This paper shows an image/video application using topological invariants in human gait recognition. The 3D volume of a gait cycle is built stacking silhouettes extracted using a background substraction approach. Ideally, the border cell complex is obtained from the 3D volume with one connected component and one cavity. Then, it is necessary to apply a topological enrichment strategy in order to obtain a robust and discriminative representation for person recognition. Using a sliding cutter plane normal to some direction of view it is possible to divide the border cell complex in different parts. The incremental algorithm is used to compute the homology on each part. A vectorial representation is built ordering the number of connected components and tunnels obtained for each cut. In order to evaluate the robustness of this representation the silhouettes were diminished to a quarter of the original size. At the same time, this is considered a simulation of a human gait captured at long distance. Even, under these difficult conditions it was possible to get a 74% of correct classification rates on CASIA-B database

García Reyes, Edel

González Díaz, Rocío

Lamar León, Javier

idUS. Depósito de Investigación Universidad de Sevilla

Human Gait Recognition Using Topological InformationJavier Lamar Leo´n1, Edel Garc´ıa Reyes2 and Rocio Gonzalez Diaz31,2 Patterns Recognition Department, Advanced Technologies Application Center (CENATAV), LaHabana, Cuba.3 University of Sevilla, Dept, School of Computer Engineering, Sevilla, Spain.jlamar@cenatav.co.cu, egarcia@cenatav.co.cu, rogodi@us.esAbstract This paper shows an image/video application using topological invariants inhuman gait recognition. The 3D volume of a gait cycle is built stacking silhouettes extractedusing a background substraction approach. Ideally, the border cell complex is obtainedfrom the 3D volume with one connected component and one cavity. Then, it is necessaryto apply a topological enrichment strategy in order to obtain a robust and discriminativerepresentation for person recognition. Using a sliding cutter plane normal to some directionof view it is possible to divide the border cell complex in different parts. The incrementalalgorithm is used to compute the homology on each part. A vectorial representation isbuilt ordering the number of connected components and tunnels obtained for each cut. Inorder to evaluate the robustness of this representation the silhouettes were diminished to aquarter of the original size. At the same time, this is considered a simulation of a humangait captured at long distance. Even, under these difficult conditions it was possible to geta 74% of correct classification rates on CASIA-B database.Keyworks gait recognition, topology, cell complex, homology.1 IntroductionGait recognition is a challenging problem that gives the possibility to identify persons at a distance,without any interaction from the subjects, which is very important in real surveillance scenario[4, 7]. Methods based on feature extraction using contour of silhouettes have been usually used[2]. However, many silhouettes obtained are incomplete due to illumination changes, occlusions,and others. These factors severely affect recognition accuracy. Even though, a recent study [2] isaimed at suppressing the effect of silhouettes incompleteness to improve performance on previousapproach, we do not pre process the silhouettes in this paper.Topology has been previously used to match nonrigid shapes [5, 1]. In this paper, the changesof silhouettes induced by gait are considered as a moving nonrigid object. To the best of theauthors knowledge this approach has never been applied to gait recognition.The aim of this paper is to propose a novel topological representation for gait recognition builton the 3D volume gait and tested on CASIA-B database using a similar experiment set up forthe Set A [7]. Furthermore, we reduce the sizes of silhouettes to simulate images obtained at longdistance and to alleviate computational cost of the homological algorithm.113The rest of the paper is organized as follows. In section 2, we describe the new methods indetail. Experimental results are then reported in section 3. We conclude this paper and discusssome future works in section 4.2 The new methodFig. 1 shows the chain of processing to obtain the gait signature to carry out lateral view gaitrecognition. First, the moving object (person) is segmented for each frame applying backgroundmodeling and substraction [6]. The sequence of silhouettes is analyzed to extract the gait cycle.The 3D volume of a gait cycle is built stacking silhouettes aligned by the gravity centers. Theborder cell complex is created by triangles (2-cells) on surface of the 3D gait volume. Finally,the gait signature is obtained based on the topological invariants extracted from the border cellcomplex.Input videoBackgroundsubtractionTopological descriptionGait cycleextraction3D gait volumeBorder  cell complexSignatureFigure 1: Extracting the gait topological signature.In the gait cycle extraction the silhouette with the maximum length of the step is the oneselected as the first image (with foot right or