Statistical Edge Detection of Concealed Weapons UsingArtificial Neural Networks.

Ian Williamsa, David Svobodab, Nicholas Bowringa, and Elizabeth Guestc.

aDepartment of Engineering and Technology, Manchester Metropolitan University,Manchester, UK;

bCentre for Biomedical Image Analysis, Faculty of Informatics, Masaryk University, Brno, CZ;c School of Computing, Leeds Metropolitan University, Leeds, UK

ABSTRACT

A novel edge detector has been developed that utilises statistical masks and neural networks for the optimaldetection of edges over a wide range of image types. The failure of many common edge detection techniques hasbeen observed when analysing concealed weapons X-ray images, biomedical images or images with significantlevels of noise, clutter or texture.

This novel technique is based on a statistical edge detection filter that uses a range of two-sample statisticaltests to evaluate any local image texture differences and by applying a pixel region mask (or kernel) to the imageanalyse the statistical properties of that region. The range and type of tests has been greatly expanded fromthe previous work of Bowring et al.1 This process is further enhanced by applying combined multiple scale pixelmasks and multiple statistical tests, to Artificial Neural Networks (ANN) trained to classify different edge types.Through the use of Artificial Neural Networks (ANN) we can combine the output results of several statisticalmask scales into one detector. Furthermore we can allow the combination of several two sample statistical testsof varying properties (for example; mean based, variance based and distribution based). This combination ofboth scales and tests allows the optimal response from a variety of statistical masks. From this we can producethe optimum edge detection output for a wide variety of images, and the results of this are presented.

Keywords: Edge Detection, Segmentation, Neural Networks, Statistics, Cluttered Images, X-ray Baggagescreening.

1. INTRODUCTION

Most traditional edge detectors work on the assumption that an edge in a digital image is a discrete change inthe intensity profile of the neighbouring pixels.2 Where this is assumed the derivative of the pixel grey levels canbe computed to accurately determine the edge location, and many of the earliest derivative based edge filterswere based in this principle. Like the Roberts,3 and Sobel4edge detectors.

Gradient based edge detectors perform effectively on many synthetic or real images where the pixel intensitychange is clear, or on images with very little noise. If the edge intensity difference becomes corrupted with noiseor is eliminated completely by image texture or excess clutter as in figure 1, these derivative based edge detectorsperform more poorly as discussed by Lim.5 In these situations an image pre-processing noise suppression stagesuch as Gaussian and median filtering as detailed in Gonzalez,6 or nonlinear filtering techniques described byPerona,7 can be applied to reduce the noise effects.

Underpinned by a pre-processing smoothing stage, Canny8 introduced an analytically optimal step edgedetector based on the first derivative of a Gaussian filter. Since it’s development, Canny’s edge detector hasbeen seen as the benchmark and consequently sets the standard for all newly developed detectors, as discussedby Lim.9 However, using Gaussian smoothing prior to any edge detection is not always ideal and any thresholdvalues used in post processing steps may not always be accurate.

For further information please send any correspondence to Ian Williams or Nicholas Bowring.Ian Williams.: E-mail: i.williams@mmu.ac.uk, Telephone: +44 (0)161 244 1666Nicholas Bowring.: E-mail: n.bowring@mmu.ac.uk, Telephone: +44 (0)161 244 2246

Image Processing: Algorithms and Systems VI, edited by Jaakko T. Astola,Karen O. Egiazarian, Edward R. Dougherty, Proc. of SPIE-IS&T Electronic Imaging,

SPIE Vol. 6812, 68121J, © 2008 SPIE-IS&T · 0277-786X/08/$18

SPIE-IS&T Vol. 6812 68121J-12008 SPIE Digital Library -- Subscriber Archive Copy

Figure 1. A sample of the hand baggage x-ray images containing threat items. Images courtesy of Rapid Scan Ltd.

