Incremental Oblique Random Forest

Robust Visual Tracking Using Oblique Random Forests
Le Zhang, Jagannadan Varadarajan, Ponnuthurai Nagaratnam Suganthan,
Narendra Ahuja and Pierre Moulin


Random forest has emerged as a powerful classification technique with promising results in various vision tasks including image classification, pose estimation and object detection. However, current techniques have shown little improvements in visual tracking as they mostly rely on piece wise orthogonal hyperplanes to create decision nodes and lack a robust incremental learning mechanism that is much needed for online tracking.  In this paper, we propose a discriminative tracker based on a novel incremental oblique random forest. Unlike conventional orthogonal decision trees that use a single feature and heuristic measures to obtain a split at each node, we propose to use a more powerful proximal SVM to obtain oblique hyperplanes to capture the geometric structure of the data better. The resulting decision surface is not restricted to be axis aligned, and hence has the ability to represent and classify the input data better. Furthermore, in order to generalize to online tracking scenarios, we derive incremental update steps that enable the hyperplanes in each node to be updated recursively, efficiently and in a closed-form fashion. We demonstrate the effectiveness of our method using two large scale benchmark datasets (OTB-51 and OTB-100) and show that our method gives competitive results on several challenging cases by relying on simple  HOG features as well as in combination with more sophisticated deep neural network based models.
Figure 1. A toy example of classification boundary generated by orthogonal and oblique decision trees. Orthogonal RaF selects a single feature at each node to conduct a split. This results in an piece-wise axis orthogonal hyperplane (in green color). Oblique RaF, on the other hand, uses more than one feature at each nodeand thus results in an oblique hyperplane (in red color) that classifies the data better.

Our proposed Oblique Random Forest can better capture the  geometric structure of the data and result in much smoother decision boundary.

Figure 2. Decision boundary of the spirals dataset learned by different methods. (a) Ground truth, decision boundary from a (b) single decision tree, (c) Orthogonal RaF, (d) Oblique RaF.

We propose an efficient approach to incrementally learn oblique random forest and demonstrate its feasibility in visual tracking with HOG feature on OTB51 tracking benchmark.

Figure 3. Comparison of the simple Obli-RaF tracker to other methods on OTB-51. Precision plots obtained with a threshold of 20 pixels are shown on the left. Success plots measured using AUC values are shown on the right. We see that our simple Obli-RaF method outperforms all existing methods. 

Figure 4. The histogram of the average tree depth of the forest. The Proposed method is much shallower than orthogonal Random Forest. 

We also combine Random Forest with a ConvNet to further boost its performance.

Figure 4.  Performance of the hybrid tracker on OTB51.

Figure 5.  Performance of the hybrid tracker on OTB100.


Kindly cite our work if it helps your research:

  title={Robust visual tracking using oblique random forests},
  author={Zhang, Le and Varadarajan, Jagannadan and Suganthan, Ponnuthurai Nagaratnam and Ahuja, Narendra and Moulin, Pierre},
  booktitle={IEEE International Conference on Computer Vision and Pattern Recognition. IEEE},