Moving Object Detection Using MRF Model and Entropy based Adaptive Thresholding

Transcription

1 Moving Objec Deecion Using MRF Model and Enropy based Adapive Thresholding Badri Narayan Subudhi, Pradipa Kumar Nanda and Ashish Ghosh Machine Inelligence Uni, Indian Saisical Insiue, Kolkaa, , India, and Dep. of E&TC, ITER, Siksha O Anusandhan Universiy, Bhubaneswar, , India, pknanda_d13@yahoo.co.in Absrac. In his aricle, we propose an algorihm for moving objec deecion which includes wo segmenaion schemes: spaial segmenaion and emporal segmenaion. For spaial segmenaion we have used a compound Markov Random Field (MRF) Model for aribue modeling in he emporal direcion and he corresponding problem is formulaed using maimum a poseriori probabiliy (MAP) esimaion principle. For emporal segmenaion we propose a label frame difference based change deecion mask (CDM). The difference image hreshold value is obained by he proposed enropy based adapive windowing scheme. A combinaion of boh spaial and emporal segmenaions deecs he moving objecs. I is observed ha enropy based adapive windowing scheme gives beer resuls owards moving objec deecion wih less effec of silhouee han using he non window based global hresholding approach. Keywords: Objec deec ion, MAP esimaion, Modeling, Simulaed annealing, Enropy, Threshold, Gaussian disribu ion, Image segmenaion 1 Inroducion De ec ion of moving objecs from a video scene is a challenging ask in Video Processing and Compu er Vision [1]. Based on he movemens of objecs and background, video sequences can be ca egorized ino wo ypes, such as moving objec s wi h moving background and moving objec wi h fied background. In he laer case moving objec de ec ion can be accomplished by moion de ecion/ emporal segmena ion approach alone. Bu, i does no yield good resul in absence of reference frame or for he case where angible movemen of objec s is no here. A combinaion of bo h emporal segmena ion and spa ial segmenaion proved o be a beer approach owards his [1]. Moving objecs de ecion highly depends on he robus ness of he spa ial segmenaion. Markov Random Field (MRF) model [2], in his cone, is proved [3] o be beer. An early work on MRF based objec deecion scheme was proposed by Hwang e al. [3]. In his approach he spaial segmenaion was obained wih aribue modeling by MRF and Disribued geneic Algorihm (DGA) was used for MAP esimaion. Similarly he Temporal segmenaion was obained by direc combinaion of video objec plane (VOP) of he previous frame wih he

2 curren frames change deecion mask (CDM). The objecs of he previous frame were assumed o be presen in he curren frame also. This assumpion creaed difficuly in eac deecion of moving objecs and gave rise o an effec of silhouee. The effec of silhouee was less in he recenly proposed algorihm of Kim e al. [4]. They had used an evoluionary probabiliy o updae he crossover and muaion rae hrough evoluion in DGA. In order o reduce he effec of noise and illuminaion variaion in he objec deecion, Su e al. [5] had proposed an adapive hresholding approach of change deecion. In his approach, each difference image was divided ino a number of blocks and is esed for presence of region of change (ROC) wih an ROC scaer esimaion algorihm. The hreshold values all marked block conaining ROC was obained and were averaged o obain a global hreshold. In his aricle, for spaial segmenaion, we have used an edgebased compound MRF model for aribue modeling of a given video image frames [6] followed by he MAP esimaion by a hybrid algorihm (hybrid of boh simulaed annealing (SA) and ieraed condiional mode (ICM)). The compound MRF uses spaial disribuion of color in he curren frame, color coherence in he emporal direcion and edge maps in he emporal direcion. The difference images obained from he given video frames are largely affeced by illuminaion variaion and noise ha propagaes in he form of silhouee o he VOP. Hence, we propose an adapive emporal segmenaion scheme ha reduces he effec of noise. Insead of segmening he whole image a a ime by a single hreshold, we pariion he inpu image ino differen windows/blocks and segmen he objecs in each of hese windows. Then we combine he segmened objecs from each window. The window size is deermined by he enropy conen of he considered window. I is observed ha he proposed enropy based adapive window scheme gives beer resuls han ha of non window based global hresholding approach [7], where a large effec of silhouee eiss. The spaial segmenaion is combined wih adapive hresholding based emporal segmenaion o consruc he VOPs and hence moving objec deecion. The organizaion of his aricle is as follows. Secion 2 represens he moving objec deecion scheme using spaio-emporal spaial segmenaion and proposed emporal segmenaion scheme. Secion 3 represens simulaion and resul analysis. Conclusion is presened in Secion 4. 2 Moving Objec Deecion In his scheme moving objecs are deermined as follows. In a given image frame, he spaial segmenaion is obained by modeling he aribues of he image frames by an edgebased compound MRF Model followed by he MAP esimaion wih a hybrid algorihm [6]. The difference image obained from he given image frames is hresholded by he proposed enropy based adapive window scheme. The hresholded image is fused wih he labels obained from he spaial segmenaion resul o obain he final emporal segmenaion. Subsequenly, he piels corresponding o he foreground par of he emporal segmenaion is used o display he VOP.

