Spatio-Temporal Detection and Isolation: Results on PETS 2005 Datasets

Richard Souvenir John Wright Robert PlessComputer Science and Engineering Electrical and Computer Engineering Computer Science and Engineering

Washington University University of Illinois at Urbana-Champaign Washington UniversitySt Louis, MO 63130 Urbana, IL 61801 St Louis, MO 63130

Abstract

Recently developed statistical methods for backgroundsubtraction have made increasingly complicated environ-ments amenable to automated analysis. Here we illustrateresults for spatio-temporal background modeling, anomalydetection, shape description, and object localization on rel-evant parts of the PETS2005 data set. The results are ana-lyzed both to distinguish between difficulties caused by dif-ferent challenges within the data set, especially droppedframes, recovery time from camera motions, and what canbe extracted with very weak assumptions about object ap-pearance.

1 Introduction

Automated surveillance algorithms are most useful if theconditions under which they are effective are well under-stood. Comparing different algorithms for real-world sceneanalysis is challenging because different applications as-sume different constraints or prior assumptions on the en-vironment. The performance of an algorithm then dependson the implementation, the choice of representations, andwhether or not the environment being imaged fits the as-sumptions implicit in the algorithm. Since the current setof environments amenable to automated analysis is small,there is value in new algorithms demonstrating capabilitieson new data sets in new environments. The PETS data setsserve to highlight specific environmental conditions and al-low comparative analysis.

The 2005 PETS data sets [1] contain surveillance videoof coastal regions. The video is comprised of jpeg com-pressed frames whose background includes shore, waves,and sky, and whose foreground may include small and largeobjects on water. The data is challenging in several re-spects: (a) the view is not stationary, but pans-tilts-zooms tonew locations requiring the analysis of background motionto adapt to new situations, (b) the images are significantlycompressed, noisy, and the video includes dropped frames,

and (c) in some scenes the objects to be detected are quitesmall.

A collection of statistical techniques that fall under therubric of spatio-temporal video analysis have recently beenproposed for the analysis of video data. These techniquescapture spatio-temporal statistics of the video and identifypixels or regions that do not fit this statistical model. Thesetechniques have been applied globally, using PCA decom-position of the image sequence to create a set of basis func-tions to reconstruct the background [13], but it is not clearthat relevant surveillance scenes with natural backgroundmotions are well modeled with a small set of linear basisfunctions.

The opposite end of the spatio-temporal analysis spec-trum includes models that are local at each pixel, represent-ing either the intensity and variance at each pixel [9], orthe local optic flow and its variance [7]. These models suf-fer, respectively, from the inability to identify anomalousobjects at locations with large intensity changes caused byconsistent motions, and the classical challenges with com-puting optic flow in real environments.

Our approach, VAnDaL (Video Anomaly Detection andLocalization) is to model the joint distribution of spatio-temporal derivative values at each pixel; these measure-ments are well defined in each frame, the distribution cap-tures the statistics of consistent motions at a pixel, and em-pirical evaluation has in the past indicated much better per-formance in many different environments over pixel basedintensity models [8]. Furthermore, recent work shows thatthese local models at each pixel can be cleanly clustered tocapture consistent motion patterns across the entire scenein, for example, traffic scenes with different global motionpattern [12].

This paper explicitly studies two questions. The firstis: How effective are spatio-temporal derivative models incapturing the statistics of the background water motion inthe PETS2005 database? In particular, what is the effectof dropped frames and how does the time over which themodel is accumulated affect the model?

Robust image derivative measurements are estimated us-

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ing filters of large support, so when objects are detected,their position may not be accurately identified. This leadsto the second question: Given an approximate model of anunknown object in a scene with a complicated background,are there natural statistical techniques to improve the accu-racy of the object position estimate and to define a morespecific figure-ground segmentation? Our main results arethe following:

• First, dropped frames in a video have a significant im-pact on the performance of local spatio-temporal back-ground models. Automatically detecting the droppedframes and discarding corrupted temporal derivativesresults in good models of the background, at the cost ofmissing anomalous objects appearing in frames beforeand after the dropped frames. If the temporal deriva-tives are rescaled to account for the dropped frames,then the specificity of the background model recoverspartially, and does not miss the analysis of any of theframes present.

