Motion representation using composite energy features

Motion Representation using Composite Energy Features Raquel Dosil Corresponding Author Dep. de Electrónica e Computación, Univ. de Santiago de Compostela, Campus Universitario Sur, s/n, 15782, Santiago de Compostela, Spain e-mail address: rd[email protected] Phone: +34 981 563 100 Fax: +34 981 528 012 Xosé R. Fdez-Vidal Escola Politécnica Superior, Univ. de Santiago de Compostela, Campus Universitario, s/n, 27002, Lugo, Spain E-mail address: [email protected] Xosé M. Pardo Dep. de Electrónica e Computación, Univ. de Santiago de Compostela, Campus Universitario Sur, s/n, 15782, Santiago de Compostela, Spain E-mail address: [email protected] Abstract. This work tackles the segmentation of apparent-motion from a bottom-up perspective. When no information is available to build prior high-level models, the only alternative are bottom-up techniques. Hence, the whole segmentation process relies on the suitability of the low-level features selected to describe motion. A wide variety of low-level spatio-temporal features have been proposed so far. However, all of them suffer from diverse drawbacks. Here, we propose the use of composite energy features in bottom-up motion segmentation to solve several of these problems. 1 Composite energy features are clusters of energy filters –pairs of band-pass filters in quadrature–, each one sensitive to a different set of scale, orientation, direction of motion and speed. They are grouped in order to reconstruct independent motion patterns in a video sequence. A composite energy feature, this is, the response of one of these clusters of filters, can be built as a combination of the responses of the individual filters. Therefore, it inherits the desirable properties of energy filters but providing a more complete representation of motion patterns. In this paper, we will present our approach for integration of composite features based on the concept of Phase Congruence. We will show some results that illustrate the capabilities of this low-level motion representation and its usefulness in bottom-up motion segmentation and tracking. Keywords: Spatio-temporal energy filtering; Feature integration; Composite energy features; Apparent-motion segmentation and tracking. 1. Introduction Many recent motion segmentation techniques have been very successful due to the use of topdown approaches [1][2]. These techniques can be applied as long as there is some available prior model or template of the target object. If this is not the case, the performance of segmentation depends on the rules applied to infer high level representations from low level data –bottom-up process–, but also on the quality of the low level representation itself. A wide variety of low-level spatio-temporal features have been proposed in literature so far [3]. However, all of them suffer from diverese drawbacks. They can be classified into motion detection and motion estimation techniques. Motion detection methods classify points into static or mobile. As a consequence, they are only valid for static background scenes, and can not classify motion patterns according to their velocity and direction of motion. A very popular class of approaches for motion detection is background subtraction. Moving objects are identified as groups of connected pixels whose 2 features differ from those of the background model. Background modelling is usually accomplished using Gaussian mixture models [4]. Although these techniques are the most widely used, they are not free of limitations. They are very sensitive to scene changes in illumination and motion. Another solution for background modelling is PCA analysis within spatio-temporal pixel blocks, which reduces uncertainty and provided more stability to noise and illumination changes [5]. Finally, temporal differencing approaches, detect moving pixels by differencing between two or three adjacent frames [6]. They are highly adaptive to scene changes but fail to extract full foreground regions when foreground objects have uniform texture or move. On the other hand, motion estimation computes the parameters of some motion model based on some low-level motion feature. The most popular low-level motion feature is optical flow. Many techniques have been proposed for the estimation of optical flow, but they all present diverse kinds of problems [7][8]. Allowed motions are usually restricted to some specific model, such as translational or affine motion. Moreover, motion in homogeneous regions is not detected by optical flow. In general, most optical flow estimation techniques assume brightness constancy along frames, which in real situations does not always hold. Particularly, differential methods for optical flow estimation that are consistent with the brightness constancy assumption are not very robust to noise and aliasing. Finally, most optical flow estimation techniques present strong limitations in the allowed displacements of the objects from one frame to the next one. Differential methods try to find the position of a pixel in the next frame, but search is restricted to