© 2014 ACEEE DOI: 01.IJSIP.5.1. ACEEE Int. J. on Signal and Image Processing , Vol. 5, No. 1, January 2014 Full Paper 13 3-D FFT Moving Object Signatures for Velocity Filtering G. Koukiou 1 and V. Anastassopoulos 2 1 Electronics Laboratory, Physics Department ,University of Patras, Patras, Greece 26500 Email: gkoukiou@upatras.gr 2 Electronics Laboratory, Physics Department ,University of Patras, Patras, Greece 26500 Email: vassilis@upatras.gr Abstract— In this paper a bank of velocity filters is devised to be used for isolating a moving object with specific velocity (amplitude and direction) in a sequence of frames. The approach used is a 3-D FFT based experimental procedure without applying any theoretical concept from velocity filters. Accordingly, each velocity filter is built using the spectral signature of an object moving with specific velocity. Experimentation reveals the capabilities of the constructed filter bank to separate moving objects as far as the amplitude as well as the direction of the velocity are concerned. Accordingly, weak objects can be detected when moving with different velocity close to strong vehicles. Accelerating objects can be detected only on the part of their trajectory they have the specific velocity. Problems which arise due to the discontinuities at the edges of the frame sequences are discussed. Index Terms—Velocity filters, filter banks, 3-D FFT. I. INTRODUCTION Detection and tracking of moving objects (such as vehicles, people, planes, etc.) is one of the complex topics in the field of automotive applications, covered by many researchers all around the world. Several approaches have been made to detect multiple objects, their velocity or estimate the varying velocities of these objects using different kinds of sensors and procedures [1,2]. Velocity filters have been used so far for the detection of multiple moving odjects in image sequences [3] as well as in three-dimensional imagery [4-5]. Especially, the work in [3] extends the method of velocity filter banks by a heuristic search of possible target trajectories. In [4] a motion-based approach is presented to simplify the detection of moving objects, where the image sequence containing the moving object is interpreted as a three-dimensional signal. Also, in [5] an approach for detecting moving objects is presented, which is based on three-dimensional filters not only taking spatial but also temporal information into account. In [6] and [7] velocity filter banks were applied for moving object detection. Finally, in [8] a novel motion detection technique was proposed for multiple objects detection in image sequence. The algorithm is based on directional filtering in the spatio-temporal frequence domain using 3-D FFT. In this paper, a bank of velocity filters is built for separating multiple objects with different velocities in a sequence of frames. In this procedure the 3-D FFT transformation of a large variety of different velocities has been used. The proposed approach is based on experimentation and avoids to employ theoretical concepts. Accordingly, an object moving each time with different velocity and various directions has been used in order to construct the filter bank. Multiple moving objects can be isolated from other objects with different velocities or from objects with the same amplitude of velocity but having different directions. Experimentation with objects having various velocities, accelaration or varying strenght in their illumination has been carried out in order to test the capabilities of the constructed velocity filter bank. Discontinuities of the signal are thorounghly discussed and ways to cope with signals that suddenly appear at the edges of the data cube are given. The organization of the paper is as follows. In section 2 the data used are described while in section 3 the construc- tion of the velocity filter bank is analytically explained. The experimentation regarding the performance of the filter bank on various data is carried out in section 4. Finally, the conclu- sions are drawn. II. DATA BASE DESCRIPTION Each simulated data set that was used in order to create the spectral signatures of different moving objects consists of 256 frames, of 256x256 pixels each. Accordingly, a data cube (shown in Figure 1) is formed of 256 3 pixels. The number 256=2 8 was selected to fit the FFT requirements for fast evaluation of the 3D spectrum. Figure 1. 256 frames of 256x256 pixels each (Data cube) The time parameter is considered to be the distance from frame to frame. Based on this remark, the amplitude of the radial velocity of each object is reffered to as the number of pixels it comes across from one frame to the next. A simple example of one object of size 10x10 pixels that is moving with radial velocity of 1/3 pixels per frame is shown in Figure 2. 71