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Lossless compression of radiographic non-destructive testing images by region-based and entropy-optimal predictive coding L.-K. Shark, X. Y. Lin, M.R. Varley, B.J. Matuszewski Department of Engineering and Product Design University of Central Lancashire Preston, PR1 2HE, UK J. P. Smith BAE SYSTEMS Warton, Preston, PR4 1AX, UK Contact

Abstract

A novel lossless compression method to reduce the storage requirement and transmission time for radiographic non-destructive testing images of aircraft components is presented in this paper. The proposed method is shown to be highly efficient, because it utilises the availability of the component CAD model to divide the radiographic image of an aircraft component into different regions according to its material structure, thereby allow the use of different predictors in different regions. Furthermore, the parameters of predictors are optimised according to the specific image features contained in each region based on the minimum entropy criterion.

1. Introduction

Non-destructive testing (NDT) is a vital part of the quality control process in the manufacturing industries to detect defects in a manufactured component without affecting its serviceability. In the aerospace industry, the radiographic inspection method is commonly employed to detect possible anomalies in the internal structure of an aircraft component. Due to the very high resolution associated with the radiographic inspection technique and the very large physical size of aircraft components, an enormous amount of storage and an extremely large channel capacity are required to archive and to transmit radiographic NDT data. Figure 1 shows the X-ray image acquired from a relatively small aircraft component. At 8 bits per pixel, the size of 693 x 1581 pixels for this X-ray image translates into a storage requirement of over 1.04 Mbytes.

Fig 1: X-ray image of an aircraft component

Applying the LOCO-I (Low Complexity Lossless Compression for Images) method which is the kernel technology used in the JPEG lossless scheme [1] to the X-ray image shown in Figure 1, the storage required by the compressed image is 636 Kbytes which is still a considerable amount. To further reduce storage requirement and transmission time, a region-based predictive coding method was previously proposed by the authors [2], whereby different predictors are used in different regions of the radiographic NDT image with each region having the same material structure. The storage required by the region-based predictive coding method with Huffman coding is 452.68 Kbytes, giving a compression ratio of 2.36. Compared with the compression ratio of 1.68 achieved by the LOCO-I method, the overall improvement about 40%. This paper extends the previously proposed method to entropy-optimal predictive coding by optimising the parameters of the predictors according to the specific image features contained in each region to satisfy the minimum entropy criterion.

The main processing stages in the proposed method can be described as:

1. Image alignment and decomposition to map the radiographic image of an aircraft component to its wire-frame CAD model and to use the boundary information available in the CAD model to divide the radiographic image into different regions having similar material structures.
2. Entropy weighted texture-based pre-processing to identify the spatial regularity of the material structure within each decomposed region of the radiographic NDT image and to produce an entropy weighted residual image with reduced spatial redundancy.
3. Region-based and entropy-optimal predictive coding of the residual image of each decomposed region with the parameters of the predictor optimised according to the unique characteristic pattern in the residual image satisfying the minimum entropy criterion.

Using the X-ray image shown in Figure 1, these stages are presented in detail in the following sections.

2. Image alignment and decomposition

If an aircraft component is manufactured using different materials and/or structures, it will result in a radiographic NDT image consisting of different regions with different image features. Since the philosophy of predictive coding is to use local statistics of the image data to construct an estimate of the grey-level value of an image pixel, it is natural to divide the radiographic NDT image into several regions with each region having a similar image characteristic, thereby allowing the use of different predictors in different regions to improve the overall compression performance.

