Grayscale enhancement techniques of x-ray images of carry-on luggage (original) (raw)

Grayscale enhancement techniques of x-ray images of carry-on luggage

Besma Abidi*, Mark Mitckes, Mongi Abidi, and Jimin Liang
University of Tennessee - Imaging, Robotics, and Intelligent Systems Laboratory 317 Ferris Hall, Knoxville, TN 37996-2100

Abstract

Very few image processing applications dealt with x-ray luggage scenes in the past. In this paper, a series of common image enhancement techniques are first applied to x-ray data and results shown and compared. A novel simple enhancement method for data de-cluttering, called image hashing, is then described. Initially, this method was applied using manually selected thresholds, where progressively de-cluttered slices were generated and displayed for screeners. Further automation of the hashing algorithm (multi-thresholding) for the selection of a single optimum slice for screener interpretation was then implemented. Most of the existing approaches for automatic multi-thresholding, data clustering, and cluster validity measures require prior knowledge of the number of thresholds or clusters, which is unknown in the case of luggage scenes, given the variety and unpredictability of the scene’s content. A novel metric based on the Radon transform was developed. This algorithm finds the optimum number and values of thresholds to be used in any multi-thresholding or unsupervised clustering algorithm. A comparison between the newly developed metric and other known metrics for image clustering is performed. Clustering results from various methods demonstrate the advantages of the new approach.

Keywords: luggage scenes, threat detection, x-ray, image enhancement, decluttering, auto-thresholding, cluster validity

1. INTRODUCTION

Luggage inspection is an essential process for airports and airplane security due to the presence of large crowds (customers and personnel) and a history of terrorists’ patterns in airports and on airplanes. On the other hand, luggage inspection has always been a challenge due to the complexities present in knowing the content of each individual bag. The drastic growth in various technologies has also led to an increase in the level of sophistication and methods of device concealment by terrorists. The problems are compounded by considerations of a screener constantly gazing at a screen and seeing almost the same type of objects over and over again.

By automating or semi-automating the process of inspection at carry-on luggage stations, an increase in operator alertness, inspection speed, and customer convenience will accrue. This automation process, even at very low levels, entails processing images, highlighting items, de-cluttering scenes, and cleverly displaying information.

Intensity manipulation is used to generate richer, brighter, clearer, and cleaner versions of an image. Images’ gray-level distributions are modified using a number of common and newly developed image enhancement techniques for the purpose of increasing contrast and adjusting brightness to make the various components of the luggage scene more distinct and reduce the amount of clutter in the image. Common enhancement techniques are first applied to x-ray luggage scenes and results shown in Section 2. Section 3 deals with a novel image decluttering method, the image hashing algorithm, its variations, and its applications to x-ray luggage images. In Section 4, automation, via the use of a newly developed metric, of various aspects of the hashing algorithm and comparison to other cluster validity measures are presented.

2. APPLICATION OF COMMON ENHANCEMENT TECHNIQUES TO LUGGAGE SCENES

In this section, common image enhancement methods are applied to raw x-ray data of luggage scenes and results generated in an effort to demonstrate the valuable support image processing techniques could bring to screeners and the performance improvement that will ensue from incorporating these techniques in luggage inspection tasks.

2.1. Linear regression

The first basic procedure applied to x-ray luggage data is linear regression which provides for the “stretching” of the pixel range within a given image so that the maximum and minimum pixel values cover a wider range (or all of the range), providing an enhanced image from the original. Linear regression can be mathematically formulated by equation (1)

g(x,y)=a×f(x,y)+bg(x, y)=a \times f(x, y)+b

[1]

1. • besma@utk.edu; phone 865 974-9918; fax 865 974-5459
     ↩︎

where f(x,y)f(x, y) is the value of the original image at pixel location (x,y)(x, y) and g(x,y)g(x, y) the resulting enhanced image value at the same location; aa and bb are coefficients to be computed according to the desired output images’ range. Figure 1 shows two examples of x-ray luggage scenes before and after linear regression.

