Application of the Cascade and Results

Several experiments have been done to evaluate the performance of the proposed approach with two different kinds of images, namely, reflectance and depth images. Both types are acquired by the AIS 3D laser range finder and are light invariant. Figure 1 shows two examples of the training data set. Around 200 representation of an ``office chair'' were taken in addition to a wide variety of negative examples without any chair, e.g., the scene given in Figure 1. The detection starts with a classifier of size $20 \times 40$ pixels. The image is searched from top left to bottom right by applications of the cascade. To detect objects on larger scales, the detector is rescaled. An advantage of the Haar-like features is that they are easily scalable. Each feature requires only a fixed number of look-ups in the integral image, independent of the scale. Time-consuming picture scales are not necessary to achieve scale invariance.

Table 1 summarizes the results of the object detection algorithm with a test data set of 30 scans that are not used for learning. Some examples of the detection of an ``office chair'' in 3D scans are given in Figure 4. Hits as well as missed and false alarms are documented. In addition, the figure presents the scaling feature of the detector, since the last two images of the third row were rendered with a wide apex angle of the virtual projection camera. In addition some results of the proposed object detection with partial occlusions are shown (bottom row). The cascade in Figure 3 presents the first three stage classifiers for the object ``office chair'' using depth values. One main feature is the horizontal bar (first stage).

The experiments inspired us to combine the cascades of the depth and reflectance images. Figure 5 shows two variants of the combination: Either the two cascades run interleaved (left) or serial (right) and represent a logical ``and''. The joint cascade decreases the false detection rate close to zero. To avoid the reduction of the hit rate, 6 different off-screen rendered images are used, where the virtual camera is rotated, i.e., the rotation by the Euler angles $(\theta_x,\theta_y) \in \{ (0,0), (-20,-20), (-20,20), (20,-20), (20,20)\}$ is applied. The 6th image is generated with a wide apex angle of 150 deg.

Table 1: Number of stages versus hit rate and false alarms. The last row shows the result of the combined classifier for reflectance and depth images. A detection including searching in the image using the combined cascade with 15 + 15 stages needs 376ms (Pentium-IV-2400).

number of	hit rate		false alarms
stages	reflect. img.	depth img.	reflect. img.	depth img.
15	0.9	0.866	0.067	0.067
30	0.867	0.767	0.067	0.033
(15 + 15) applied to 6 img.	0.967		0.0

Figure: Detection results using the classifier with 15 stages. The classified object is marked by a rectangle. Top row: Detection in reflectance and depth images. Second row: A false classification in a reflectance image is not present in the depth image (left). An object might be detected with different detector scales (right). Third row: Rotated images (left) and wide angle projections (right). Bottom row: Detection results under presence of partial occlusions. Small changes of the viewpoint are tolerated, e.g., a view from the side (left). If the main features are occluded the object detection fails (right).