left) and the next silhouette of maximum length ofthe step with the same foot (right or left) is the last image (Fig. 2).Maximum length with   right footMaximum length with left footMaximum length with right footFigure 2: Gait cycle.3D gait volume belonging to one gait cycle is built by aligning temporal silhouettes by itsgravity center (gc) (Fig. 3(a)) and may be viewed as a 3D image (Fig. 3(b)), where each vertexcan have at most 26 neighbors. Hereafter, we will use GC when we refer to the gravity center on3D gait volume and border cell complex. In the 3D space t is defined as the frame number in thegait cycle, x and y are coordinates of the pixels on the image referred to gc of each silhouette.Border cell complex is formed by triangles (2-cells) on bordered surface of the 3D gait volume.Triangles can only be built between vertexes of the same t, t and t+1 or t and t−1, i.e, vertexes ofthe same silhouette or between neighbor silhouettes. In this complex all 0-cell (vertex) and 1-cell(edges) belong, at least, to a 2-cell (triangle), which is the maximum dimension of the border cellcomplex, so we may store triangles and infer the existence of lower dimension simplices (0-cellsand 1-cells). The border cell complex is not a manifold , that is, there are 1-cells (edges) that donot have only two 2-cells (triangles) as neighbors. An example of border cell complex is showed inFig. 4. After having built the border cell complex belonging to one gait cycle, coordinates (x, y, t)114txyxytgcGC(a) (b)Figure 3: 3D space (x,y,t).are normalized according to [4]. This defines a cube C, where axes x and y are between 0 and 1and T is defined as the percentage of gait cycle (between 0 and 100) (Eq. 1).T = [0, 1 ∗ 100G− 1 , 2 ∗100G− 1 , ..., (t− 1) ∗100G− 1 , ..., 100] (1)Where G is the number of silhouettes in a cycle and t is the number of the silhouette.Txy010011Figure 4: Border cell complex.2.1 Topology enrichmentThe topology of the border cell complex of a gait cycle, in general, is very poor, because it hasone connected component and one cavity. In this section we present a strategy to increase thetopological information of the border cell complex. The relations among the parts of the humanbody when walking are characterized by the number of connected components and tunnels, theseare created by cuts of normal planes to the line defined by a viewing angle that goes through GCof the border cell complex. The intersection of the line with the cube (C) are two points a andb, which are the beginning of the cuts, i.e, n cuts from point a to GC and n cuts from point b toGC. The distance between two continuous planes for [a GC] and [b GC] is computed according115to Eq. 2 and Eq. 3 respectively.for interval [a GC] ∆[a GC] =D(a,GC)n(2)for interval [b GC] ∆[b GC] =D(b,GC)n(3)where ∆[a GC] is the distance between contiguous planes in the interval from point a to GC,∆[b GC] is the distance between contiguous planes in the interval from point b to GC, D(a,GC) isthe distance from point a to GC, D(b,GC) is the distance from point b to GC, n is the number ofcuts, the same to both intervals [a GC] and [b GC]). At the same time 2 cuts are made, one in theinterval [a GC] and other [b GC], where we get two features by cut (amount of connected com-ponents and tunnels) on two new cell complex generated between cut planes and points a and b.These features can be stored in a matrix (n∗m), where n is the number of cuts andm is the numberof topological features. An incremental algorithm [3] is used to determine connected componentsand tunnels. This allows to obtain topological invariants using the information of the previous cut.Let us now use an example according to Fig. 5. The border cell complex had been cut usingnormal planes to the line defined by points a and b. We made n ∗ 2 cuts (n = 5) of plane, five inthe interval [a GC] and five in the interval [b GC]. Topological information for each cut is showedin the table.Where VCC[a GC] is the vector of numbers of connected components for interval [a GC], VT[a GC]is the vector of numbers of tunnels for interval [a GC], VCC[b GC] is the vector of numbers ofconnected components for interval [b GC], VT[b GC] is the vector of numbers of tunnels for interval[b GC].The similarity between two vectors may be calculated using Eq. 4. In this approach, a vectoris formed by the number of connected components or tunnels in each cut plane defined by aviewing angle for one of the intervals [a GC] or [b GC]. In the above example, we have four5-dimensional vectors (VCC[a GC] , VT[a GC] , VCC[b GC] , VT[b GC]) (see table (Fig. 5)), and the angle iscomputed as:α = cos−1( ∑ni=1 viri(∑ni=1 v2i )1/2(∑ni=1 r2i )1/2)(4)Where n is the number of cut numbers for one of the intervals [a GC] or [b GC] according toa viewing angle, v is a column of the table in Fig. 5 for a person and r is the same column v foranother person. We computed four similarity measures si, i.e, four angles, between two persons.The total similarity value S(Pi, Pj) is the weighted sum of these similarities (Eq. 5).S(P1, P2) = w1s1 + w2s2 + w3s3 + w4s4 (5)11601000 01xty1  line de!ned       by theviewing angle          1 1 0 3 0 2 4 1 3 2 3 7 4 6 8 