Kernel PCA and approximate pre-images to extract the closest ultrasonic arc from the scanning of indoor specular environments

In this paper, the authors firstly develop a general detailed acoustic waves propagation model validated by the comparison with different types of ultrasonic sensors and then they deal with the problem of extracting an arc from the ultrasonic scan in order to differentiate direct reflections from other spurious readings. They use a mechatronic system to scan an indoor environment, locating their scanner in front of a regular target surface. The scanning device allows the rotation of ultrasonic sensors with a view for detecting strong echoes in each pointing direction. The first echo permits to estimate the time-of-flight (TOF) and subsequently to obtain the distance covered by the sonic pulse. The scanned space is approximated as being two-dimensional and the scanner is treated as a ray-tracer placing a dot along the sensor axis at the measured distance. In case the reflected-back energy is not able to exceed the detector threshold, the dot is plotted at the appropriate maximum range value. The process of drawing a set of points relating to the closest target surface was achieved by means of the Kernel Principal Component Analysis (KPCA) that maps the original data into a higher-dimensional feature space. The obtained data were then projected into a subspace of the feature space and the approximate pre-images were calculated to extract the looked-for arc. Simple matrix algebra makes the method an efficient alternative to other techniques based on distance threshold that generally require a priori information on the explored environment. The arc permits to estimate location and orientation of the target surface with respect to the scanning device. Several tests were carried out in order to appreciate the effectiveness of the described approach and the results were compared to the outcome of other existing techniques.