One possible way to achieve region-based image decomposition is to align the radiographic image acquired from the component under inspection to its corresponding wire-frame CAD model. An automatic image registration method for aligning NDT images with the CAD model has been previously proposed [3] and consists of four main processing stages, namely:

1. Feature selection to obtain a set of straight lines from the wire-frame CAD model for alignment. This is only performed once for each component type and the features selected correspond to the most visible lines in the radiographic NDT image.
2. Feature detection to extract a set of lines from the component radiographic NDT image according to the set of lines selected for alignment from the component CAD model. This is achieved by using the Hough transform operated in an iterative mode.
3. Feature matching between the set of lines detected in the radiographic image and the corresponding set of lines selected from the CAD model. This involves generation of a better correspondence between two sets of lines using a numerical combinatorial optimisation method, and minimisation of the matching error by selecting the best transformation to rotate, translate and scale the lines in the radiographic NDT image to reduce their distances to the corresponding lines in the CAD model.
4. Matching refinement to achieve high precision image alignment of the radiographic NDT image with an accuracy of 1 ± pixel. This is based on a numerical minimisation method to estimate the position and orientation of the component in 3D space projecting to the image plane.

With the radiographic NDT image correctly aligned to the corresponding CAD model, it is a relatively easy matter to utilise the structural and material information available in the CAD data to divide the radiographic image into regions of similar image properties. For the X-ray image shown in Figure 1, Figures 2 and 3 show the two regions obtained with the former corresponding to the thin carbon fibre region and the latter corresponding to the thick honeycomb region. From the viewpoint of image compression, an immediate advantage of image alignment is that the number of pixels to be coded is reduced by ignoring those image pixels belonging to the background.

Fig 2: Thin carbon fibre region

Fig 3: Thick honeycomb region

3. Entropy weighted texture-based pre-processing

According to Shannon's noiseless coding theorem [4], the entropy, which is a measure of the information content in an image, gives the minimum number of bits required to encode each pixel. If the image size is denoted by M x N pixels and the number of times that grey-level k occurs in the image is denoted by h_k , then the entropy of the image with 8 bits/pixel can be estimated as

(1)

Using Equation (1), the entropy value of the original X-ray image shown in Figure 1 is found to be 7.5073 bits/pixel. After image decomposition with the original X-ray image divided into two regions of similar image properties, the entropy value decreases to 6.8879 bits/pixel for the thin carbon fibre region and 7.1040 bits/pixel for the thick honeycomb region.

While the image of the thin carbon fibre region shown in Figure 2 is smooth with no obvious regular patterns, the image of the thick honeycomb region shown in Figure 3 is dominated by regular hexagon patterns. The spatial regularity of each region can be determined by computing the correlation coefficients of the image along the horizontal and vertical directions using

(2)

where f _x,y and f_x+Dx,y+Dy are the grey-level values of the two pixels at co-ordinates (x, y) and (x+Dx, y+Dy), and and are the expectation values(mean-grey level values of and respectively. While the lack of significant local maxima in R_Dx,Dy indicates no spatial regularity for the thin carbon fibre region, the periodicity in the occurrence of maximum R_Dx,Dy for the thick honeycomb region indicates a correlation with similar grey-level values between two image pixels separated by 11 pixels along the horizontal direction and by 8 pixels along the vertical direction.

To reduce the spatial redundancy, the thick honeycomb region can be more efficiently represented by a residual image which is the weighted difference between the grey-level values of the image pixels separated by either every 11 pixels in the horizontal direction or every 8 pixels in the vertical direction. That is

(3)

where w _x and w _y are weights for the subtraction to be performed either in the horizontal direction or in the vertical direction. To search for the optimum weight value, a convenient criterion is minimum entropy and a convenient weight for starting the search is the correlation coefficient. Based on a linear refinement strategy, the search interval is initially centred around the correlation coefficient, the entropy values are computed by stepping through the search interval with a relatively large step size, and the weight corresponding to the minimum entropy value over the search interval becomes the centre of the next search interval with a reduced width and a reduced step size. The process is repeated until the required accuracy is achieved for the weight.

For the thick honeycomb region shown in Figure 3, using equal weighting with w_y = 1 yields an entropy value of 6.2000 bits/pixel for the residual image, whereas using entropy weighting with w _y = 0.8910 produced by the search routine yields a lower entropy value of 6.1618 bits/pixel for the residual image.