a small neighbourhood. This limitation can be overcome by coarse-to-fine analysis or by imposing smoothness constraints [7]. Still, large displacements are usually problematic, as well as occlusions. Sato and Aggarwal [9] have proposed an original approach for motion estimation based on the representation of linear motion patterns using the so-called Temporal Spatio-Velocity (TSV) transform. It consists of a Hough transform evaluated over windowed spatio-temporal images. Segmentation is accomplished by simple thresholding of the TSV image. Each resulting blob represents a local linear motion pattern. Conversely, the TSV transform has proved to be very 3 robust to noise and to easily deal with large displacements and occlusions. Its main drawback is that it is limited to translational motion with constant velocity. Here, we have paid attention to an early approach to low level motion representation based on the concept of energy filtering [10][11][12][13][14]. It consists in the estimation of motion from the amplitude of the responses of spatio-temporal filter pairs in quadrature, tuned to different scales and orientations. Spatio-temporal orientation sensitivity is translated into sensitivity to spatial orientation, speed, and direction of motion. These techniques are known to be robust to noise and aliasing, to give confident measurements of velocity, and to allow an easy treatment of the aperture problem, i.e., the reliable estimation of the direction of motion. However, to the best of our knowledge there is no motion segmentation method based on energy filtering. Energy filtering performs a detection of planar structures in a spatio-temporal domain. Hence, it is straightforward to correlate pixels of a moving object from different frames, avoiding problems with occlusions and large displacements. Moreover, energy filtering is robust to noise and aliasing. Besides, energy features are suitable for texture description in MPEG-7 video sequences for content-based retrieval applications [15]. The main limitation of energy features for motion representation is being restricted to translational motion with constant velocity. In this paper, we propose the use of composite energy features in bottom-up motion segmentation to cope with this inconvenience. Composite energy features are clusters of energy features, this is, the responses to band-pass pairs of filters in quadrature, each of them sensitive to a different set of scale, orientation, direction of motion, and speed. Energy features are grouped together in order to identify and reconstruct independent motion patterns in a video sequence. This means that the elements to be clustered are whole features, not pixels. A composite energy feature is built as a combination individual energy features in a cluster. Therefore, it inherits the desirable properties of energy features but providing a more complete representation of motion patterns. Composite energy features have proved to be a powerful tool for the representation of visually independent spatial patterns in 2D data [16], volumetric data [17][18], and video sequences [19]. To identify relevant composite features in a sequence, it is necessary to define an integration 4 criterion able to relate band-pass energy features contributing to the same motion pattern. Earlier approaches [16][19] use complex statistical measures with high computational cost. In previous works [17][18][20], we have introduced an integration criterion that improves computational cost and performance. Instead of applying arbitrary statistical rules, our criterion is inspired in biological vision. It is based on the hypothesis of Morrone and Owens [21] that the Human Visual System (HVS) perceives features at points of locally maximal Phase Congruence (PC). PC is the measure of the local degree of alignment of the local phase of Fourier components of a signal. The sensitivity of the HVS to PC has been studied by other authors as well [14][22][23][24]. Here, we have extended this concept to spatio-temporal signals to define our criterion for clustering of spatio-temporal energy features. We will show that composite features clustered under this criterion represent visually independent motion patterns in a video sequence, with different velocity, direction, and/or scale content, and that it performs motion estimation without the imposition of any motion model. We will see that, unlike many of the previously cited method, this representation is robust to noise and illumination changes. Besides, it naturally correlates information from different frames, so that it easily deals with occlusions and large inter-frame displacements, while common low level features need the aid of tracking techniques to find the correspondence of the position of an object from different frames. We have applied the composite feature representation as the basis of a method for segmentation and tracking. Typical bottom-up methods for motion tracking include active models [25][26], Bayesian region classification [27][28], and Kalman filtering [29]. A comprehensive survey can be found in [3]. We have chosen a