As an alternative to the gradient based methods and to avoid these noise filtering problems one can look foredges differently. An edge within a noisy or cluttered image like the X-ray luggage images shown in Figure. 1can be represented as an interface between two regions of differing texture as opposed to differing intensities.Representing an image edge as an interface of texture and processing on the texture allows the edge to be locatedwithout using either derivatives or smoothing techniques. If derivatives were used instead the response wouldbe unreliably noisy and many spurious false edges or edgels detected. Likewise using smoothing techniques canreduce some of the texture by representing it as image noise, which could eliminate the edge altogether.

Texture based analysis techniques are becoming more widely used for edge detection, particularly whenapplied to images corrupted with noise. DeSouza10 first described a comprehensive analysis of five parametricand non-parametric statistical tests for the detection of edges, particularly rib structures in X-ray imagery. In hiswork DeSouza10 introduced the notion of one dimensional statistical edge detection, and successfully comparedhis principle using the Student’s T test, the Fisher test, the Chi Square (χ2) test, the likelihood ratio test, andthe tau (τ) test. Although the results presented used only a single dimension of the image they can be easilyextended into two dimensional image data. The theoretical use of non-parametric statistical tests within twodimensional images has since been described by Bovik et al.11 This work detailed the successful use of two non-parametric rank based statistical edge detectors using the Wilcoxon and median rank tests. Bovik did clearlyillustrate how these rank based statistical edge detectors can outperform order statistic detectors with both noisyand clean sample images. The author further showed a comparison with a linear scheme edge detector usingan novel implementation of the Difference Of Boxes (DOB) detector.11 Subsequent work by Bovik et al12 hasenhanced this two sample statistical edge detection technique, and by using the average values of the underlyingpixels developed the Ratio of Averages (ROA) detector,12 which was suitable for overcoming high levels of specklenoise.

The authors developed two further edge detectors based around the same original two sample statistical

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principle, namely the Ratio of Order Statistics detector (ROS) and the Ratio of Blues detector (ROB).13 Bothof these detectors outperformed the original ROA detector both on edge localization and noise suppression andare described in their work (Brooks and Bovik 39).

Similar order and ranking based statistical tests were described by Beauchemin et al,14 namely the Wilcoxon-Mann-Whitney test (WMW) to effectively overcome a low signal to noise ratio of Synthetic Aperture Radar(SAR) images. Beauchemin’s work showed a robust response from this implementation of the rank based WMWtest indicating how the advantages of using similar ranking statistics come from their statistical significance beingindependent of the distribution, and also how they are robust against the presence of extreme observations.14

However the author did note that the use of statistical rank based tests for edge detection will show a loss in theoutput efficiency because only the rank of the pixel distributions is used. Huang15 also approached the notionof ranking statistical edge detection for noisy images, stating how the edge filtering and the noise suppressionshould take place at the same time to overcome the blurring effect evident with Gaussian smoothing filters.

Two dimensional edge detection using image region statistics was first described by Guest.16 Here the authorintroduced a novel edge detection filter using a pixel image mask and two sample statistical tests, namely thestudent’s T test and the Fisher test to accurately located edges in noisy histological images. Fesharaki andHellestrand17 also used a similar technique, this time implementing the T test only to successfully detect edgesin both noise-free and noise-corrupted images.

