Preliminary validation of content-based compression of mammographic images

Transcription

1 Preliminary validation of content-based compression of mammographic images Brad Grinstead I, Hamed Sari-Sarraf I, Shaun Gleason II, and Sunanda Mitra I I Department of Electrical and Computer Engineering, Texas Tech University II Oak Ridge National Laboratory ABSTRACT This paper presents some preliminary validation results from the content-based compression (CBC) of digitized mammograms for transmission, archiving, and, ultimately, telemammography. Unlike traditional compression techniques, CBC is a process by which the content of the data is analyzed before the compression takes place. In this approach the data is partitioned into two classes of regions and a different compression technique is performed on each class. The intended result achieves a balance between data compression and data fidelity. For mammographic images, the data is segmented into two non-overlapping regions: (1) background regions, and (2) focus-of-attention regions (FARs) that contain the clinically important information. Subsequently, the former regions are compressed using a lossy technique, which attains large reductions in data, while the latter regions are compressed using a lossless technique in order to maintain the fidelity of these regions. In this case, results show that compression ratios averaging 5-10 times greater than that of lossless compression alone can be achieved, while preserving the fidelity of the clinically important information. Key Words: fractal encoding, content based compression, digital mammography, mammogram compression, region of interest 1. BACKGROUND Throughout the years there has been significant improvements in the transmission and archiving of digital information. However, these achievements cannot rival the perpetual growth in the amount of data produced. This is especially true in the medical field, where there is a unified movement toward the digital age. This movement faces difficult challenges in the areas of transmission and archiving for telemedicine applications. As a specific example, consider that there is a movement towards full-field digital mammography, which is motivated primarily by the improved image quality of digital mammograms over the traditional film-based approach. In fact, early in 2000, the FDA approved for the first time a digital mammography system that can now be used for routine breast cancer screening. Using the statistics from , there are 61 million women in the U.S. who need mammograms. With a targeted 75% compliance, there would be 46 million screening exams per year. At 250 megabytes of data per exam (using digital mammography), the annual volume could exceed 11.5 petabytes. To handle (i.e., archive, transmit, and process) this volume of data requires significant advances in all areas of telecommunication, especially, in information compression. 2 For years there has been a debate among researchers over which class of compression techniques is appropriate to employ for medical images in general, and for mammograms in particular. 3-5 The signal processing community has been advocating lossy compression techniques on the grounds that they can achieve a large reduction in data (compression ratios of up to 100:1). However, these techniques do not retain all of the original information contained in the data. In other words, these techniques produce a decompressed, or reconstructed, image that is not identical to the original image. It is for this very reason that the medical community has sided with lossless compression techniques that retain all of the information content of the original data (resulting from a perfect reconstruction) at the cost of achieving only a small reduction in data (compression ratios of no more than 3:1). In a previous paper 6, the authors presented an alternative compression approach that aims to achieve a balance between data reduction and data fidelity. In this approach, prior to compression, the mammogram is automatically segmented into two non-overlapping regions: (1) focus-of-attention regions (FARs) that contain the important segments of the data, and (2) Corresponding Author Bradley.Grinstead@ttu.edu

2 background regions. Subsequently, the former regions are compressed using a lossless compression technique (maintaining fidelity), while the latter regions are compressed using a lossy technique (attaining large reductions in data). This process is referred to as content-based compression (CBC). Content-based compression is not a new concept in itself, 7,8 but the automatic segmentation of the image into focus-of-attention regions and background regions is. 2. SEGMENTATION OF DIGITAL MAMMOGRAMS FOR CBC In screening mammography the important information sought by radiologists includes microcalcifications, masses, ducts, and the breast boundary. These regions often constitute a small portion (less than 15%) of the mammogram. Thus, a successful segmentation of these events from the background regions will make this a prime candidate for CBC. In this case, background regions can be defined as connective tissue plus the non-breast regions of the image. Recall that subsequent to this segmentation step a combination of lossy and lossless compression techniques can be employed to achieve large reductions in data while maintaining data fidelity within the areas of interest. Our approach to accomplishing this segmentation step for mammographic images employs fractal encoding. The primary motivation for pursuing a fractal-based approach for data segmentation is that fractal encoding is ideal for characterizing the cloud-like texture that represents the normal background tissue in mammograms (see Figure 1) 9,10. Therefore, this scheme can be used to flag structures that appear to be different from the background tissue. Fractal encoding exploits the property of partitioned self-similarity of images. 11 This means that the image can be composed of transformed parts of itself. In computing the coefficients of this transform, or map, it is assumed that each sub-region of the image can be described (in the sense of minimizing a dissimilarity metric) in terms of another sub-region. The latter sub-region belongs to a pool of domains, D, of the map, while the former belongs to the range pool, R. If a given sub-region in D cannot be mapped to any region in R (i.e., their measure of dissimilarity is greater than a specified threshold), then R is further partitioned into smaller sub-regions. This process continues until either a similar sub-region from D is found, or a specified minimum partition size, S min, is reached. (a) Figure 1. Texture similarity between (a) a synthesized fractal image and (b) the normal background tissue in a digitized mammogram. (b) In the first of two pilot studies conducted thus far 9, it was shown that for sub-regions in R containing the clinically important information, S min would be reached. The reason for this is that the visual appearance of such events is significantly different from that of the background structures. Therefore, the sub-regions in D that can be mapped to those areas are expected to be nonexistent [Figures 2(a) and 2(b)]. Sub-regions for which S min is reached along with their 8-neighbors make up the FARs, as is seen in Figures 2(c) and 2(d). This hypothesis was further tested in the second pilot study. 12 This process of automatically segmenting FARs from background regions is known as FAR generation, or FarGen.