(a)

Figure 1. (a) original scene (left) and linearly regressed image (right) of an x-ray luggage scan containing low density threat items; (b) original and linearly regressed images of an x-ray scene with high density threat items

2.2. Gamma intensity adjustment

This is a non-linear enhancement method based on the relationship given in equation (2), where gamma values less than 1 emphasize light areas and values greater than 1 emphasize dark areas of the original image when performing the conversion. II and I′I^{\prime} are the original and enhanced images, cc a scaling factor, and γ∈(−∞,+∞)\gamma \in\left(-\infty,+\infty\right).

I′=cIγI^{\prime}=c I^{\gamma}

Figure 2 illustrates the results of the gamma adjustment of an x-ray luggage image for gamma values less than and greater than 1 .

Figure 2. Gamma adjustment of original image on left using various gamma values

2.3. Logarithmic intensity adjustment

Logarithmic intensity adjustment can take several forms but typically might be expressed as:

I′=s×abs(ln⁡(I))I^{\prime}=s \times a b s(\ln (I))

I′I^{\prime} and II are the output and input gray scale images and ss is a scaling factor. This type of logarithmic intensity adjustment can produce an enhanced image as shown in Figure 3.

2.4. Standard measure technique

Another form of intensity adjustment studied and applied to x-ray images of luggage was the σ\sigma-norm or standard measure expressed as in equation (4),

Figure 3. Two examples of logarithmically enhanced x-ray scenes; original luggage scenes (left of each set) and logarithmically enhanced versions (right of each set)

I′=I−IˉSσSI^{\prime}=\frac{I-\bar{I}_{S}}{\sigma_{S}}

Where II is the original pixel value, IˉS\bar{I}_{S} the mean gray value in a neighborhood ss of image I,σSI, \sigma_{S} the standard deviation of ss, and I′I^{\prime} is the output pixel value. Figure 4 illustrates the results from the application of a standard measure technique to an xray image of low density knives.

Figure 4. Original scan (left) and its standard measure enhanced version (right)

2.5. Histogram equalization

This is a known image enhancement technique based on the alteration of the image’s histogram characteristics to provide as close to a uniform distribution as possible. Enhancement obtained by this process is shown in Figure 5.

Figure 5. Histogram equalization performed on left image and shown on right

2.5. Edge and morphological operations

The images in Figures 6 illustrate how edge detection, morphological operators, and overlay of the edge map on original image can yield much clearer and easier to interpret images.

Figure 6. Results of edge and morphological processing; (a) original image, (b) Sobel edge image of (a), © is result of (a) + (b), and (d) is a dilation of (b) overlaid on (a)

3. THE IMAGE HASHING ALGORITHM

Image hashing is done via intensity slicing and involves selecting some portion of the range of pixel values of an original image and producing an image slice containing only the selected portion of that pixel range. The objective is to progressively de-clutter an image scene and produce in separate image slices objects of different intensity values. This process should ease the screener’s task by making the threat more visible and reducing interference of harmless items within the inspection process. Intensity slicing can be performed in varying manners.

3.1. Equal interval image slicing

With this method of slicing, equal width slices are taken generally covering the entire spectrum of the pixel range. Figure 7 depicts a simple graphical representation of this process. Each one of the slices produced can also be stretched to reveal items previously hidden by lack of dynamic range. Examples of six-way image hashing at equal intervals is given in Figure 8 .

Figure 7. Illustrative schematic for the equal interval image hashing algorithm

Figure 8. Results of a six-slice equal interval image hashing algorithm applied to the two original images shown at top

3.2. Cumulative image slicing

This method of intensity slicing is similar to the equal interval slicing in that a number of equal intervals are selected first. Here however, the slices are cumulative. For example, if the original image is divided into six sub-images, the first image slice shows all pixels in sub-images 1−51-5, the second slice all pixels in sub-images 1−41-4, and so on. An example of results obtained from this technique is shown in Figure 9.