• Second, local spatio-temporal background models caneffectively accommodate applications that require dif-ferent time scales of adaptation. Furthermore, they canbe fielded effectively on cameras which pan, tilt, andzoom, as they can rapidly adapt to the new backgroundwhen the camera stops at a new viewing direction.

• Third, simple EM style algorithms can refine thespatio-temporal anomaly detection results, to providea very accurate object position, shape, and orientation,and appearance without strong priors on object appear-ance.

The next section provides a brief introduction to thespatio-temporal background modeling methods used, fol-lowed by results illustrating the quality of the backgroundmodel for different scenes using different time-decay con-stants, and in conditions with and without dropped frames.The following section considers the problem of more accu-rately localizing the anomalous object.

2 Spatio-Temporal Background Modeling

This section gives the mathematical framework for onemethod of spatio-temporal background modeling. Themethod works by keeping a model, at each pixel, of thejoint distribution of thex, y, t derivatives of intensity. Themethod described has been implemented in a real time sys-tem that runs on an 800 MHz laptop for image resolutionsup to 640 by 480, using openCV and the Intel Image Pro-cessing Library.

2.1 Spatio-Temporal Structure Tensor Field

Let ∇I(~p, t) = (Ix(~p, t), Iy(~p, t), It(~p, t))T be thespatio-temporal derivatives of the image intensityI(~p, t) atpixel ~p and timet. At each pixel, the structure tensor,Σ, isdefined as

Σ(~p) =1f

f∑t=1

∇I(~p, t)∇I(~p, t)T

wheref is the number of frames in the sequence and~p isomitted after this for clarity’s sake.

To focus on scene motion, the measurements are filtered,only considering measurements that come from motion inthe scene, that is, measurements for which|It| > k, sothat the model only considers the spatio-temporal deriva-tives with significant temporal change (in the experimen-tal section, we choosek = 10, requiring that a pixel in-tensity change by 10 grayscale values (out of 255) for thederivative measurements to be testbed by or incorporatedinto the model). Furthermore, we assume the mean of∇Ito be zero (which doesnot imply the motion is 0). Underthis assumption,Σ defines a Gaussian distributionN (0,Σ).Anomalous measurements can then be detected by compar-ing the Mahalanobis distance,∇IT Σ−1∇I to a preselectedthreshold [8]. For anomaly detection, then, this is a two partmodel, that classifies a pixel as belonging to the backgroundif either (a)It < 10, or (b)∇IT Σ−1∇I < threshold. Thisthreshold needs to be set to accommodate application spe-cific trade-offs between allowable false positive and falsenegative rates.

The structure tensor is related to optic flow. If a pixelalways views the same optic flowu, v, then all derivativemeasurements exactly fit the optic flow constraint equation:Ixu + Iyv + It = 0 [5], and the structure tensor has rank≤2. Its third eigenvector is a homogeneous representation ofthe total least squares estimate of the optic flow [3, 6, 11].

Under the assumption of stationarity,Σ can be estimatedonline as the sample mean of∇I∇IT . For non-stationarydistributions, the model can be allowed to drift by insteadassigning a constant weight,α ∈ [0, 1], to each new mea-surement:

Σt = (1− α)Σt−1 + α∇I∇IT .

This update method causes the influence of a given mea-surement onΣ to decay exponentially, with decay con-stant −1

ln(1−α) . Section 2.2 investigates the effect of spe-cific choices the forgetting factor,α. The results in the fol-lowing section mostly focus on the statistics of the spatio-temporal structure tensor. This has been used to detectanomalies in the video by comparing the Mahalanobis dis-tance,∇IT Σ−1∇I to a preselected threshold [8].