geodesic active model [25] for tracking. We apply our representation for both the initialization of the model at each frame and as a low level feature to guide the evolution of the model. The outline of this chapter is as follows. In section 2, we describe in detail the composite feature detection process. Section 3 explains how the geodesic active model uses the low level motion representation to guide segmentation. In section 4, we illustrate the behaviour of the composite feature representation in different problematic situations, including some standard video 5 sequences. We will also show the results of segmentation and tracking. In section 5, we expound the conclusions of the work. 2. Composite-Feature Detector Synthesis As aforementioned, composite energy features are clusters of energy features. Then, in the first place, we must perform a multiresolution decomposition to obtain the individual energy features. To this end, we apply a bank of non-causal spatio-temporal energy filters to the video sequence. The complex-valued volume generated as the response of a spatio-temporal energy filter to a given video sequence is here called a band-pass energy feature. We will call composite energy features to motion patterns with multiple speed, direction and scale contents generated as the combination of band-pass energy features in a cluster. The set of filters associated to an energy feature cluster are referred to as composite-feature detector. Feature grouping is accomplished by applying cluster analysis to the set of band-pass features of the video sequence. We perform clustering of the features as a whole, not point wise, since a point in space can be occupied by several visual patterns with different frequency content. Hence, more that one composite feature can have large response in the same location in space and time. This is not allowed by crisp clustering of pixels. Besides, pixel clustering is more sensitive to local variations and noise. Clustering is accomplished using a hierarchical algorithm, which is based on a dissimilarity matrix reflecting the distances among band-pass features. The dissimilarity measure is defined in order to identify band-pass features contributing to the same local maxima of Phase Congruence (PC). We will see that the correlation coefficient can provide a good global measure of the PC between band-pass features [17][20]. Finally, each composite feature is reconstructed as a combination of the responses of the filters in a given cluster. Instead of a simple linear combination, we propose a more sophisticated pooling expression, in order to enhance the representation. The next subsections present the details of the process. 6 2.1 Bank of Spatio-Temporal Filters The basis function of the bank of spatio-temporal filters applied here [17][20] is an extension to 3D of the log Gabor function [30]. The filter is designed in the frequency domain, since it has no analytical expression in the spatial domain. Filtering is realized as the inner product between the transfer function of the filter and the Fourier transform of the sequence. Filtering in the Fourier domain is very fast when using Fast Fourier Transform and Inverse Fast Fourier Transform algorithms. The filters’ transfer function T is designed in spherical frequency coordinates as the product of separable factors, R and S, in the radial and angular components respectively, such that T=R·S. The radial term R is given by the log Gabor function [30] , (1) where  i is the standard deviation and  i is the central radial frequency of the filter. The angular component is designed to achieve orientation selectivity in both the azimuthal component  i of the filter, which reflects the spatial orientation of the pattern in a frame and the direction of movement, and the elevation component  i, related to the speed and direction of motion. For static patterns,  i=0. To achieve rotational symmetry, S is defined as a Gaussian on the angular distance  between the position vector f of a given point in the spectral domain and the direction of the filter v=(cos  i·cos  i,cos  i·sin  i,sin  i) [31] , with , (2) where f is expressed in Cartesian coordinates and  i is the angular standard deviation. Active filters are selected from a predefined band partitioning of the 3D spectral domain. Frequency bands are described by the central frequency (  i,  i,  i) of the filters and their width parameters (  i,  i). The selection of these parameters determines the kind of energy features yield by the multiresolution decomposition. In this application we desire to get wide coverage of 7 the scale space, uniform sampling of the orientation space, and high orientation sensitivity. To this end, the parameters of the bank are established as follows. Frequency is sampled so that  i={1/2, 1/4, 1/8, 1/16}, in pixels1. Parameter  i is determined for each band in order to obtain a 2 octave bandwidth.  i is sampled uniformly while the number of  i samples decreases with elevation.  i are determined in order to keep a constant “density” of filters, by maintaining equal arc-length between adjacent  i samples over the unit radius sphere.  