3.3. H-domes image slicing

HH-domes slicing is slightly different from the two previous hashing techniques and involves the use of the original image as a mask. Markers are constructed by subtracting a fixed value hh from the mask. The mask is morphologically reconstructed using the marker and the reconstructed image is subtracted from the mask providing hh domes of the original image. Lastly, the hh domes are structurally opened to remove small grains. Figure 10 shows a graphical representation of the h-domes concept and an image enhancement performed using this methodology. Figure 11 illustrates the algorithm application with various magnitudes of the domes.

Figure 9. (a) Results of six-slice cumulative image hashing of original images shown in Figure 8(top left and top right respectively)

Figure 10. (a) Representation of the h-domes methodology, (b) original image of luggage, © negative image of (b), and (d) result of hdomes applied to ©

Figure 11. H-domes algorithm applied to negative of original (top left) using various dome magnitudes

3.4. Histogram-based image hashing

Additional methods of intensity slicing researched included histogram based slicing. In this procedure, slicing is accomplished based upon the modified 2D histogram of the image of interest. This process is defined by bins h(i)h(i) as shown in equation (5), which are determined from the Laplace function gradient e(m,n)e(m, n) and a mapping function g(m,n);fg(m, n) ; f is the original image. An example of original and modified histograms are shown in Figure 12 (a) and (b); the corresponding original image and one slice from the automatic hashing using the modified histogram are shown in © and (d).

h(i)=∑m=1M∑n=1Ng{e(m,n)}⋅δ{f(m,n)−i}e(m,n)=∣f(m,n)−14{f(m,n−1)+f(m,n+1)+f(m−1,n)+f(m+1,n)}∣g(m,n)={1+e(m,n)}−1 or e(m,n)\begin{aligned} & h(i)=\sum_{m=1}^{M} \sum_{n=1}^{N} g\{e(m, n)\} \cdot \delta\{f(m, n)-i\} \\ & e(m, n)=\left|f(m, n)-\frac{1}{4}\{f(m, n-1)+f(m, n+1)+f(m-1, n)+f(m+1, n)\}\right| \\ & g(m, n)=\{1+e(m, n)\}^{-1} \quad \text { or } \quad e(m, n) \end{aligned}

Figure 12. Histogram-based image hashing: (a) histogram of original image, (b) transformed histogram, © original image, (d) one slice from histogram-based applied image hashing

4. AUTO-THRESHOLDING AND CLUSTER VALIDITY

In Section 3, the image hashing algorithm was applied after a user-selected number of slices had been set beforehand. Equal size intervals and equidistant locations were therefore set by dividing the overall dynamic range of the original image by the number of slices wanted by the user. In this section, the goal is to automatically select the optimum number and locations of slices, or clusters, by automatically defining threshold values in a way that results in the best quality image (or slice) for the screener’s use.

4.1. Automatic thresholding and data clustering

Scene decluttering can be achieved by either multi-thresholding or by data clustering for the purpose of slice generation. Thresholding is a simple but effective technique for image segmentation. A variety of thresholding methods have been developed 1−3{ }^{1-3}. The limitation of these techniques is that they only apply to a single-band image, such as a grayscale image or a single band of a multi-band image. For most multi-thresholding methods, the appropriate number of thresholds should be determined beforehand.

Data clustering is another effective technique for image segmentation. The advantage of the data clustering technique is that it can be applied to a multi-band image, such as a color image, a remote sensing image, or an image composed of multiple feature layers. The main disadvantage of the data clustering method is again that the number of clusters must be determined first 4−6{ }^{4-6}.

Otsu 7^{7} presented a global thresholding method using the image histogram. The scheme chooses the single optimal threshold by maximizing the between-class variance with an exhaustive search. Otsu’s method belongs to the category of clusterbased thresholding. It gives satisfactory results when the numbers of pixels in the classes are similar. Reddi 1{ }^{1} presented a fast implementation of Otsu’s thresholding method and extended it to multi-thresholding situations. The number of thresholds should however be pre-selected. Wang and Haralick 2{ }^{2} presented a recursive technique for automatic multiple threshold selection. The local properties of the image (edges) are used to find the thresholds. Pixels are first classified as edge pixels or non-edge pixels. Edge pixels are then classified, on the basis of their neighborhoods, as being relatively dark or relatively light. Histograms of the relatively dark and light edge pixels are then used to select a threshold, which corresponds to the highest peaks from the two histograms. The procedure can be recursively applied to find multiple thresholds.