Comparisons to gradient techniques have since illustrated how these statistical methods have a robust per-formance in the presence of noise, notably Kundu et al18 who introduced a novel three phase edge detectorbased on edge detection, line detection and finally edge refinement and also by Hou19 who showed how robuststatistics can outperform derivative methods on images corrupted with high levels of impulsive noise. Qiu20 alsoillustrated how a combination of statistical hypothesis testing and dual local smoothing windows could be aneffective detector of noisy step and roof edges. Dual window methods of non-linear edge detection have recentlygrown in popularity. Cafforio et al21 used a simple isotropic dual circular window for noise robust edge detectionwhich gave a comparable response to the Canny filter.22 Lim and Jan235 showed how a T test implementationcould be outperformed by the non-parametric Kolmogorov Smirnov (KS) test on images with intense noise levels.This observed robustness to noise using these dual window techniques effectively eliminated the need for anyprior image smoothing as commonly used by the gradient techniques. Work by Bowring et al1 has since describedthe possibility of producing images superior to both the Canny filter, and Smith’s SUSAN filter24 using suchnovel statistical methods without the need for this confidence check, by simply varying the pixel mask size usedin the tests. This method was further adapted by Fan et al25 who incorporated an Artificial Neural Network(ANN) to be a fuzzy classifier for the strength of the edge found by the statistical masks. Finally more recentwork by Williams et al2627 has illustrated how combined multiple-scale masks26 and multiple tests27 can give animproved and more consistently robust response for textured edges.

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Original Grey-Scale Edge Pixel Intensity Values Statistical Mask Applied

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Figure 2. (a) An example of nine statistical masks, and (b) four different masks superimposed to an image. Each mask isdivided into two regions A and B surrounding the central pixel. The pixel values of the two regions are defined as dataset A and data set B (right). A statistical analysis of these two data sets will indicate the location of an edge with theorientation of the central line in the mask indicating the edge direction and also the mask angle.

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2. STATISTICAL EDGE DETECTION FILTER

The statistical filter used here was initially described by Guest16 and Bowring et al,1 and has been furtherdeveloped in this work. The principle of this novel filter is briefly illustrated in Fig. 2 and will be described infurther detail here.

Figure 2b shows an image section with a clearly defined edge and four statistical masks applied. These masksrepresent the different angle masks used by the statistical filer (see Fig. 2a), and are used to detect the localtexture differences in the image pixels. The principle idea behind this filter is based on the analysis of two-samplestatistical tests evaluated over these two image regions covered by each mask (A and B). On these pixel patternsa consecutive decision can be made to whether the inspected mask area contains an edge or not.

The process of the filter can be defined by the following steps:

For each pixel in the image apply the masks. For both mask regions (A and B) extract the underlying imagepixels (See Fig 2 right). Now organize these extracted image pixels into two data sets A and B. Now performa statistical analysis on these two data sets using two sample statistical tests. The value returned indicates thetextural differences in the two data sets. Rotate the mask for each mask angle used by the filter (See Fig 2a)and repeat the previous steps. Now we find the maximum of these computed statistical tests. This maximumindicates the strength or height of the texture edge and the corresponding mask angle (see Fig. 2 a) indicates theedge orientation. This process is repeated for each pixel in the image with the output edge image reconstructedpixel by pixel using these statistical test values.

This statistical difference will have a peak response when the mask lies over the intersection of two differentimage regions and therefore at the location of an edge (see Fig. 2 b mask 4). The angle of each mask alwayscorresponds to the orientation of the centre line in the mask, therefore will indicate the angle perpendicular tothe actual edge orientation. The maximum response from each test can then be used to reconstruct the outputimage pixel by pixel, with and the perpendicular mask angle Fig.(2 a) being useful in post processing and edgethinning stages.

3. STATISTICAL TESTS

Mean Based Tests The Student’s T test is a common mean based statistical test, based on the hypothesisthat two distributions will have the same or a similar mean value. The two-sample T test for two equally sizedregions is given as:

T = |x̄A − x̄B|√

N − 1sA + sB

(1)

where x̄A and x̄B is the mean of region A and B, respectively. N is the number of pixels in one region with sA

and sB being the variances of the two regions A and B.

