoost from Fisher LDA). Both of them can be used to select features that is optimal for achieving the node learning goal in training a cascade classifier.

  • LACBoost and FisherBoost share similarities with LPBoost in the sense that both use column generation—a technique originally proposed for large-scale linear programming (LP). Typically, the Lagrange dual problem is solved at each iteration in column generation. We instead solve the primal quadratic programming (QP) problem, which has a special structure and entropic gradient (EG) can be used to solve the problem very efficiently.

  • We apply LACBoost and FisherBoost to face detection and better performances are observed over the state-of-the-art methods. The results confirm our conjecture and show the effectiveness of LACBoost and FisherBoost.

  • We also analyze the condition that makes the validity of LAC, and show that the multi-exit cascade might be more suitable for applying LAC learning of (and our LACBoost) rather than Viola-Jones standard cascade.

Approach

Fisher LDA maximizes the between-class variance and minimizes the within- class variance. This can be written as

 max_{ {mathbf w} } frac{ {mathbf w}^T C_b {mathbf w} }{ {mathbf w}^T C_w {mathbf w} },

where C_b and C_w are the between-class and within-class scatter matrices. The problem can be equivalently reformulated as,

 min_{ {mathbf w} } {mathbf w}^T C_w {mathbf w} - theta (mu_1 - mu_2),

where mu_1 and mu_2 are the projected centers of the two classes.

The above problem can again be re-written as,

 min_{ {mathbf w, rho} } {mathbf rho}^T Q {mathbf rho} - theta {mathbf e}^T {mathbf rho} quad textrm{subject to} quad {mathbf w} geq 0, 1^T {mathbf w} = 1, rho_i = ( {mathbf Aw})_i, i = 1,cdots, m.

Since the number of constraints could be infinite (the number of constraints is equal to the number of possible weak classifiers), we solve the above problem using column generation.

Interestingly, the algorithm is almost idential to AdaBoost. The only difference is that AdaBoost minimizes the exponential loss function while FisherBoost minimizes the LDA criterion.

Pedestrian detection results (here is the orignial PDF plot)


Demonstration (real-time face detection using FisherBoost)

Demonstration (real-time pedestrian detection using FisherBoost)

References
  • Training effective node classifiers for cascade classification.
    C. Shen, P. Wang, S. Paisitkriangkrai, A. van den Hengel. International Journal of Computer Vision, 2013.

  • LACBoost and FisherBoost: optimally building cascade classifiers.
    C. Shen, P. Wang, H. Li. European Conference on Computer Vision (ECCV), 2010.

Other related work
  • Fast and robust object detection using asymmetric totally-corrective boosting.
    P. Wang, C. Shen, N. Barnes, H. Zheng.
    IEEE Transactions on Neural Networks and Learning Systems, 2012.

  • Incremental training of a detector using online sparse eigen-decomposition.
    S. Paisitkriangkrai, C. Shen, J. Zhang.
    IEEE Transactions on Image Processing, 2011.

  • Efficiently learning a detection cascade with sparse eigenvectors.
    C. Shen, S. Paisitkriangkrai, J. Zhang.
    IEEE Transactions on Image Processing, 2011.

  • Fast pedestrian detection using a cascade of boosted covariance features.
    S. Paisitkriangkrai, C. Shen, J. Zhang.
    IEEE Transactions on Circuits and Systems for Video Technology, 2008.

  • Efficiently training a better visual detector with sparse eigenvectors.
    S. Paisitkriangkrai, C. Shen, J. Zhang.
    Proc. IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2009.

Funding

C. Shen's participation in this research was supported by Australian Research Council Future Fellowship FT120100969.

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