In general, the optimal number of thresholds or clusters for an image is not known in advance. To determine this parameter, a common approach is to segment the image with all feasible number of clusters and then use a validity measure to compare the segmentation results 8{ }^{8}. But even when the number of thresholds or clusters in an image is the same, different methods of multi-thresholding/clustering are very likely to produce different segmented images because they are usually based on different image features. The question is then: which segmented image is best. Cluster validity indexes have been developed to compare multi-thresholding/clustering results and therefore find the optimal number of clusters. Several widely used cluster validity indexes for hard clustering analysis include the Davies-Bouldin’s index (DB) 9{ }^{9}, the Beta index 4{ }^{4}, and the Generalized Dunn’s index (GD) 6{ }^{6}. These indexes fall into the category of statistical cluster validity measures. They use cluster properties such as compactness (intra-cluster distance) and separation (inter-cluster distance) to check the quality of the clustering results. Different validity indexes of this kind vary only in the way they measure the compactness and/or separation and in the way they combine information about these two properties 5{ }^{5}. When such indexes are used to evaluate image segmentation results, they tend to select a small number of clusters as the optimal solution, therefore generating under-segmented images. These under-segmented images usually cannot provide enough spatial details in the image, especially about low intensity objects, and therefore generate biased evaluations compared to human visual assessment.

In Subsection 4.3., a new metric that determines the optimal number of clusters by comparing the spatial information changes between two consecutive segmented results is proposed. The method is based on the Radon transform, which is used to measure the spatial information of the segmented image. The number of clusters increases until the spatial information of the segmented image stops increasing and the attained number of clusters is chosen as the optimal number. This spatial information measure is also used to evaluate the segmented results obtained by different thresholding and clustering methods. Other validity indexes are first compared in Subsection 4.2.

4.2. Comparison of validity Indexes

Image segmentation involves partition of a given image into regions or segments such that pixels belonging to a region are more similar to each other than pixels belonging to different regions. Data clustering is an efficient method for image segmentation, especially useful for multi-band and multi-feature images. There are many models and algorithms for clustering, such as hard/fuzzy CC-means, ISODATA, single linkage, etc. We utilized the well-developed, hard CC-means segmentation method for comparison purposes.

As mentioned earlier, even for the same number of thresholds or clusters, different multi thresholding/clustering methods often produce different segmented images because they utilize different image features. So the problem is which segmented image is the best? Some indexes of cluster validity were proposed that can be used to compare multithresholding/clustering results.

Cluster validation refers to procedures that evaluate the results of cluster analysis in a quantitative and objective fashion. An index for cluster validity measures the adequacy of a structure recovered through cluster analysis 8{ }^{8}. The following are several of the most widely used cluster validity indexes reviewed for this research task: (a) Davies-Bouldin’s Index 9{ }^{9}; the minimization of this index appears to indicate natural partitions of the data sets. The smaller the index, the better the partition; (b) Modified Hubert’s Index 12{ }^{12} is a measure of correlation between the matrix of inter-pattern distances and the distances recovered from the clustering solution. For well separated clusters, a sharp knee is expected at the partition which contains the number of clusters that provide the best fit to the data set as measured by this statistic; © Beta Index 4{ }^{4}; the beta index is the ratio of the determination of the between-to-within cluster scatter measure. The within-cluster and betweencluster measures are derived from within- and between-cluster scatter matrices. These measures are intended to measure the separability of the data. The Beta index attains at least one (and perhaps several) maximum value(s) somewhere in the interval of cluster numbers. The ideal behavior for a Beta index would be for it to attain a unique maximum at a clustering of the data that would be regarded as “good” by a human observer; (d) Generalized Dunn’s Index 6{ }^{6}; several generalized Dunn’s indexes have been presented to overcome deficiencies in the original Dunn’s index. In our experiments v53v_{53} was used for its good performance and ease of computation. v53v_{53} is defined as