A coding issue arises for those pixels lying along the image boundary which cannot be applied to the entropy weighted subtraction. With the subtraction operation performed along the vertical direction, the first 8 rows of the image pixels in the thick honeycomb region need to be stored. To reduce storage, they are coded using the predictive coding to yield a storage requirement of 8.49 Kbytes instead of 12.00 Kbytes using 8 bits/pixel.

4. Region-based and entropy-optimal predictive coding

In region-based predictive coding, two different predictors are designed for the thin carbon fibre region and the entropy weighted residual image of the thick honeycomb region based on the local statistics of each image. From Equation (2), the three largest correlation coefficients for both images were found to be R_0,-1 , R_-1,0 and R_-1,-1 , which correspond to the correlation of the current pixel with the adjacent pixels in the vertical, horizontal and diagonal directions. By linear combination of the grey-level values of these three pixels to predict the grey-level value of the current pixel, the predictor can be expressed as

(4)

where a₁, a₂, and a₃ correspond to the prediction coefficients in the vertical, horizontal, and diagonal directions, respectively. The optimal predictive coding can be based on different criteria. Minimum mean square error (MMSE) is one of them. Based on the Orthogonality Principle [5], the optimal values (in term of MMSE) of the prediction coefficients are obtained by solving the three simultaneous linear equations expressed in matrix form as

(5)

Applying Equation (4) with the two different sets of the prediction coefficients obtained from Equation (5) yields an entropy value of 3.4619 bits/pixel for the error image of the thin carbon fibre region, and 5.1595 bits/pixel for the error image of the entropy weighted residual image of the thick honeycomb region.

A better criterion for optimal predictive coding is minimum entropy, and a numerical optimisation method based on the Nelder-Mead Simplex algorithm [6,7] is used to search the optimum prediction coefficients with the objective of minimising the entropy value for each decomposed region with similar image features. The prediction coefficients produced by Equation (5) was used as the initial guess for the first iteration. Each time the algorithm produces a new set of prediction coefficients with a reduced entropy value for the error image of a decomposed region by moving from one vertex to another in a multidimensional space containing possible solutions.

Based on the two sets of optimum prediction coefficients produced by the Nelder-Mead Simplex algorithm to satisfy the minimum entropy criterion, the final entropy value is 3.4545 bits/pixel for the error image of the thin carbon fibre region, and 5.1275 bits/pixel for the error image of the entropy weighted residual image of the thick honeycomb region. Using Huffman coding, to code error images results in 145.08 Kbytes required for the thin carbon fibre region and 280.36 Kbytes required for the thick honeycomb region. Taking into consideration the initial pixels required for prediction, which are 6.25 Kbytes for the thin carbon fibre region and 11.16 Kbytes for the thick honeycomb region (including those required for generating the entropy weighted residual image), the final storage required by the compressed image is 435.47 Kbytes, giving a compression ratio of 2.46. Compared with the compression ratio of 1.68 achieved by applying the LOCO-I method to the X-ray image shown in Figure 1, the incorporation of the entropy-optimal constraint to the texture-based pre-processing and the design of predictors is seen to extend the improvement on the compression ratio from about 40% offered by the previously proposed region-based predictive coding method to about 46%.

5. Concluding remarks

By incorporating the minimum entropy criterion, this paper presents an improved region and texture based predictive coding method for compression of radiographic NDT images. The proposed method is shown to offer a significantly higher compression ratio than the LOCO-I method. Although the use of numerical optimisation methods to search the optimum weighting factor to produce the residual image and the optimum prediction coefficients is computationally intensive, it is only required to perform once for each component type. Furthermore, the similarity of image features in each decomposed region can be used to reduce the computation time by limiting the application of the minimum entropy criterion to a smaller part of each decomposed image instead of the entire decomposed image.

Acknowledgement

The support of BAE SYSTEMS for this research is gratefully acknowledged.

References

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3. Matuszewski, B.J., Shark, L.-K., Smith, J.P., and Varley, M.R., (1999). ``Automatic fusion of multiple non-destructive testing images and CAD models for industrial inspection'', IEE 7 th Int. Conf. on Image Processing and its Applications, IPA'99, pp661- 665.
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