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Figure 1. Plots of the determinant of Σ accu-mulated over time with different decay fac-tors (starting from the top left, correspondingto zod5a, zog6, zod7a, zod9). The x-axis isthe frame number, and the y-axis is the mean,over the whole image, of det Σ.

Defining a threshold allows the covariance matrix to beused as a classifier to determine if a current x,y,t derivativetriple is background or foreground. For a given threshold,τ , all measurements lying inside the equi-probability ellip-soid,ε = {∇I : ∇IT Σ−1∇I = τ}, will be judged to comefrom the background distribution. The volume of this el-lipsoid is 4

3πτ32 |Σ| 12 . Suppose the foreground distribution

is taken to be uniform over a regionV ⊂ R3 containingε. Then the probability of misclassifying a measurement

generated by an anomalous object is4πτ32 |Σ|

12

3×volume(V ) , giving

P (false negative) ∝√

detΣ. Because the probability ofmisclassifying a background pixel is related todetΣ, thisvalue serves as a summary statistic, which can be used toevaluate the likelihood that foreground pixels will be inac-curately classified as background model, without consider-ing a specific threshold.

2.2 Results

This section considers the variation in the backgroundmodel specificity as a function of the time constants used inthe creation of the model, the data in the scene, and droppedframes. We give a brief description of methods to exploreeach source of variation and discuss the findings one by one.

Time decay constantsAn important free variable in defin-ing the behavior of the spatio-temporal structure tensor isthe decay factor. This factor defines the effective time win-dow used to generate the current model. For a time constant,

c, the influence of a given measurement fromt-frames ear-lier falls asexp(−t/c). The data at the output is 63% deter-mined by the pastc frames. For different time constants, weare interested in the specificity of the background models.We consider the determinant of the covariance matrix as anindicator of this specificity.

Figure 1 shows the effect of different choices of timeconstants on the convergence of the model. The spike nearframe 600 is caused by a man walking across the screenin a way that violates the background model. In practice,measurements judged to come from foreground objects canbe excluded from the model.Discussion.Several interesting features come to light; firstthe rate of convergence to a background model depends onboth the decay rate and the scene. Second, even at steadystate, the determinant ofΣ is smaller for a time constant of5 but roughly equal for time constants of 10 and 20, indicat-ing the background model distribution is non-stationary forvery short image sequences.

Data dependenceThe effectiveness of the backgroundmodel also depends on the characteristics of the scene.Since the spatio-temporal background models we considerare local, the effectiveness depends upon the local sceneappearance. Figure 2 attempts to characterize the specici-ficity of the background models for difference image re-gions. These maps are made as thedet Σ value of the pixelsover the whole video, using a time constant of 100. Theevolution of the the model over two specific pixels is shownin Figure 3.Discussion.These image maps indicate several importantproperties of the spatio-temporal background model.

The zod5 image has a largerdetΣ in the image center onthe water than the surrounding water areas. This is causedby the higher contrast in that part of the video; insofar asthis image contrast variation is due to the camera, the con-trast would also be higher in this area for anomalous objects,so the actual sensitivity to objects (as opposed to sensitivityto image derivatives not fitting the model) may be approx-imately constant. The bright spot at the waterline is due tovariations caused by significant compression artifacts thatchange the appearance of the bright white signpost. Thebright edge shown on the bottom right corner is due to smallcamera motions and a very high contrast edge in the scene.

The zod6 video illustrates two features. First, on the wa-ter, the model is less specific in the areas near the camerawhere the largest and most varied wave motion appears.Additionally, thedetΣ score is large in the sky region —this region sees large and varied motion at the beginningof the sequence as the camera pans past a large ship, afterwhich there is no variation in the area so the backgroundmodel is not updated.

The zod7a video consists of many different camera viewsand the camera pans to keep a boat approximately in the

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zod5a zod6

zod7a zod9

Figure 2. Plots of the determinant of Σ at eachpixel. Bright white corresponds to det Σ ≥2.55× 105.

field of view. Effective analysis of this video probably re-quires algorithms to explicitly detect camera motion to resetthe background background model at each new static view-ing direction.