v53=min⁡1≤i≤K{min⁡1≤j≤Kj≠i{δ5(i,j)max⁡1≤k≤K{Δ3(k)}}v_{53}=\min _{1 \leq i \leq K}\left\{\min _{\substack{1 \leq j \leq K \\ j \neq i}}\left\{\frac{\delta_{5}(i, j)}{\max _{1 \leq k \leq K}\left\{\Delta_{3}(k)\right\}}\right\}\right.

where δ5(i,j)\delta_{5}(i, j) is given by

δ5(i,j)=1ni+nj(∑i∈Cid(xi,mj)+∑j∈Cjd(xj,mi))\delta_{5}(i, j)=\frac{1}{n_{i}+n_{j}}\left(\sum_{i \in C_{i}} d\left(x_{i}, m_{j}\right)+\sum_{j \in C_{j}} d\left(x_{j}, m_{i}\right)\right)

and Δ3(k)\Delta_{3}(k) defined by

Δ3(k)=2(1mk∑k∈Ckd(xk,mk))\Delta_{3}(k)=2\left(\frac{1}{m_{k}} \sum_{k \in C_{k}} d\left(x_{k}, m_{k}\right)\right)

where xkx_{k} is a data point, mkm_{k} the mean value of the cluster, and dd is a distance function.
Here δ5(i,j)\delta_{5}(i, j) measures the set distance (interclass distance) between the ith i^{\text {th }} and jth j^{\text {th }} cluster. Δ3(k)\Delta_{3}(k) measures the scatter volume (intra-class distance or within class dispersion) for the kth k^{\text {th }} cluster. The geometric objective of data clustering is to maximize the interclass distances while minimizing the intra-class distances. By the definition of v53v_{53}, a large value corresponds to good clusters. Hence, the number of clusters that maximizes v53v_{53} is taken as the optimal value of the cluster number, KK.

Experimental results were obtained from five x-ray luggage images selected to test the thresholding/segmentation methods and the validity indexes. The multi-thresholding methods, Reddi’s, Wang and Haralick’s, and the hard C-means clustering method were applied to these images. The thresholding/clustering results were evaluated by the Davies-Bouldin’s index (DB), Beta index, and Generalized Dunn’s index, respectively.

Evaluation of the segmentation results obtained indicated, in most cases, that the three types of validity indexes showed Reddi’s method to be better than Wang’s method. This was not; however, in accord with the visual evaluation. Because Wang’s method uses edge information to perform thresholding, the sliced images it produces have more structural details and better contrast and are more suitable for threat detection. The reason for this is that all three validity indexes determined their values by using the statistical characteristics of the grayscale distribution only without consideration of the spatial characteristics. The same criterion used for segmentation evaluation will produce this kind of biased results 9{ }^{9}. The following subsection describes a Radon-based metric that avoids this type of problem by accounting for the spatial information in the image in addition to statistical information.

4.3. Radon based cluster validity metric

To overcome the drawbacks of statistical cluster validity indexes, a new method utilizing both spatial and statistical information to compare segmented images is proposed. The new method is based on the Radon transform. The widely used definition of the Radon transform is given in equation (9) 10{ }^{10},

g(ρ,θ)=∫−∞∞∫−∞∞f(x,y)δ(ρ−xcos⁡θ−ysin⁡θ)dxdy0≤θ<π−ρmax⁡≤ρ≤ρmax⁡\begin{aligned} g(\rho, \theta) & =\int_{-\infty}^{\infty} \int_{-\infty}^{\infty} f(x, y) \delta(\rho-x \cos \theta-y \sin \theta) d x d y \\ 0 \leq & \theta<\pi \quad-\rho_{\max } \leq \rho \leq \rho_{\max } \end{aligned}

where g(ρ,θ)g(\rho, \theta) is the one-dimensional projection of image f(x,y)f(x, y) at offset ρ\rho and angle θ;δ(⋅)\theta ; \delta(\cdot) is the Dirac delta function. The Radon transform is commonly used in algorithms for detecting linear features in an image. It has the advantage of preserving the spatial information of the original image. In [11], an image signature based on the Radon transform is proposed. The signature has the property of reflecting both spatial and statistical information of the image.