i is set to 25º for all orientations. Following this criterion, the filter bank has been designed using 23 orientations, i.e. (  i,  i) pairs. In total, we have 23 orientation  4 scales = 92 bands with a certain overlapping between neighbouring bands, yielding a redundant decomposition and a wide coverage of the spectrum. 2.2 Selection of Active Bands To achieve improved performance, it is convenient to reduce the number of bands involved in cluster analysis. The exclusion of frequency channels that are not likely to contribute to motion patterns facilitates the identification of clusters associated to composite motion features. Furthermore, it reduces computational cost. Features selected for clustering are called active. A previous solution for active band selection, applied in [17], consisted in the detection of bands enclosing spectral amplitude values over a maximum noise level. This implies the setting of a threshold parameter and the use of a radial median filter, which is highly computationally expensive. Here, we have introduced a channel selection stage based on a statistical analysis of the amplitude responses of the band-pass features. This solution outperforms that in [17] in both computational cost and efficiency. Our method for the selection of active channels is based on the works of Field [32] and Nestares et al. [33]. Field has studied the statistics of the responses of a multiresolution decomposition based on log-Gabor wavelets that resembles the coding in the visual system of mammalians. He has observed that the histograms of the filter responses are not Gaussian, but leptokurtic distributions –pointed distributions with long tails–, revealing the sparse nature of both the 8 sensory coding and the features from natural images. According to Field, when the parameters of the wavelet codification fit those in the mammalian visual system, the histogram of the responses is highly leptokurtic. This is reflected in the fourth cumulant of the distribution. Namely, he uses the kurtosis to characterize the sparseness of the response. Regarding spatio-temporal analysis, Nestares et al. [33] applied channel selection to a bank of third order Gaussian derivative filters based on the statistics of filters responses. They have observed that features corresponding to mobile targets present sparser responses than those associated to background –weather static or moving. This fact is illustrated in Fig. 1. They measure different statistical magnitudes reflecting sparseness of the amplitude response, realize a ranking of the channels based on such measures, and perform channel selection by taking the n first channels in the ranking, where n is a prefixed number. Based on these two works, we have designed our filter selection method. The statistical measure employed to characterize each channel is the kurtosis excess  2 ,(3) where k4 and k2 are respectively the fourth and second cumulants of a histogram. If the kurtosis excess takes a positive value, the distribution is called leptokurtic and presents a narrow peak and long tails. If it is negative, the distribution is called platykurtic and presents a broad central lobe and short tails. Distributions with zero kurtosis excess, like the Gaussian distribution, are called mesokurtic. We measure γ2 for both the real and imaginary components of each feature  i and then we compose a single measure  (4) Instead of selecting a fixed number of channels with the larges values of  , we perform cluster analysis to identify two clusters, one for active channels, with large values of  , and another for non active channels. Here, we have applied a k-means algorithm. The cluster of active channels is identified as the one with higher  on average. 9 remapped to the interval [–1,1]. The zero-level of the resulting image is the initial state of the contour. (13) When the object remains static during a number of frames the visual pattern has a null response. For this reason, the initial model is defined as the weighted sum of two terms, respectively associated to the current and previous frames. The contribution from the previous frame must be very small. (14) with wk and wk– 1 being positive real constants that verify wk+wk– 1 =1. In the experiments presented in next section, wk=0.9, wk – 1=0.1, K=20 and 0=0.1. 4 Results In this section, some results are presented to show the behaviour of the method in problematic situations. The complete video sequences with the original data and the segmentation results are available at http://www-gva.dec.usc.es/~rdosil/motion_segmentation_examples.htm.They are summarized in the next subsections. Example #1 The following example shows the ability of the method to deal with complex motion patterns with variations in illumination, non linear motion and deformations. In particular, the following sequence, a fragment of 27 frames of the standard movie know as “silent” – top row of Fig. 7–, presents a mobile object, with variable shape, speed and direction. As can be appreciated, the motion pattern of the hand can not be properly described by an affine