The zod9 video is much like the zod5a video, with thesame pattern of of higher contrast in the middle of the im-age. The largedetΣ values along the horizon line arecaused by compression artifacts at this high contrast edge.

Dropped FramesFinally, we consider the effects of tem-poral discontinuities; dropped frames in the video se-quence. These have the potential to significantly affectspatio-temporal methods, because the difference betweenconsecutive frames is no longer an estimate of the temporalderivatives. Figure 4 shows the meandet Σ in three cases,(a) when the algorithm ignores the fact that some frames aremissing (just analyzes the video as is), (b) when the algo-rithm ignores all derivative estimates corrupted by missingdata, and (c) when the algorithm rescales the estimated tem-poral derivative to account for the missing frame.

Discussion.The effect of temporal discontinuities on con-vergence of the mean ofdet Σ. The red (middle) line showsresults with discontinuities removed. Note the qualitativedifference in convergence behavior, as well as the doubling

(a) video

(b) Pixel 1

(c) Pixel 2

Figure 3. Plots of the determinant of Σ overtime for two particular pixels in the videozod5a. Axes are labeled as in Figure 1. Thelarger magnitude derivatives at pixel 1 lead toa more stable model.

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(a) Determinant ofΣ

(b) Without Discontinuities (c) With Discontinuities

Figure 4. The effect of temporal discontinu-ities on convergence of the mean of det Σ.The red line (the middle of the three lines)shows results with discontinuities removed.(b) and (c) show the effect on anomaly detec-tion, pixels where the Mahalanobis distanceexceeds 15 are marked. More of the objectis marked when discontinuities are removedfrom the model.

of P (false negative) in the steady state. (b) and (c) showthe effect on anomaly detection. In each, pixels where theMahalanobis distance exceeds 15 are marked. The lowerleft corner of (c) shows the failure to mark the shoulder of apassing person because of the weaker model.

2.3 Lessons Learned

Real world applications demand robustness to video. Al-though spatio-temporal methods are affected by noisy data,they may still be effective despite temporal discontinuitiesand dropped frames (zod5aand zod9), gross quantizationartifacts (zod9), and interlacing artifacts in fast moving se-quences (zod6aandzod7).

The next section considers what might be a subsequentstep in a complete surveillance system, the analysis of alarge set of image regions identified as being anomalous.

3 Localization and appearance modeling

The results of background subtraction often comprisean incomplete and inaccurate segmentation of the figure orobject from the background. This is especially true withspatio-temporal background models that use filters withlarge support to make robust image measurements. Moreaccurate isolation of the object position and refinement ofobject appearance would facilitate higher level object recog-nition. This section considers the following problem:

Problem: Given a sequence of images, anda sequence of approximate locations of an ob-ject within each image, find a generalized objectmodel and the exact object location and orienta-tion in each frame.

We consider this problem in the context of thezod6videodata set. A representative collection of images of the zodiacand the immediately surrounding area is shown in Figure 5.

Figure 5. Six frames approximately centeredof the zodiac boat.

Given that there is no explicit model for the object be-ing tracked and each frame only contains low-quality, low-resolution representations of the object, we make the fol-lowing assumptions to make this problem tractable for thePETS zodiac boat data set zod6. First, we assume that thebackground intensity (the intensity of the water) is drawnfrom a stationary distribution. Second, we assume that theshape of the foreground object is a rigid 2D shape that maytranslate and rotate. Third we assume that the intensity ofthe foreground object (the boat) is drawn from a differentdistribution than the background (the water). We feel thatthese, or similar, assumptions may apply to a broad categoryof detection and isolation problems in surveillance.