We propose a method based on the Radon transform to determine the optimal number of clusters and to evaluate the segmented images acquired by different methods. After segmenting via a thresholding or clustering method, the original grayscale image f(x,y)f(x, y) is transformed into a new image s(x,y)s(x, y) with only KK gray levels. KK is the number of clusters. The gray values of s(x,y)s(x, y) are set to

s(x,y)=mk if f(x,y)∈kth cluster s(x, y)=m_{k} \quad \text { if } \quad f(x, y) \in k^{t h} \text { cluster }

where 1≤k≤K1 \leq k \leq K and mkm_{k} is the mean value of the kth k^{\text {th }} cluster. For thresholding methods, the kth k^{\text {th }} cluster is defined as

{f(x,y)∣Tk−1≤f(x,y)≤Tk}\left\{f(x, y) \mid T_{k-1} \leq f(x, y) \leq T_{k}\right\}

T1<T2<⋯TK−1T_{1}<T_{2}<\cdots T_{K-1} are the thresholds with T0=0T_{0}=0 and TK=Vmax⁡.Vmax⁡T_{K}=V_{\max } . V_{\max } is the maximum gray level of the image.
For a specific thresholding or clustering method, the optimal number of clusters is determined in the following manner:

1. Initialization: given an initial number of clusters k0k_{0}, segment f(x,y)f(x, y) into s0(x,y)s_{0}(x, y). Calculate the Radon transform of s0(x,y)s_{0}(x, y) in the horizontal and vertical directions, i.e., θ=0\theta=0 and θ=π/2\theta=\pi / 2 only. Denote py0=g0(ρ,0)p y_{0}=g_{0}(\rho, 0) and px0=g0(ρ,π/2)p x_{0}=g_{0}(\rho, \pi / 2)
2. Segmentation: for cluster kik_{i}, segment f(x,y)f(x, y) into si(x,y)s_{i}(x, y);
3. Projection: compute the Radon transform of si(x,y)s_{i}(x, y) in the horizontal and vertical directions to get pyip y_{i} and pxip x_{i};
4. Correlation: let

corr⁡X=h(pxi,pxi−1)corr⁡Y=h(pyi,pyi−1)\begin{aligned} & \operatorname{corr} X=h\left(p x_{i}, p x_{i-1}\right) \\ & \operatorname{corr} Y=h\left(p y_{i}, p y_{i-1}\right) \end{aligned}

where function h(a,b)h(a, b) represents the correlation coefficient between vectors aa and bb.
If corr⁡X>ε\operatorname{corr} X>\varepsilon and corr⁡Y>ε\operatorname{corr} Y>\varepsilon, go to step 5 ; else let ki+1=ki+1k_{i+1}=k_{i}+1, and go to step 2 . Here ε(>0)\varepsilon(>0) is a given threshold to stop the segmentation procedure;
5. Conclusion: select the final kik_{i} as the optimal number of clusters and si(x,y)s_{i}(x, y) as the optimally segmented image.

Because the Radon transform preserves the spatial information in the image, this method increases the number of clusters until the spatial information in the segmented image stops increasing significantly. Due to the integration process when calculating the Radon transform, this method erases the effects of noise points and small variations in the spatial information. Therefore the optimal segmented image contains enough spatial information and is not over-segmented.

