Fig 1.
The original LBP and MB-LBP with a scale parameter s.
Fig 2.
Nine uniform LBP patterns.
Fig 3.
Randomized trees including a root node, internal nodes, and leaf nodes and edges.
The random forest consists of the trees.
Fig 4.
The processing pipeline of the head pose estimation in the proposed technique.
Fig 5.
MB-LBP based feature set including the size of the block s, the center position k, and the scale of the Gaussian image pyramid g, and the upper and the lower thresholds, which are used for establishing a split function in each node of a randomized tree.
Fig 6.
Construction of a randomized tree.
Fig 7.
Estimation accuracies of the proposed technique with respect to the number of the classes, as compared to the conventional algorithms.
Proposed (NL) refers to the technique where the uniform MB-LBP is extracted from non-overlapped block patches in the proposed technique while Proposed (OL) uses overlapped block patches in the generation. The error bars represent 95% binomial confidence intervals.
Fig 8.
Estimation accuracies of the proposed technique with respect to the number of the classes, as compared to the conventional algorithms when the facial images have occlusions.
The error bars represent 95% binomial confidence intervals.
Fig 9.
Confusion matrices of “Proposed (NL)” in 7 class case.
Fig 10.
Confusion matrices of “Proposed (OL)” in 7 class case.
Fig 11.
Confusion matrices of “Proposed (NL)” in 9 class case.
Fig 12.
Confusion matrices of “Proposed (OL)” in 9 class case.
Table 1.
Proportions of MB-LBP block sizes, selected as the best feature at each node in a random forest.
Fig 13.
Performance changes with respect to the number of the MB-LBP feature planes.
s refers to the size of the MB-LBP block. The error bars represent 95% binomial confidence intervals.
Fig 14.
Performance changes with respect to the number of the maximum depth (MD) of the random tree.
The error bars represent 95% binomial confidence intervals.
Fig 15.
Performance changes with respect to the number of the minimum samples (MS) in the tree.
The error bars represent 95% binomial confidence intervals.
Fig 16.
Performance changes with respect to the number of the forest size (FS).
The error bars represent 95% binomial confidence intervals.
Table 2.
The classification errors (CE), the mean absolute errors (MAE) in degree of the head pose estimation algorithms using different features and classifiers in intra-bases experiments, and the standard deviation (STD) of the degrees.
Fig 17.
Cumulative head pose estimation error (%) of test images with respect to a degree.
Fig 18.
Performance changes with respect to the number of the MB-LBP feature in 3-pose case, using different features selectors and classifiers.
Fig 19.
Performance changes with respect to the number of the MB-LBP feature in 7-pose case, using different features selectors and classifiers.
Fig 20.
Cumulative head pose estimation error (%) of test images with respect to a degree in inter-db experiments.
Table 3.
The classification errors (CE)%, the mean absolute errors (MAE) in degree of the proposed technique, and the standard deviation (STD) of the degrees in inter-bases experiments.
Table 4.
The classification errors (CE)%, the mean absolute errors (MAE) in degree of the proposed technique, and the standard deviation (STD) of the degrees in mixed inter-bases experiments.