3 Eighty, 12-bit, 50 micron/pixel mammographic images were obtained from the University of Chicago s database and were used to carry out this second pilot study. These mammograms were collected from 4 different hospitals and included 45 normal and 35 abnormal cases. Cases containing biopsy-proven microcalcifications were chosen at random and the microcalcification locations were marked by experienced radiologists. Each of the mammograms was divided into nonoverlapping 512x512 sub-images in order to mitigate problems caused by global nonuniformities. Analysis of the data generated by performing FarGen on these mammograms showed that on average FARs constituted only about 17% of the input data, but, at the same time, these FARs contained 92% of the clinically important information (in this case, biopsyproven microcalcifications). (a) (b) (c) Figure 2. (a) A sub-image of a digitized mammogram with microcalcifications clustered in the lower right hand corner of the image. The microcalcifications have been circled for ease of viewing. (b) Quadtree partitioning of (a) as a result of fractal encoding. (c) Those sub-regions in (b) that never satisfied the similarity condition and their 8-neighbors. (d) Input sub-image (a) segmented into FARs and background regions (black areas). (d) 3. COMPRESSION STRATEGY The performance of CBC on a mammographic image depends on two things: (1) the successful segmentation of the clinically important data from the background regions, and (2) the compression strategies employed to obtain a balance between data reduction and data fidelity. Therefore, once FARs have been generated, separate compression techniques can be applied to the FARs and the background regions. In this case, it was decided to perform lossless compression (no distortion, low data reduction) on the FARs, and lossy compression (high data reduction, some distortion) on the background regions.

4 Notice the irregular shapes of the FARs in Figure 2(d). These irregular shapes make it difficult to perform CBC. There are a few techniques we can use in order to simplify the encoding process. Observe the fact that in some cases FARs surround small areas of background regions. Including these small islands of background regions with the FARs simplifies the encoding process while preserving some contextual information for the radiologists. Therefore, an area-opening operation is performed to incorporate these small islands into FARs [Figure 3(a)]. This operation has the effect of simplifying the boundaries, which allows us to grow bounding boxes within the FARs. These bounding boxes give the locations of a set of small images that collectively make up the FARs, as seen in Figure 3(b). Once the locations of the FARs have been determined, there are several content-based compression strategies that can be employed. (a) Figure 3. (a) FARs after the area-opening operation, and (b) the set of small images that collectively make up the FARs. (b) First, knowing that FARs constitute, on average, roughly 17% of the image, a compression ratio of approximately 5:1 can be achieved by setting the background regions to zero and keeping only the FARs. Using a standard lossless coding technique could bring that compression ratio up to 10:1. This however, would not allow the background structures, which are used by radiologists for context, to be seen. Another strategy is to use a combination of lossy and lossless coding to preserve the contextual tissue and structures, while preserving the fidelity of the data within FARs. This is the strategy that we have chosen to employ. The contextual structures can be retained by using a standard lossy compression technique on the background areas, while losslessly encoding the FARs preserves the fidelity in the areas of interest. Decoding the image consists of superimposing the results of the lossless decoding of the FARs on top of the results of performing the lossy decoding on the background regions. The cost of retaining the contextual structures comes in the form of lowering the overall compression ratio. There are several directions that can be taken when performing the lossy coding on the background structures. The first method can be seen in Figures 4(a)-4(d). In this situation, FARs are segmented out of the original image and lossy compression is performed on the resultant image. 6 The decoded FARs are then superimposed over the decoded background. This is not a very good solution because many transform-based compression techniques cause ringing to appear around the hard edges and transitions as seen in Figure 4(c). Subsequently, when the decoded FARs are superimposed over the decoded background the eye is drawn to the artifacts rather than to the microcalcifications, as is seen in Figure 4(d). However, if lossy encoding is performed on the entire sub-image, the decoded image can be combined with the losslessly decoded FARs to produce the results shown in Figure 4(e). In this case, there are no ringing artifacts to obscure the presence of the microcalcifications. There is a small amount of overhead involved in lossily compressing 100% of the image, rather than the average of 83% obtained by the removal of FARs. However, this extra overhead is trivial compared to the amount of data generated by the lossless coding of FARs. The results presented in this paper were obtained using this last technique.