The previous algorithm applies to each specific thresholding or clustering method. But in general, the optimal number of clusters and optimal segmented image depend highly on the segmentation method used. A method based on the Radon transform is also proposed to compare segmented images obtained by different segmentation methods. The emphasis here is on the segmentation of low density threat items in x-ray images. The steps are:

1. Find the low intensity component fL(x,y)f_{L}(x, y) of the original image f(x,y)f(x, y) as

fL(x,y)={f(x,y), if f(x,y)<T0, else f_{L}(x, y)= \begin{cases}f(x, y), & \text { if } f(x, y)<T \\ 0, & \text { else }\end{cases}

where TT is a given threshold defining the low intensity interval of the image;
2. Calculate the horizontal and vertical Radon transforms of fL(x,y)f_{L}(x, y) respectively denoted by pyLp y_{L} and pxLp x_{L};
3. Assume two segmented versions sA(x,y)s^{A}(x, y) and sB(x,y)s^{B}(x, y) of the same image are being compared. Define their low intensity components as

sLA(x,y)={sA(x,y), if fL(x,y)>0,0, else sLB(x,y)={sB(x,y), if fL(x,y)>0,0, else \begin{aligned} & s_{L}^{A}(x, y)= \begin{cases}s^{A}(x, y), & \text { if } f_{L}(x, y)>0, \\ 0, & \text { else }\end{cases} \\ & s_{L}^{B}(x, y)= \begin{cases}s^{B}(x, y), & \text { if } f_{L}(x, y)>0, \\ 0, & \text { else }\end{cases} \end{aligned}

1. Then calculate the horizontal and vertical Radon transforms of sLA(x,y)s_{L}^{A}(x, y) and sLB(x,y)s_{L}^{B}(x, y) denoted by pyLA,pxLA,pyLBp y_{L}^{A}, p x_{L}^{A}, p y_{L}^{B}, and pxLBp x_{L}^{B}, respectively;
2. Define the correlation between the segmented image and the original image as

corr⁡A=h(pxLA,pxL)+h(pyLA,pyL)2corr⁡B=h(pxLB,pxL)+h(pyLB,pyL)2\begin{aligned} \operatorname{corr} A & =\frac{h\left(p x_{L}^{A}, p x_{L}\right)+h\left(p y_{L}^{A}, p y_{L}\right)}{2} \\ \operatorname{corr} B & =\frac{h\left(p x_{L}^{B}, p x_{L}\right)+h\left(p y_{L}^{B}, p y_{L}\right)}{2} \end{aligned}

where function h(a,b)h(a, b) represents the correlation coefficient between vectors aa and bb.
6. If corr⁡A<corr⁡B\operatorname{corr} A<\operatorname{corr} B, we select sA(x,y)s^{A}(x, y) as the optimally segmented image. Otherwise, select sB(x,y)s^{B}(x, y). We call this “the less correlated, the better” criterion.

This method can be easily extended to compare more than two segmented images. Equation (15) reveals the correlation of low intensity spatial information between the segmented and the original images. The more clusters the low intensity portion of the original image is divided into, the more clear profiles of the low intensity objects that will be shown in the segmented image. Therefore more low intensity details are presented in the segmented image and, according to equation (15), the segmented image will be less correlated with the original image in the low intensity portion.

4.4. Results and comparison

Five images were selected to test both the validity index methods and our new algorithm. The threat objects contained in these images include: a carbon/epoxy fiber knife in xray1, an aluminum knife and an ice pick in xray2; a carbon/epoxy fiber knife, a plexiglass knife, and a green glass knife in xray3; a plastic toy gun in xray4; and 8 different-material knives in xray5.

To segment these images, two multi- thresholding methods, Reddi’s 1{ }^{1} and Wang’s 2{ }^{2} methods, and a data clustering method, hard CC-means 6{ }^{6} were used. Three validity indexes, the DB, the Beta, and the GD (v53)\left(v_{53}\right), were applied to evaluate the segmented images and to determine the optimal number of clusters. The experimental results showed that these validity indexes tend to select a small number of clusters (mostly 2 or 3 ). This is because they only utilize statistical information from the image. A large inter-cluster distance value occurs when the number of clusters is small, resulting in the validity index value being small (for DB index) or large (for Beta and GD indexes), and relatively optimal. However, segmenting the original image into a small number of clusters can not isolate the objects from each other and is not helpful for low intensity threat detection.