transformation. Moreover, the brightness constancy assumption is not verified in this case. The middle row of Fig. 7 shows one of the two identified composite patterns, representing the 16 moving hand. It can be seen that, despite the complexity of the image, the composite-feature representation model is able to isolate the hand and properly represent its changing shape in different frames. Images in the bottom row of Fig. 7 present the segmentation results. Example #2 In this example, we use a fragment of 27 frames of the well-known sequence “flower garden” – see Fig. 9. It is a static scene recorded by a moving camera, so that all the pixels in the scene are moving. The composite energy feature representation identifies two motion patterns, one for the moving tree and one for the moving background. This is possible because the tree is placed in a foreground plane, so that its speed is larger. When visualizing a cut in the x-t plane on both the image and the motion patterns –Fig. 8–, it can be seen that different speeds are translated into different orientations in the spatio-temporal domain. The composite energy feature representation has been able to cluster energy features with similar frequencies –speeds, orientations and sizes. The result of segmentation using one of the detected motion patterns is shown in Fig. 9. The image potential in that example is computed from the composite energy feature corresponding to the tree. Hence, there are not deep minima of the potential caused by moving background contours, which leads to a correct segmentation. Example #3 In this example we use a fragment of 22 frames of the well-known “table tennis” video sequence, shown in first row of Fig. 10, which presents non linear motion patterns and large inter-frame displacements, due to a small sampling rate. This makes it difficult to find the correspondence between the positions of the object in two consecutive frames. The composite feature representation is able to identify the energy components of the motion pattern, and to generate a composite feature in which the motion pattern is isolated from the static background –see Fig. 10, middle row. The result of segmentation is shown in bottom row of Fig. 10. Since the active model is initialized from the motion pattern at each frame, the large 17 inter-frame displacements do not influence tracking. Example #4 Occlusions give rise to the same problem as with fast objects. In the next example, in Fig. 11, a sequence of 31 frames is showing a cylinder rolling behind another object, completely disappearing from the scene during some frames. The middle row in Fig. 11 shows one of the composite features identified by our representation method, corresponding to the moving cylinder, in its amplitude representation. The other composite feature detected, not shown here, corresponds the static objects. The result of segmentation using this composite feature is shown in last row of Fig. 11. As can be seen, initialization with the composite energy feature leads to a correct segmentation, even when the object disappears from the scene during several frames. The model collapses when the cylinder disappears behind a static object and is reinitialized automatically when it reappears, without the need of a prior model. Example #5 The next example, in Fig. 12, with 39 frames, presents occlusions as well, but now the occluding object is also moving, which complicates tracking. The scene shows two people walking in opposite directions. The second and third rows in Fig. 12 show two of the composite features identified by our representation method, corresponding to the two moving persons. The remainder composite features detected, not shown here, correspond to static objects. Again, the representation model is capable of decomposing the scene into visually independent motion patterns by integrating band-pass energy features. Two active models have been optimized, each guided by one of these composite features. Segmentation results are presented in the fourth and fifth rows of Fig. 12. The use of composite features for both initialization and definition of image potential avoids interferences between different motion patterns during model optimization. Besides, tracking is straightforward since there is only one model for each pattern in each frame, although it may be split. 18 Example #6 The following example is a fragment of the standard video sequence “coast guard”, comprising 48 frames. This sequence shows two mobile objects, one of them being followed by the camera. The results for this sequence are presented in Fig. 13. The model classifies the filters corresponding to the moving background as non active, excluding them from the subsequent analysis. The model is able to identify two motion patterns, one for each of the moving objects. Segmentation of the static object is not interfered by background texture or background mobile contours. Example #7 The last example, in Fig. 14.a and e, is a sequence of 126 frames showing two motion patterns with different scales, speeds and directions of motion. Both patterns are occluded in different