3 2.1 Spaial Segmenaion: Spaio-emporal image Modeling and MAP Esimaion Here i is assumed ha he observed video sequence y is a 3-D volume consis ing of spaio- emporal image frames. y represen s he video image frame a ime. Each piel in y is a si e s deno ed by y s. Le Y represen a random field and y be a realiza ion of i a ime. Thus, y s deno es a spaio- emporal co-ordina e of he grid (s, ). Le denoe he segmenaion of video sequence y and he segmen ed version of y. Le us assume ha X represen he MRF from which is a realiza ion. Similarly he piels in he emporal direc ion are also modeled as MRFs. We have considered he second order MRF modeling bo h in spaial and in emporal direc ions. In order o preserve he edge feaures, ano her MRF model is considered wi h he linefield/ edge map of he curren frame and he linefields/ edgemaps of 1 and 2. In spaial domain, he prior probabiliy can be epressed as Gibb s U ( X ) disribuion 1 T,wih where z is he pariion funcion epressed T z as, e,u(x ) is he energy funcion (a funcion of clique poenial). We have considered he clique poenial in spaial direcion as V sc ( ) = α if all labels in possible se of cliques (C) are equal, oherwise V sc ( ) = α. Analogously in he emporal direcion, V ec ( ) = β if all labels in C are equal, oherwise V ec ( ) = β and for he edgemap in he emporal direcion as V eec ( ) = γ if all labels in C are equal, oherwise V eec ( ) = γ. We have used he addiional feaure in he emporal direcion and he whole model is referred as edgebased model. In our a priori image modeling he clique poenial funcion is he combinaion of he above hree erms. Hence, he prior energy funcion is of he following form U ( X ) V ( ) V ( ) V ( ). (1) cc sc cc ec The observed image sequence y is assumed o be a degraded version of he acual image sequence. The degradaion process is assumed o be Gaussian. Thus, he label field can be esimaed from he observed random field Y. The label field is esimaed by maimizing he following poserior probabiliy disribuion. P Y arg ma cc eec y X P X P Y y where ˆ deno es he es ima ed labels. The prior probabili y P( Y y ) is consan and can be discarded. Assuming decorrelaion of he hree RGB planes for he color image and he variance o be he same among each plane, he likelihood funcion P Y y X ) can be epressed as P ( N P ( X ) U ( ) y e z ( X, ) 1 3 (2 ) 3 e, 1 2 ( y )

4 In (3), variance σ 2 corresponds o he Gaussian degrada ion. Here n is a realizaion of he Gaussian noise N (µ, σ). Now using eqs (1) and (3) in eq (2) we may obain arg min y V sc ( ) V ec ( ) V eec ( ) c C. 4 ˆ is he MAP esima e and is obained by a hybrid algori hm (hybrid of SA and ICM algori hm)[6]. 2.2 Temporal Segmenaion If a global hresholding algori hm is applied in a difference image, affec ed by noise, illumina ion varia ion or shading: (i) few piels ha ac ually correspond o he background in an image frame are iden ified as changed piels, whereas hese are ac ually no, (ii) i also happens ha a piel in he difference image ha correspond o ac ual change region and lies in he lower range of he his ogram may be idenified as an unchanged piel. An adapive hresholding approach can be used o overcome hese problems. However he choice of window size is an issue. In his regards we propose an enropy based adapive window selec ion scheme o de ermine he block/ window size. Here he hreshold value for a paricular window is obained by Osu s hresholding [7] scheme. To enhance he segmena ion resuls, he resuls hus obained from CDM are verified and compensa ed by considering he informa ion of he piels belonging o objecs in he previous frame. This is represen ed as R = {r s 0 s (M 1) (N 1)}, (5) where R is a mari having he same size of he frame, s is he elemen number in he mari and r s is he value of he VOP a loca ion s. If a piel is found o have r s = 1, i is a par of he moving objec of he previous frame; o herwise i belongs o he background of he previous frame. Based on his informaion, CDM is modified as follows: if i belongs o a moving objec par in he previous frame and is label obained by spa io- emporal segmen aion is he same as one of he corresponding piels in he previous frame, he piel is marked as he foreground area in he curren frame else as a background. The modified CDM hus represen s he emporal segmena ion resul. E n r op y Based W ind ow G rowing: The basic no ion of window growing approach is o fi he window size primarily focusing on he informa ion measure of he image a differen scales. In o her words, fiing he size of he window depends on he enropy of he chosen window. In his approach an arbirarily small window (here he window size w is chosen as 5 5) is considered iniially and he enropy of he window is compu ed from he gray level dis ribu ion of he window and is deno ed by H w G 1 H log w pi e (6) i1 pi where p i is he probabili y of occurrence of i h gray level and G is he maimum