The results obtained by different segmentation methods were compared using the DB and GD v53v_{53} indexes. Some conclusions gained from the comparison were:

1. The DB index has nearly the same value using either the Reddi’s or CC-means methods. This is reasonable because if only grayscale information is used to segment the image, Reddi’s and CC-means methods have the same objective, i.e., minimizing the intra-cluster distance;
2. The DB index ranks Wang’s method lower than the Reddi’s or CC-means methods;
3. The GD v53v_{53} index ranks the CC-means method best, then Reddi’s method, and finally Wang’s method.

However, we reached different conclusions from the human assessment results. Figure 13 shows the segmented images of xray3 produced by CC-means, Reddi’s, and Wang’s methods, respectively, with 10 clusters each. It can be seen that the segmented images using CC-means and Reddi’s method look very similar (the result coincides with that of using validity indexes). The segmented image using Wang’s method obviously has stronger contrast, clearer object edges, and provides more low intensity spatial details than the other two images. Considering the objective of detecting low intensity threats, Wang’s segmented image looks more appealing. Slightly different conclusions were reached for the images in Figure 14, segmented in the same manner.

Figure 13. Segmented images of xray3 produced by CC-means (left), Reddi’s (middle) and Wang’s method (right) each with 10 clusters

Figure 14. Segmented images of original (a) produced by CC-means (b), Reddi’s © and Wang’s method (d), each with 10 clusters

Table 1 shows the experimental results derived using the proposed Radon transform based correlation method. The results were verified by visually checking the segmented images with a continuously increasing number of clusters. It is very difficult to find noticeable spatial structure changes in the segmented images with cluster numbers larger than the values shown in Table 1. This indicates that it is reasonable to use the Radon transform of the segmented image as a signature to measure the spatial information contained therein.

Table 1. Optimal number of clusters found by the Radon transform-based correlation method

Figure 15. Low intensity portion of the optimally segmented image of xray4 produced by CC-means (a, 10 clusters), Reddi’s (b, 9 clusters) and Wang’s (c, 10 clusters) using method based on the Radon transform correlation metric. In (d), (e) and (f) the same algorithms were applied but the number of clusters determined by the DB index instead as being respectively 3,1 , and 2 .

To compare the optimally segmented images obtained by different segmentation methods, the low intensity portion ( TT in equation (13) equals one third of the maximum intensity value) correlation coefficients between every optimally segmented image in Table 1 and the original image were calculated. Using our proposed “the less correlated, the better” criterion, all the results produced by Wang’s method were ranked as the best-segmented images. The results are consistent with those of human visual assessment. This can be seen in Figure 15, which shows the optimally segmented images of xray4 obtained by the CC-means (a), Reddi’s (b) and Wang’s © methods, respectively as opposed to the segmentation results obtained by a different validity metric.

5. CONCLUSION

This paper presented developments and results of a number of image enhancement techniques applied to x-ray images of luggage scenes. Common methods were first applied and a novel image de-cluttering technique was introduced and applied to luggage scenes. Variations of this technique were studied and automation of parameter selection addressed via the introduction and application of a cluster validity metric based on the Radon transform. The new method is proposed to determine the optimal number of clusters or thresholds when segmenting x-ray images and to evaluate the results acquired by different segmentation methods. The Radon-based metric was shown to be superior to other existing metrics, especially for the enhancement and clustering of low density threat items in luggage. Compared with other statistical validity index methods, the new method considers both the spatial and statistical information of the image. Preliminary experimental results show that the Radon-based method produces results consistent with human assessment and is also computationally efficient. Future efforts will involve more testing of the metric and slicing of low density threat images based on this metric.

ACKNOWLEDMENTS

This work was supported by TSA/NSSA grant #R011344089.

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