parts of the sequence. The background is not completely static, but there are also local motion patterns –branches in the trees are moving due to the wind. It is a low resolution video, with a high noise level. The proposed model classifies the filters contributing to the background as non active, including local motion in the branches of the trees –see Fig. 15.b– and active filters give place to two motion patterns, one for each moving object –Fig. 15.c, d, f and g. Segmentation results for both composite features are shown in Fig. 15. Initialization with composite features solves the problem of occlusions in both situations. Image potentials from composite features avoid interferences between the two motion patterns and interferences with motion in background pixels. 5 Discussion and conclusions Results show that the proposed model for the representation of motion is able to group bandpass features associated to different motion patterns in a scene without the use of prior 19 information, and to isolate visually independent motion patterns. The studied examples cover some of the most common problems in motion estimation, namely, presence of noise, moving background, variations in illumination, non affine motion patterns, scenes with multiple motion patterns, occlusions, and large displacements between neighbouring frames. As summarized in the introduction, other common low level motion representations present difficulties in some of these situations. The key characteristic of the composite feature representation is that integration is accomplished by clustering of spatio-temporal energy features as a whole, not by point-wise region classification. This fact yields a representation that intrinsically correlates information from different frames. This property is responsible for the robustness to partial and total occlusions and large inter-frame displacements or deformations. This property allows the direct use of this representation in guiding a high level segmentation technique like the active model, without any intermediate step of region classification or object search from one frame to the next. Segmentation results prove the success of the combination of composite feature representation and high level modelling by a level-set approach. The problem of the initialization of active models is easily solved using the amplitude representation of composite features. 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Terzopoulos, Snakes: Active Contour Models, Int. Journal of Computer Vision, 55 (1988) 321-331. 23 [38]. V. Caselles, R. Kimmel, G. Sapiro. Geodesic Active Contours, Int J Comput Vis, 22, (1997) 61-79. [39]. J. Weickert, G. Kühne, Fast Methods for Implicit Active Contour Models, in: S. Osher, N. Paragios (Eds.), Geometric Level Set Methods in Imaging, Vision and Graphics, Springer, New York, 2003, pp. 43-58. [40]. R. Dosil, X.M. Pardo, Generalized Ellipsoids and Anisotropic Filtering for Segmentation Improvement in 3D Medical Imaging, Image and Vision Computing, 21 (2003) 325-343. 24 (a) (b) (c) (d) (e) Fig. 1. (a) A frame of the “Silent” standard sequence, showing a moving hand. (b) and (d) A frame of the real part of two band-pass features of the Silent video sequence. (c) and (e) Histograms corresponding to band-pass features in (b) and (d) respectively. 25 Fig. 10. Top: Left and centre images correspond to two consecutive frames of the “table tennis” video sequence. The image at the left is a traversal cut in the y-t plane. For frames on top row, Middle Row: amp of the selected composite-feature, and Bottom: Segmentation obtained with one of the detected composite-features. 32 Fig. 11. Top: Three frames of a video sequence where a moving object is totally occluded during several frames. Middle Row: Initialization of the frames using the amp representation of one of the detected composite-feature. Bottom: Segmentation using initialization with the composite feature 33 Fig. 12. Three frames of a sequence showing two occluding motion patterns. 1st row: Input data. 2nd and 3rd rows: even of two of the obtained composite-features, corresponding to the two motion patters. 4th and 5th rows: Segmentations produced using composite-features from rows 2nd and 3rd respectively. 34 Fig. 13. Top and bottom row correspond to two frames of the “cost guard” video sequence: 1st column: Input data. 2nd and 3rd columns: abs of the two motion patterns isolated by the composite-feature representation mode and 4th column: segmentations produced using the composite feature in 3rd column. 35 (a) (b) (c) (d) (e) (f) (g) Fig. 14. (a) A frame of the input sequence. (b) real from the group of non active filters. (c) and (d). real from the composite features detected by the model. (e) Traversal cut of the input sequence –frame index increases from top to bottom. (f) and (g) Traversal cut of abs from the two composite features detected. Occlusions are better appreciated in this view. 36 Fig. 15. Left column: Several frames of the input sequence. Center and Left columns: Corresponding segmentations produced using each of the two detected composite features. 37