4 4 11 4 12 5 2 11 1 21 abCutsCut 5[a GC] Cut 5 [b GC] Cut 1[a GC] Cut 1[b GC] ]GC  [aCCV]GC  [aTV]GC  [bCCV]GC  [bTVFigure 5: Cuts plane on a border cell complex.3 Experimental resultsIn this section, we demonstrate the performance of the proposed method on the lateral view ofthe CASIA-B database, which contains 124 subjects. There are six normal walking sequences foreach person. CASIA-B database provides image’s sequences with background subtraction for eachperson as proposed in [6]. The cycle’s silhouettes are scaled with factor 0.25 to simulate imagesobtained from a long distance (Fig. 6).For topologically enriching the border cell complex, we used 4 viewing angles, with n cuts fromthe point a to GC and from the point b to GC. Each viewing angle has 4 feature vectors, then wehave 16 feature vectors. The first viewing angle is the same as in the above example for n = 30,i.e, 30 cuts for [a GC] and 30 cuts [b GC], these cut planes can be called Pyt (Fig. 7a). The secondviewing angle is orthogonal to the first viewing angle with n = 30 too and it is called Pxt (Fig. 7b).The third viewing angle (line (a, b)) forms a 450 angle with the axes x and y, 900 with t and goesthrough GC (Fig. 7c). We performed 60 cuts from point a to GC and 60 cuts from b to GC. Wecalled this set of planes Pob1. The planes generated by the fourth viewing angle are orthogonal tothe planes of the third viewing angle and n = 60 too. We called this set of planes Pob2 (Fig. 7d).117(a) (b)Figure 6: (a) size of the frame from the CASIA-B database (320x240), (b) scaled frame usingfactor 0.25 (80x60).The features matrix for this experiment is showed in Fig. 8. The weights according to Eq. 5 arein value 1.(a) (b)(c) (d)Pyt PxtPob1 Pob2ababababGCxytxyttyxxytFigure 7: Viewing angles used in the experiments.The experiment was carried out using the first four sequences for training, and the last two astesting set. Topological information is computed in each plane cut by incremental algorithms [3]using matlab 1. The results are compared with paper [2]. Table 1 shows the correct classificationrates at rank 1 (CCR), it is also considered the correct classification rates when at least onesubject, of the two used as test is correctly classified (ALS). The results from paper [2] mentionedin table 1 were obtained using the original images without scaling to factor 0.25, therefore wecannot compare directly these values with our method.1http://comptop.stanford.edu/programs/plex-2.0.1-windows.zip118----------------------------------------3132...60----------------30------------------------------------------------...----------------2----------------1Pob2Pob1PxtPytCutTimes][ GCaCCV  ][ GCaTV  ][ GCbCCV  ][ GCbTV  ][ GCaCCV  ][ GCaTV  ][ GCbCCV  ][ GCbTV  ][ GCaCCV  ][ GCaTV  ][ GCbCCV  ][ GCbTV  ][ GCaCCV  ][ GCaTV  ][ GCbCCV  ][ GCbTV  Figure 8: Matrix of features.Table 1: The average recognition rates.Method CCR ALSFrieze(BI) C. H. Chen (2009) [2] 79.8Frieze(FD) C. H. Chen (2009) [2] 91.1Wavelet(BI) C. H. Chen (2009) [2] 77.4Wavelet(FD) C. H. Chen (2009) [2] 90.3Our method (silhouettes reduced (Fig. 6b)) 74.0 904 Conclusion and future worksIn this paper, we propose a new representation based on topological invariants for human gaitrecognition. A new approach called topological enrichment is proposed to improve the discrimi-native capacity of the representation. The experimental results demonstrate that it is possible toobtain good classification rates even though the silhouettes are reduced to factor 0.25, simulatinga video sequence captured at a long distance. It is important to notice that silhouettes incom-pleteness was not taken into account in this moment. In future works we will use other cut planesand we will study the influence of different weights to be used in Eq. 5.References[1] A. M. Bronstein, M. M. Bronstein, and R. Kimmel. Topology-invariant similarity of nonrigidshapes. International Journal of Computer Vision, 81(3), March 2009.[2] C. H. Chen, J. M. Liang, H. Zhao, H. H. Hu, and J. Tian. Frame difference energy imagefor gait recognition with incomplete silhouettes. Pattern Recognition Letters, 30(11):977–984,,August 2009.119[3] Delfinado and Edelsbrunner. An incremental algorithm for betti numbers of simplicial com-plexes on the 3-sphere. CAGD, 12, 1995.[4] M. Goffredo, J. N. Carter, and M. S. Nixon. Front-view gait recognition. In Biometrics:Theory, Applications, and Systems, pages 1–6, 2008.[5] M. Hilaga, Y. Shinagawa, T. Kohmura, and T. L. Kunii. Topology matching for fully automaticsimilarity estimation of 3D shapes. In SIGGRAPH01, pages 203–212, 2001.[6] Liang Wang, Tieniu Tan, Huazhong Ning, and Weiming Hu. Silhouette analysis-based gaitrecognition for human identification. IEEE Trans. Pattern Anal. Mach. Intell, 25(12):1505–1518, 2003.[7] S. Q. Yu, D. L. Tan, and T. N. Tan. A framework for evaluating the effect of view angle,clothing and carrying condition on gait recognition. In ICPR, pages IV: 441–444, 2006.120

Human gait recognition using topological information

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Human gait recognition using topological information

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