5 (a) (b) (c) (d) Figure 4. (a) A sub-image of a digitized mammogram. (b) Sub-image with FARs removed. (c) Results of lossy compression of (b). (d) The losslessly encoded and decoded FARs superimposed over (c). Notice that the presence of the microcalcifications is obscured by the ringing artifacts. (e) Results of performing lossy compression on the entire sub-image and then superimposing the decoded FARs. There are no disturbing artifacts here. (e)

6 4. RESULTS There are 2 main formats used for the storage and processing of digital mammograms. Most digital film scanners have a resolution of 50-micron/pixel, while most computer-aided diagnosis (CAD) systems perform their operations on 100- micron/pixel data. In order to validate CBC for digital mammograms we have processed mammograms of both types. For this study, 35, 50-micron/pixel and 50, 100-micron/pixel mammographic images were obtained that contained biopsy-proven microcalcifications. Microcalcification locations for each mammogram were marked by experienced radiologists. As in the pilot study, the images were divided into 512x512 non-overlapping sub-images (see Figure 5), each of which were processed independently. The FarGen parameter controlling the minimum partition size, S min, was held constant for each dataset, as was the parameter threshold, which controls how likely it is that the minimum partition size will be reached for regions in R that contain clinically important information. (a) Figure 5. (a) Original 100-micron/pixel mammogram and (b) its non-overlapping 512x512 sub-images (b) Once FARs have been generated for each sub-image, they are encased in bounding boxes [Figure 3(b)] by a simple region growing technique. Next, the information contained within these bounding boxes is losslessly compressed using adaptive arithmetic coding 16, while the entire sub-image is lossily compressed using Embedded Zerotree Wavelets (EZW) 14 at a compression ratio of 80:1. Hereafter, we will denote any image that has been compressed and decompressed using CBC to be a CBC image. Table I shows the CBC results generated using this technique. The column for Threshold gives the value for the threshold parameter used in the fractal encoding process for each run. Notice that the higher the threshold value, the more likely it is that a given sub-region in R will have a match and, therefore, the lower the percentage of the image contained within FARs and the higher the compression ratio.

7 Table I. Microcalcification coverage and compression results for the 100- and 50-micron/pixel mammograms Threshold Average Percent of Image Contained w/in FARs Average Percent of Microcalcifications Contained w/in FARs 100-micron Data Average Min Max Median % % % % Lossless Threshold Average Percent of Image Contained w/in FARs Average Percent of Microcalcifications Contained w/in FARs 50-micron Data Average Min Max Median % % % % % % Lossless The expression for calculating the CBC compression ratio for a single mammogram is: O CR =, O S + 80 (1) where O is the original file size of the mammogram, S is the size of the file generated by performing the lossless encoding on the image FARs, and 80 is the compression ratio used when performing EZW on the entire image. Recall that FarGen is based around minimizing a dissimilarity metric, i.e., the information in the image that is different from the rest of the image is contained within FARs. Thus, by lowering the dissimilarity threshold, more of the image is contained within FARs. Therefore, in order to increase the microcalcification coverage it is necessary to lower the dissimilarity threshold and increase the percent of the image contained within FARs, which consequently lowers the compression ratio. This tradeoff between compression ratio and microcalcification coverage can be seen in Figure 6. Here we use the term microcalcification coverage to denote the percent of all microcalcifications that actually lie within FARs. Notice in Table I that there is a rather large difference in the CBC compression ratios for the 50- and 100-micron/pixel datasets. There are a couple of reasons for this difference. The mammograms in the 100-micron/pixel dataset were cropped to contain the breast and a small amount of the non-breast portion of the film, whereas the 50-micron/pixel images are the complete mammogram (i.e., the breast and all of the non-breast portions of the film). The larger amount of non-breast area in

