Highly Parallelizable Algorithm for Keypoint Detection in 3-D Point Clouds

Abstract

In computer vision a reliable recognition and classification of objects is an essential milestone on the way to autonomous scene understanding. In particular, keypoint detection is an essential prerequisite towards its successful implementation. The aim of keypoint algorithms is the identification of such areas within 2-D or 3-D representations of objects which have a particularly high saliency and which are as unambiguous as possible. While keypoints are widely used in the 2-D domain, their 3-D counterparts are more rare in practice. One of the reasons often consists in their long computation time. We present a highly parallelizable algorithm for 3-D keypoint detection which can be implemented on modern GPUs for fast execution. In addition to its speed, the algorithm is characterized by a high robustness against rotations and translations of the objects and a moderate robustness against noise. We evaluate our approach in a direct comparison with state-of-the-art keypoint detection algorithms in terms of repeatability and computation time.

Appendix—Additional Examples

Happy Buddha

This object is obtained from ‘The Stanford 3-D Scanning Repository’ [19] and is characterized by the following properties:

• Points: 144647

• $pcr = 0.00071$

• Voxel grid: $135 \times 299 \times 135$

• $r_{conv} = 10 \cdot pcr$

• $\sigma = 0.124884$

• Bins: 121

• Keypoints: 210

The histogram below illustrates the distribution of convolution values for the ‘Happy Buddha’. To save space the labels are not included in the histogram. They correspond to those shown in Fig. 5, i.e., the abscissa shows the bin number, while the ordinate shows the number of elements per bin.

The 3-D point cloud of the ‘Happy Buddha’ shown right is a combination of two types of figures which have already been used to illustrate the results of the ‘Stanford Bunny’. The color gradient used to tint the point of the point cloud illustrates the convolution values from the smallest value (red) to the largest value (blue). This was already used in Fig. 4. The purple markers illustrate the final keypoints. This was already used in Fig. 6d.

Dragon

This object is obtained from ‘The Stanford 3-D Scanning Repository’ [19] and is characterized by the following properties:

• Points: 100250

• $pcr = 0.00097$

• Voxel grid: $236 \times 174 \times 120$

• $r_{conv} = 10 \cdot pcr$

• $\sigma = 0.124507$

• Bins: 107

• Keypoints: 92

The histogram below illustrates the distribution of convolution values for the ‘Dragon’. To save space the labels are not included in the histogram. They correspond to those shown in Fig. 5, i.e., the abscissa shows the bin number, while the ordinate shows the number of elements per bin.

The 3-D point cloud of the ‘Dragon’ shown above is a combination of two types of figures which have already been used to illustrate the results of the ‘Stanford Bunny’. The color gradient used to tint the point of the point cloud illustrates the convolution values from the smallest value (red) to the largest value (blue). This was already used in Fig. 4. The purple markers illustrate the final keypoints. This was already used in Fig. 6d.