The second mean based test used in this work is the Difference of Boxes test. This calculates the differencein the means of the two regions of the statistical mask. Usually two varying size mean filters are used,28 howeverhere we simply use the mean of the two different mask regions A and B, given as D = |x̄A − x̄B |.Variance Based Tests In some circumstances, particulary on biomedical images, the mean of the two maskregions does not differ significantly and a more robust test for statistical edge detection is to analyze the varianceof the regions. The Likelihood Ratio test based on the work of DeSouza10 is defined as:

L = −N · loge

4v2Av2

B

v4A∪B

, where v2A =

∑x∈A

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(∑x∈A

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)2

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Here vB and vA∪B are defined analogously.

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Ranking Distribution Tests The last statistical test used here checks neither the variance or the mean ofthe two regions, but simply via sorting or ranking checks for any difference in the two distributions. The testpresented here is the Mann Whitney U test. It checks the hypothesis that the two data sets under evaluationare taken from the same distribution. The statistical value U = min(RA, RB) corresponds to a rank score whichis calculated for both data sets. Here

RA =∑x∈A

⎛⎝ ∑

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⎞⎠ (3)

refer to the data originating from mask region A and region B, respectively. Measure U is the overall statisticalsignificance relating to the minimum value between RA and RB.

4. EDGE DETECTION OVER MULTIPLE SCALES

Scale is a fundamental problem within image processing. Scale apace analysis was initially defined by Witkin29

and underpins many techniques of edge detection, with the correct selection of an appropriate scale of resolutionfor processing images still being an ongoing problem. Where low level image analysis is concerned there must bean awareness of the constraints imposed from subjectively defining an appropriate selection of image scale. Forexample, when using derivative filters for edge detection the computation of the derivative must be taken overa defined image region to accurately detect the correct location of the edges. If this derivative is computed overa small location then finer scale edges will be detected and the edge filter will be more sensitive of image noise.Likewise if the derivative is to be computed over a larger region then these finer scale edges will not be detectedand larger more gradual edges will be located. Moreover with the case of larger computation or smoothingregions the detected edges can become shifted from their true location, therefore introducing location errors(LOC) in the output image. This problem introduces a trade off between the localization and the detection oftrue edges, as discussed by Park et al.30

Since low level image processing operators make no presumption about any specific further steps in processing,this single scale analysis should be approached with caution, and a multi-scale or an adaptive-scale analysis shouldbe considered. This case can be evident with any implementation of the single scale Canny filter and will illustratehow the strength of the Gaussian smoothing parameter (σ) will greatly affect the output edge detected image,resulting in different edge maps being obtained for the same input image at the different Gaussian scales.

Witkin29 first illustrated this ambiguity of generating edge maps from different scales, and defined how thereis no accurate way of subjectively deciding which scale is correct. Moreover what may appear to the user to becorrect for one application may result in inaccuracies for another. Therefore with real image analysis, having noprior knowledge of the given applications, an ideal scale for processing different images cannot be defined easily.

Since the most appropriate scale for processing every edge within a complex or real image can not be defineda priori, and to avoid the ambiguity of selecting an appropriate scale for processing an image, multiple scale andmultiple resolution edge detection has grown in popularity.30

Two main techniques are commonly used to analyze image data over many scales. The first of these works bykeeping the image sized fixed and varying the size of the processing operator applied, see the work of Park et al,30

and the second by keeping the image operator fixed and varying the scale or size of the input image, as in thework of Rosenfeld.31 It is with the first technique where the image size remains fixed and the operator changesscale that this work is concerned.

Most techniques of fixed image size multi-scale operators fall into one of two main categories, these being:

• Automated and varying scale selection based on local image properties,

• Multiple image edge detection and image edge fusion.