8 the 50-micron images should mean that a higher compression ratio will be reached because less of the image is contained within FARs. However, compare the results for the 50-micron data at a threshold of 1.40 and the 100-micron data at a threshold of 1.9. In this case, the percent of the images contained within FARs is roughly equivalent, but the compression ratio is still lower for the 100-micron/pixel data than that obtained by the 50-micron/pixel data. This suggests that the resolution of the image is lowering the overall compression ratio. This effect is currently being investigated. Figure 6. The tradeoff between compression ratio and microcalcification coverage The results shown in Table I show that, depending on the desired microcalcification coverage rate, CBC compression ratios can be reached that average 5-10 times greater than lossless compression alone can achieve. In addition, the information in the areas of interest are guaranteed to be free of distortion, which would not be the case if lossy compression alone were applied to the mammogram. 4.1 Validation and discussion of results The positive impact of the use of computer-aided diagnosis systems as tools to aid radiologists is well known and well documented. 17 Research in computer-assisted screening and diagnosis has been extensive over the past few decades, 18 leading to the development of commercially available systems. The FarGen scheme for mammographic images was originally designed for use within such a system. It is for this reason that we have chosen to use a CAD system to validate our CBC results. The CAD system chosen for this validation is one designed by researchers at the University of Chicago. This CAD system utilizes a three-stage process as shown in Figure 7. The first of these is intended to remove the large background regions from the breast area of the images and to simultaneously accentuate the microcalcifications. Within the second module, the intensity values of the digitized mammogram are analyzed once more but, this time, locally and guided by the results of the first module. In the final step, the results of screening are reported after the application of a classifier to the extracted features. It was decided to use the output of Module 1 for the validation of the CBC results.

9 Figure 7. Three main modules of the University of Chicago s CAD system Module 1 employs a simple and effective method to accentuate the microcalcifications. First, a heuristic segmentation algorithm separates the breast from the non-breast regions. Then, an 11x11 convolution is performed within the breast to accentuate the microcalcifications. Finally, a global thresholding is employed to keep only the top 2% of the convolution results that lie within the breast. Figure 8(a-c) shows a sub-image of a mammogram as the convolution and thresholding are performed. Also shown, is the same process applied to a CBC image with a compression ratio of 6.32:1 [Figure 8(d-f)]. The output of Module 1 for the original images was compared to the output for the CBC images (see Table II) yielding the following results: For the highest compression ratio and lowest microcalcification coverage rate (threshold = 2.0 for the 100-micron/pixel data), 93% of the microcalcifications were detected. This is an 11% gain over the microcalcifications that were covered by FARs (see Table I). For the lowest compression ratio and highest microcalcification coverage rate (threshold = 1.7 for the 100-micron/pixel data), 97% of the microcalcifications were detected. This is a 2% gain over the microcalcification that were covered by FARs (see Table I). Higher compression does not necessarily mean lower detection rates. The mammogram from the 100-micron dataset that had the highest compression ratio (16.84:1) also had the highest detection rate (100%, see mammogram 20 in Table II), whereas the mammogram with the worst detection rate (0%, see mammogram 22 in Table II) had an average compression ratio (8.78:1). This suggests that there is not a direct relationship between microcalcification detection and the compression ratio. Notice in Table I that for a threshold of 2.0, an average of 15% of the image was contained within FARs. Keeping only the information contained within FARs (leaving the background black as in Figure 2(d)) yields a compression ratio of 6.62:1. Performing lossless compression on these FARs could give a total compression ratio of 13:1. In this case, only 82% of the microcalcifications would be detected. However, by performing CBC on the mammogram we get 93% of the microcalcifications detected, with an overall compression ratio of 8.42:1. In addition, we can provide the radiologists with the context information contained in the connective tissue.