3.1 Related Work

This problem falls between the classifications of seg-mentation, tracking, and modeling of texture and shape.There is a collection of work that studies related problems.Representative papers include the blobworld approach us-ing EM to segment regions of individual images based ontexture and color, and discovering potential objects or im-age regions useful in image retrieval [2]. For tracking, an

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online formulation uses EM to segment cars in aerial video,with a primary goal of improving tracking in multi-objectscenes [10]. Our problem differs from these works in that(a) unlike the first paper, we segment the object based onmany frames instead of just one, and (b) unlike the secondpaper, our goal is to optimize the appearance model of anobject that is visible over hundreds of frames.

3.2 Refining Localization

In this section, we formalize the problem and describeour procedure to iteratively refine the appearance and loca-tion of tracked objects in a scene.

Given a set of imagesI = {I1, I2, . . . , IN} and ap-proximate locations of an object in the corresponding imageX = {x1, x2, . . . , xN}, find the exact object location,X ={x1, x2, . . . , xN} and orientationΘ = {θ1, θ2, . . . , θN} ineach frame.

In our problem domain we consider the object to be a2D rigid object, parameterized, in framei, by positionxi

and rotationθi, although our approach allows more gen-eral transformation models. Note that we do not have aprior model of the appearance or shape of the boat. Weassume the intensity of each pixel on the object is drawnfrom a Gaussian distribution and the intensity of pixels inthe background are also drawn from a different Gaussiandistribution.

We can now describe this as a learning problem,where we observe the pixel intensities and the fore-ground/background segmentation in each frame is the hid-den data. Therefore, using an iterative-updating methodsuch as the Expectation-Maximization (EM) algorithm [4]is a natural choice. The framework of the algorithm is thefollowing is shown in Algorithm 1, which we elaborate onin this section.

The goal of this algorithm is to estimate the segmenta-tion and the texture of the foreground. This information iscaptured in the image template,M . Figure 6 shows a sam-ple template for the boat in the zod6 dataset. The choiceof initialization of the template affects the tendency of thisEM algorithm to converge to local maxima. The templatecan be randomly initialized or domain-specific knowledgecan be used to bootstrap the process. In the case of thezodiac dataset, we initialize the template with a rectangledrawn around the region detected by the spatio-temporalbackground model. The size of this rectangle was chosenby hand in the experiment, but we assume no knowledge ofthe shape of the boat within the rectangle. Figure 8 showsthe refinement of the template over the course of the EMalgorithm, and the first image shows the template used forinitialization in Algorithm 1.

Lines 5-8 describe the estimation steps of our algorithm.For each region of interest in a frame, we estimate the po-

Algorithm 1 EM Localization(I, X )1: Initialization:2: For each imageIj ∈ I create a set of equal-sized

regions of interestIROI = {IROI1 , IROI

2 , . . . , IROIN }

around the approximate locationsxj ∈ X3: Create an image maskM which contains fore-

ground/background segmentation and image texturevalues for foreground pixels.

4: repeat5: Estimation Step:6: for all IROI

j ∈ IROI do7: Using image maskM , estimate the location,xj ,

and appearance,θj , of the object inIROIj

8: end for9: Maximization Step:

10: Warp each imageIROIj ∈ IROI to align the putative

foreground pixels11: Recalculate the image mask,M , to maximize the

likelihood ofX andΘ, givenIROI .12: until image mask,M , converges

sition and appearance of the object using the template asa filter. Given our assumption that the shape of the fore-ground is constant up to a rigid transformation in the image,we convolve the template with the frame through a range arotations to find the location of highest response.

In order to maximize the likelihood that the positions,X , and appearances,Θ, estimated in line 7 represent theforeground pixels given the images,IROI , we construct atransformed stack (T-stack). The T-stack has sizeh ∗w ∗Nwhereh andw are the height and width, respectively, of theregion of interest andN is the number of images. For eachregion of interest,IROI

j ∈ IROI , we create a correspondingimage in the T-stack through translation by(xj − xj) androtation by−θj . The T-stack registers every image suchthat the pixels falling within the template — the putativeforeground pixels — are aligned along the3rd dimension.Figure 7 shows two example regions of interest, a binaryimage mask defining the valid template region, and the re-sult of warping these two images so that they are aligned inthe T-stack.