5 gray level. If he enropy of he window is comparable o some fracion of he enropy of he whole image, (represened as Th), ha window is chosen for segmenaion (by Osu s hresholding [7]); o herwise he window will be incremen ed by w (here w is considered 2) and he condi ion will be es ed again. The window will be fied if he oal image is ehaus ed. The final hresholded image is obained by aking union of each considered hresholded windows. 3 Simulaions and Resul Discussion In order o es he effec iveness of he proposed approach, we have esed our algorihm in Canada raffic video sequence as presened in Fig. 1. This video conains hree objecs such as a black car, a whi e car and a person moving a differen speeds. Fig. 1 (a) shows he original 3 rd, 4 h, 5 h and 6 h frames of Canada raffic video sequence. The corresponding spa ial segmena ion resul s obained by edgebased model approach are shown in Fig. 1 (b). The MRF model Parame ers used for Canada raffic video sequence are α = 0.01, β = 0.009, γ = and σ = 3.0. Here he MRF model parameers are deermined on rial and error basis. JSEG based spaial segmenaion of hese frames are displayed in Fig. 1(c). I is observed from hese resuls ha he region c o n a i n i n g he black car (lef side of he image) and he person in he lawn are merged in o background hence very difficul o idenify. I is o be noed ha he edge based spaial segmenaion scheme could segmen all he moving pars and he saic pars while preserving he boundary accuraely. As seen from Fig. 1(c), use of global hresholding in emporal segmenaion could no deec he black car as well as he man properly and hence he effec of silhouee is observed. As observed from Fig. 2(f), use of adapive hreshold could deec all he hree moving objecs (black car, whie car and he person) properly. In order o measure he performance quaniaively, ground ruh images have been creaed manually. The misclassificaion errors obained for differen frames are: 4h frame: 82 piels, 5h frame: 91 piels and 6h frame: 80 piels. Correspondingly Ou s mehod produced 151, 131 and 124 piels of error. 4 Conclusions In his aricle, a problem of moving objec de ecion is addressed. A compound MRF model is used here o model bo h spaial and emporal aribues of he video image frames. Corresponding MAP esima e is obained by a hybrid algori hm ha converges fas. For emporal segmenaion we have used a label frame difference as opposed o an original image frame difference. The hreshold value for he difference image is de ermined using an adapive hresholding algorihm whose window size is chosen by he enropy measure over he window. I is observed ha his approach gives beer resuls compared o original frame difference CDM followed by Osu s hresholding approach [7], as

6 he effec of silhouee is less. References 1. Bovic, A. L.: Image and Video Processing. Academic Press, New York (2000) 2. Li, San Z.: Markov Random Field Modeling in Image Analysis. Springer, New York (2001) 3. Hwang, S. W., Kim, E. Y., Park, S. H., Kim, H. J.: Objec Eracion and Tracking u s i n g Geneic Algorihms. Proceedings of Inernaional Conference on Image Processing 2 (2001) Kim, E. Y., Park, S. H.: Auoma ic Video Segmenaion using Geneic Algorihms. Paern Recogniion Leers 27 (11) (2006) Su, C., Amer, A. : A Real Time Adap ive Thresholding for Video Change Deecion. Proceedings of IEEE Inernaional Conference on Image Processing (2006) Subudhi, B. N., Nanda, P. K.: Compound Markov Random Field Model Based Video Segmenaion, Proceedings of SPIT-IEEE Colloquium and Inernaional Conference 1 ( ) Osu, N.: A Thr esho ld Selec ion Mehod from G ra y -Level Hisograms. IEEE Transacion in Sysem, M a n and Cyberneics 9 (1) ( ) (a) Original f r a me no. (3 r d, 4 h, 5 h, 6 h ) (b) Spaial segmenaion resuls using compound MRF model (c) Comparison wi h JSEG based spaial segmena ion scheme (d) Temporal segmenaion resuls using Osu s based hresholding (e) Deeced moving objecs using Osu s based emporal segmenaion (f) Temporal segmen a ion resuls using proposed adap ive hresholding (g) Deeced moving objecs using proposed adapive hresholding F ig. 1. VOP generaion of Canada raffic video sequences