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When developing multi-scale detectors, there has been extensive investigation into the merits of fine-to-coarseand coarse-to-fine approaches, notably the work of Konishi32 and Bergholm.33 The merits and pitfalls of bothtechniques were also discussed by Ziou.34 What the author defined in his work was how the use of coarse-to-finetechniques can result in problems relating to the blurring and localization of the initial coarse scale. The fine-to-coarse techniques overcome this initial ambiguity, however are presented with the same localization problemwhen combining the final coarse scales. Ziou’s work overcame this ambiguity by combining the single scale imagesusing neither the coarse-to-fine or fine-to-coarse techniques. His approach used four defined step edges, namely,the ideal, the blurred, the pulse and the staircase edge. These step edge profiles are then combined using onlytwo scales, namely the most coarse scale and the finest scale, using their representation in scale space, and thesingle output image created. More recently the Wavelet Transform (DWT) has been used for effective multiplescale edge detection, both allowing the combination of scales using the coarse-to-fine technique, as in the work ofSiddiqe and Barner35 fuzzy logic techniques like Akabari et al36 and neural network techniques, see the work ofGendron and Hammack.37 Finally the non-linear Ratio of Averages detector by Bovik et al12 has been extendedto work across multiple scales of resolution by Fjortoft et all,38 to allow successful noise robust edge detectionin Synthetic Aperture Radar (SAR) images.

The techniques developed here and detailed in this work use neural networks to combine the outputs of thevarious processing scales. Since these scales are be combined in parallel using this neural network technique,any ambiguity from the coarse-to-fine/fine-to-coarse techniques is therefore eliminated. Overall the heuristicsof combining the results from the various masks scales and the overall detector accuracy is dependent on thequality of the network used.

To accurately detect all texture based interfaces using the statistical filters described earlier it would beadvantageous to combine several statistical tests over various mask sizes into one edge detector,39 creating a“Multi-scale statistical edge detector”. Through the use of Artificial Neural Networks (ANN) the output resultsof several statistical mask scales can be combined into one detector. Therefore, by combining the optimalresponse from a variety of mask scales, the optimum output for a wide variety of images can be produced.

(a) (b) (c) (d) (e) (f) (g) (h)

(i) (j) (k) (l) (m) (n) (o) (p)

Figure 3. Neural network training set consisted of the original X-ray hand luggage threat item images (top row) and thecorresponding object boundaries.

5. NEURAL NETWORKS FOR MULTIPLE SCALE EDGE DETECTION

Neural networks are applied to many areas of image processing, ranging from direct application to an image foredge detection,40 to object recognition as in the work of Suganthan41 and Peterson,42 and also image segmentationlike the techniques of Bhandarkar43 and Piccoloi et al.44 A variety of neural networks are suitable for these tasks,with the most common being the multi-layer perceptron (MLP) feed forward network.45

In the work described here, the network will take its inputs from the output of a statistical mask with,typically, there optimum statistical tests and mask sizes applied. The combination of test and scale are determined

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objectively by assessing the entire range of statistical tests over each mask size on synthetically generated testimages.

An initial network was used which allowed three input scales/tests, but which was later expanded to takeother data from the statistical filter such as all the statistical tests or all the scales. The hidden layer then hasa set of nodes, each is identical in purpose and which sum the inputs from each of the input layer nodes. Thehidden and output layers each have an activation function (

∫) which is a either a log-sigmoid transfer function,

which has the effect of normalizing or compressing the inputs into the range between 0 (off edge) to 1 (on edge),or a linear transfer function, allowing a greater accuracy with a purely linear output range.

Test A

Scale 3

Scale 2

Input Image Output Image

InputLayer

Hidden Layer

Output Layer

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Test C

Figure 4. A typical configuration of the multi-scale combined statistical/neural network edge detector. The input imageis filtered using three scales of statistical edge detector. The peak response from each detector is then processed by thepre-trained neural network which classifies these inputs as edge or non-edge, creating the desired output edge image.

A typical multi-scale edge detector is shown in Fig. 4 and works as follows. An image is pre-processed byapplying, typically, three statistical mask sizes encompassing a combination of small, medium and large scales.For each pixel on the image the optimum tests are stored, with these forming the input to a three stage MLPneural network. The network has been pre-trained on a gold standard edge image to automatically classify theinputs into the desired output response for an edge or non-edge. The output of this multi-scale approach is thenused to create the optimum output image.

