1/1 High-speed movement analysis from log-polar images using dynamic feature extraction and correlation Esther de Ves, Fernando Pardo, Jose A. Boluda Departamento de Informática - Universidad de Valencia Avda. Vicente Andrés Estellés s/n, 46950, Burjassot, Valencia, SPAIN Esther.DeVes@uv.es, Fernando.Pardo@uv.es, Jose.A.Boluda@uv.es Abstract There are several methods to measure movement in front of a mobile vehicle (robot) equipped with a camera. Some methods detect movement from the analysis of the optical flow, while other methods detect movement from the displacement of objects or part of the objects (corners, edges, etc.) Those methods based on the optical flow are suitable for high speed analysis (say 25 images per second) but they are not very accurate and treat the image as a whole, being it difficult to separate different objects in the scene. Those methods based on image feature extraction are good for object recognition and clustering, that can be more precise than other methods, but they usually require lot of computations to yield a result, making it difficult to implement these methods in a navigation system of a robot or mobile vehicle. In this article we present a technique that allows high-speed movement analysis using the accurate displacement measure of the feature extraction and correlation method. 1. Introduction Most of 2D feature detectors employed in image processing are computationally expensive and are not suitable for high speed image analysis (25 frames/s). It is possible to increase the computation speed by loosing accuracy or employing powerful computer systems that are not adequate for mobile robots. There is a different approach to successfully employ this feature extraction on mobile robots, and it is to decrease the global visual data to be processed. This reduction is accomplished by means of the log-polar mapping that concentrates pixels in the image center (the most interesting part) and decreases resolution toward the periphery (the least interesting part) [1]. The log-polar mapping has the advantage of selective image data reduction, but also has some mathematical invariance properties (scaling and rotation) that are especially useful for image processing, particularly for a robot moving ahead. Figure 1 shows the transformation of the scaling of an approaching object into a linear displacement. The focal plane (camera) and the computational plane (array in the computer memory) are shown in this figure. The original object (black ring) is a centered ring in the focal plane, but it is converted to a straight line in the computational plane after the log-polar transformation. The scaling produced by the camera approaching the ring is converted in just a displacement in one of the orthogonal axis. This interesting property can be exploited to simplify computations of such approaching movements, commonly found in the movement of robots toward an objective. Fig. 1. Camera approaching to an object (black ring) in log-polar coordinates The log-polar transformation has also the advantage of the selective reduction of information. The special log-polar pixel distribution has more resolution in the interesting parts of the scene (center) reducing the number of pixels toward the periphery; the view field is kept while the total pixel count is reduced. We use a resolution of 76 rings by 128 pixels per ring in our experiments. This makes a total of 9728 pixels to be processed. Comparing this data (roughly 10 K), with the data of a standard 512x512 Cartesian image (256 K) the difference is quite significant. The difference in the number of pixels to be processed has a direct impact on the rates at which the images can be processed. Depending on the image analysis, this save of time can be of several orders of magnitude while the precision is still kept at acceptable values. 2. Feature extraction Not many feature extraction methods can be employed in the log-polar domain due to the special mathematic characteristics of this mapping. One of them is the distortion suffered by objects after transformation (the shape of any object is not constant and depends on its position in the log-polar plane). But there is a characteristic of the log-polar mapping that makes it possible to employ object detection methods: since the log-polar is a conformal transform, angles in Cartesian coordinates are preserved in the log-polar coordinate system. We therefore employed a feature extraction based on corner and junction detection that allows the measurement of relevant point movement and object detection despite the fact that the object changes its shape as it moves (or the robot moves). We have chosen a 2D gray-level detector based on a statistical analysis of the gradient orientations in a circular