10 (a) (d) (b) (e) (c) Figure 8. (a) On the left is a sub-image of the original mammogram. (b) Result of performing the 11x11 convolution on (a) in order to accentuate the microcalcifications. (c) The resulting image is then thresholded to keep only the top 2% of the convolution results. (d) The right column shows this same process on a CBC sub-image with a CBC compression ratio of 6.32:1. (e) The results from performing the convolution (f) and the global thresholding are also shown. The microcalcifications have been circled for ease of viewing. (f)

11 Table II. Microcalcification (MC) detection and coverage results for the 100-micron/pixel data at thresholds of 2.0 and 1.7. Here we use the term detection to denote microcalcifications that survive the convolution and thresholding process. The term coverage is used to denote microcalcifications that are contained within FARs. Threshold Mammogram Verified Microcalcifications MCs Detected in Original MCs Detected in CBC Image MCs Detected in CBC Image MCs Contained w/in FARs MCs Contained w/in FARs Microcalcifications Detected Microcalcifications Covered % 93.02% 96.87% 82.34% 95.01%

12 5. CONCLUSIONS AND FUTURE WORK In this paper, we have presented the results of a study substantiating the efficacy of applying content-based compression to mammographic images. This concept is realized by the application of fractal encoding to generate a collection of subregions, namely FARs, that contain the clinically important information of the image. Subsequently a combination of compression techniques is applied to generate results that are a balance between data compression and data fidelity. We have shown that compression ratios can be reached that average 5-10 times that which lossless encoding can achieve, while preserving the fidelity of the data within the areas of interest. The CBC results were validated using the output of the first stage of a computer-aided diagnosis system. Further work needs to be done in the FAR generation process to improve the microcalcification coverage as well as the compression ratio. In addition, we intend to conduct an observer study in which the CBC of mammographic images is validated by radiologists. ACKNOWLEDGEMENTS The authors would like to thank Dr. Bob Nishikawa of the University of Chicago for providing us with digital mammograms and their verified microcalcification locations. In addition, we would like to thank the National Science Foundation for their funding and support. REFERENCES 1. The Breast Cancer Resource Center of the American Cancer Society ( 2. S.J. Dwyer III, PACS Intra and Inter, 8 th IEEE Symposium on Computer-Based Medical Systems, M. G. Strintzis, A Review of Methods for Medical Images in PACS, Int. J. Med. Inf. 52(1-3), pp , H. P. Chan, et al., Image in Digital Mammography: Effects on Computerized Detection of Subtle Microcalcifications, Med. Phys. 23(8), pp , R. M. Gray, et al., Evaluating Quality and Utility in Digital Mammography, IEEE Int. Conf. on Image Proc., pp. 5-8, October B. Grinstead, H. Sari-Sarraf, S. Gleason, and S. Mitra, Content-Based of Mammograms for Telecommunication, 13 th IEEE Symposium on Computer-Based Medical Systems, pp.37-42, D. Nister, and C. Christopoulos, Lossless region of interest coding, Signal Processing, 78, pp. 1-17, E.J. Halpern et al., Application of region of interest definition to quadtree-based compression of CT images, Investigative Radiology, 25, pp , June H. Sari-Sarraf, et al., "A Novel Approach to Computer-Aided Diagnosis of Mammographic Images," 3rd IEEE Workshop on Applications of Comp. Vision, December H. Li, K.J.R. Liu, and S.-C.B. Lo, Fractal modeling and segmentation for the enhancement of microcalcifications in digital mammograms, IEEE Trans. Med. Imaging 16, pp , Y. Fisher, "Fractal image compression with quadtrees," Fractal : Theory and Application to Digital Images, Y. Fisher, ed., pp , Springer Verlag, New York, H. Sari-Sarraf, et al., Front-End Data Reduction in Computer-Aided Diagnosis of Mammograms: A Pilot Study, SPIE's Medical Imaging Conf., February S. Mitra, et al., High Fidelity Adaptive Vector Quantization at Very Low Bit Rates for Progressive Transmission of Radiographic Images, J. Electronic Imaging 8(1), 1999, pp J. Shapiro, Embedded Image Coding Using Zerotrees of Wavelet Coefficients, Transactions on Signal Processing, 41(12), December 1993, pp A. Said and W. Perlman, A New, Fast, and Efficient Image Codec Based on Set Partitioning in Hierarchical Trees, IEEE Transactions on Circuits and Systems for Video Technology, 6(3), pp , June P.G. Howard, and J.S. Vitter, Arithmetic Coding for Data, Proceedings of the IEEE, 82(6), June H.P. Chan, et al., Improvement in radiologists detection of microcalcifications on mammograms: The potential of computer-aided diagnosis, Investigative Radiology, 25 pp , S. S. Gleason, H. Sari-Sarraf, K. T. Hudson, and K. F. Hubner, Higher accuracy and throughput in computer-aided screening of mammographic microcalcifications, IEEE Medical Imaging Conf., 1997.