In order to update the template, we now consider eachpixel in the template model and the vector of all T-stackvalues at that pixel (some pixels may not currently not bepart of the template if they were judged to not be fore-ground in a previous iteration; we consider these pixels inthis step as well). For each vector we calculate the meanand maximum a posteriori (MAP) estimate. To segmenteach vector as foreground versus background we return toour assumption that the background, while dynamic, is reg-ular and drawn from a stationary distribution. Moreover, weassume the foreground pixels are drawn from a distinct dis-

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tribution. We employ well-known Gaussian mixture modelclustering techniques to assign each vector to one of the twodistributions and create the binary segmentation mask. Tobuild the most likely texture model for the image template,we use the MAP estimate of intensity values from the vec-tors in the T-stack in the corresponding foreground pixels ofthe image template. Figure 6 shows an example of texturedimage template.

This iterative procedure refines the image template un-til convergence. That is, the procedure terminates when theclassification of T-stack vectors does not change for consec-utive iterations. We then return the final estimate of the im-age mask,M , which represents our belief of the appearanceof the tracked object, and the positions, X, and appearances,Θ, of the object in each frame.

3.3 Results

Figure 8 shows the convergence of the model over 8 iter-ations of the algorithm, when using the longest subsequence(about 600 frames) where the camera was static. The imagetemplate was initialized using a small rectangle around theboat in the 300th frame. The convergence is quite rapid.

One question to ask is how many frames are necessaryfor this learning approach to solve for both the shape andappearance of the boat. To address this question, we ran theEM-algorithm on 5, 25, 75, 200, and the entire 640 framesubsequence. The computed template on which the algo-rithm converged is shown in Figure 9. The algorithm usesvery weak priors on object appearance and therefore re-quires many frames to converge — even using a 200 framesubsequence there are pixels far from the boat that appearin the final template.

Using the template derived from the 600 images, thecomputed rotation and orientation fits, to visual inspection,exactly on the boat in every frame (justifying the assump-tion that the object is well modeled by a rigid motion withinthe image). The position and is captured to an accuracy atleast as good as the provided ground truth data, and thereis no orientation provided in the ground truth. A video se-quence shows the results of this tracking and is available onrequest.

4 Conclusions

This report provides a performance characterization fora collection of spatio-temporal background modeling toolsfor the PETS2005 coastal data set. We consider both spatio-temporal model of dynamic background appearance, andthe subsequent, more specific isolation and localization ofindependent objects. Our conclusions may be summarizedas follows:

• Local spatio-temporal models are effective for currentsurveillance video, in spite of significant compressionartifacts, noise, and frequent pan-tilt-zoom operationof the camera.

• The affect of the current environment on the specificityof the model can be characterized and displayed do de-termine if the algorithm is likely to be effective (seeFigure 2).

• Local Spatio-temporal background models can accom-modate dropped frames, although performance de-grades significantly if the algorithm does not explic-itly check for this condition and correct the temporalderivatives.

• Finally simple EM type algorithms using very weakassumptions about object appearance can refine thespatio-temporal anomaly detection results, to providea very accurate object position, shape, and orientation,and appearance.

References

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Figure 6. A textured image template for thezodiac boat image dataset.

Figure 7. Top row shows example regions ofinterest. The middle row shows a binary im-age mask where the white pixels representthe foreground. Bottom row shows the resultof warping the top row so that the pixels ofthe image template fit the texture model ofthe boat.

Figure 8. These images show the refinementof the image template as the EM algorithmconverges.

Figure 9. The final template on which the EMalgorithm converges, for video clips of 5, 25,75, 200, and 640 frames. Note that even 200frames includes pixels that are not on the realobject, arguing the developing these modelsover very long image sequences (when avail-able) is important.

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