Several artificial neural network (ANN) configurations were investigated during the course of this work.Initially, a standard feed forward back propagation ANN with 3 input neurons (one for each mask scale), 20hidden layer neurons and a single output neuron was used. The optimum configuration was found to require twicethe number of hidden layer neurons to input neurons, all with purely linear transfer functions, rather than thelog-sigmoid functions described earlier. If the hidden layer neurons have non-linear transfer functions then theeffect on the output image would be similar to a threshold image, where the image results were restricted by someuser defined value. Using purely linear neurons in both the hidden and output layers ensures the network outputwill always remain linear, therefore more accurately representing true grey-scale image. An Adaline networkwas also tested and performed identically to the BPN, whereas both self organizing maps and Hopfield networksperformed well as angle oriented edge classifiers. Using these unsupervised neural networks networks allowed anindependent classification of edges having similar orientations or comparable texture differences. These networksperformed similar to a texture segmentation algorithm, by accurately grouping similar edge points together intoclustered regions based on the number of neurons used in the network. For the applications used here theseunsupervised neural networks proved unsuitable and the supervised feed forward back propagation networkswere the more appropriate choice.

6. RESULTS

To effectively analyze the performance of multiple scale statistical edge detection, the initial aim was to determinethe optimum combination of scales to accurately produce the best results. The single scale analysis described

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(a) Original (b) Single Scale DoB (c) Canny σ2

(d) Multi Scale/Test

Figure 5. Original X-ray hand luggage image (a) and corresponding statistical edge detection outputs (b = single scale,c = multi-scale, d = multi-test). For comparison the Canny result (d) is shown with a Gaussian σ = 2. The multi-scaleedge detector again produces a more complete boundary of the concealed object over both single scale edge detection andthe Canny edge detector.

above showed how different mask sizes for different tests had a great impact on the results. With the non-parametric or rank based tests the larger masks produced a greater edge detection performance, however withthe mean or variance based tests a greater performance was observed when the mask size remained small.Furthermore the noise robustness of all statistical filters increased as the mask size increased, however thelocalization accuracy of the filters remains best when the mask size is small. This enforces a compromise whencombining multiple mask scales for processing complex textured edge images.

For the results presented here each test is combined with the optimum three scales of resolution determinedby the single scale analysis. Three scales of mask sizes were chosen the be a suitable compromise between thecomputational cost and the peak filter response.46

The results in the initial stage of this work(see Fig. 5, 6, 7) clearly show how the multi-scale edge detectoroutperforms the traditional Canny filter at de-cluttering the x-ray images. Furthermore the boundary of con-cealed weapons become more prominent. Even in the presence of extreme texture and occlusion the boundaryof the concealed handgun can be extracted (see Fig. 7). Future work with this technique will assess the practicalapplication within inelegant object recognition systems with an aim of improving the noise and texture robust-ness of existing techniques. Also work is currently underway in objectively assessing the performance of the edgedetectors using a novel grey-scale performance metric.46

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(a) Original (b) Single Scale DoB

(c) Canny σ2 (d) Multi Scale/Test

Figure 6. Original X-ray hand luggage image (a) and corresponding statistical edge detection outputs (b = single scale,c = multi-scale, d = multi-test). For comparison the Canny result (d) is shown with a Gaussian σ = 2. The multi-scaleedge detector again produces a more complete boundary of the concealed object over both single scale edge detection andthe Canny edge detector.

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(a) Original (b) Single Scale DoB

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Figure 7. Original X-ray hand luggage image (a) and corresponding statistical edge detection outputs (b = single scale,c = multi-scale, d = multi-test). For comparison the Canny result (d) is shown with a Gaussian σ = 2. The multi-scaleedge detector again produces a more complete boundary of the concealed object over both single scale edge detection andthe Canny edge detector.

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