The Centroid method for compressing sets of similar images

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Abstract

Similar images are images with common features, similar pixel distributions, and similar edge distributions. Fields such as medical imaging or satellite imaging often need to store large collections of similar images. In a set of similar images the image similarities represent patterns that consistently appear across all images; this results in “set redundancy”. This paper presents the Centroid method that extracts and uses these similarity patterns to reduce set redundancy and achieve higher lossless compression in sets of similar images. Experimental results with a medical image database demonstrate that the Centroid method can deliver significantly improved image compression.

Introduction

Research in data compression has grown rapidly the last 50 years producing a large number of lossless and lossy compression methods (for some excellent reviews see Netravali and Limb, 1980, Jain, 1981, Bassiouni, 1985, Rabbani and Jones, 1991, Wong et al., 1995). Data compression is possible because of data redundancies. In gray-scale digital images three basic data redundancies can be identified and reduced: the coding redundancy, the inter-pixel (or spatial) redundancy, and the psychovisual redundancy. Most data compression methods are based on the same principles and on the same theoretical compression model. Fig. 1 depicts the lossless compression model and Fig. 2 shows the more general lossy model (the lossless model can be derived from the lossy one by omitting the “Quantization” step). Pixel mapping reduces the interpixel redundancy. Quantization reduces the psychovisual redundancy. The final step of symbol encoding reduces the coding redundancy.

For individual images, this general compression model is sufficient. However, sets of similar images contain additional redundancy due to the existence of common information that appears as similar patterns across these images. Compression methods based on the current compression model only eliminate intra-image redundancy, but not this type of inter-image redundancy. The term set redundancy has been introduced by Karadimitriou (1996) to describe the inter-image redundancy. It has been shown that identifying the common patterns in sets of similar images and using them to reduce set redundancy can significantly improve compression (Karadimitriou, 1996, Karadimitriou and Tyler, 1996, Karadimitriou and Tyler, 1997).

Karadimitriou (1996) proposed the Enhanced Compression Model as a more appropriate model for compressing sets of similar images. This model includes an additional step for set redundancy reduction and it is described in Section 2. Methods that achieve set redundancy reduction are referred to as SRC (Set Redundancy Compression) methods. Two SRC methods are the Min-Max Differential method (Karadimitriou and Tyler, 1996) and the Min-Max Predictive method (Karadimitriou and Tyler, 1997). In this paper a third SRC method is described, the Centroid method (Section 3). This method creates an “average image” to capture the common patterns that appear in a set of similar images. One of the best application areas for SRC methods is medical imaging. Medical image databases usually store similar images; therefore, they contain large amounts of set redundancy. Section 4 presents the application of the Centroid method on a set of CT brain scans, and Section 5 contains some concluding remarks.

Section snippets

The enhanced compression model

The Enhanced Compression Model is an extension of the basic compression model and includes an additional step, the set mapping step (Fig. 3). Set mapping reduces the set redundancy from a set of similar images and it can be realized in different ways. One way is to implement it as an N-dimensional transform by translating the origin of the N-dimensional coordinate system, where N is the number of pixels in a given image. This N-dimensional transform can reduce the dynamic range of the pixel

The “Centroid” method

In general, predictive methods are very useful for image compression. These methods create a prediction for the value of every pixel; then the encoder stores only the error between this prediction and the pixel value. If the prediction scheme is good, then the errors are very small and have a Laplacian distribution with most of the values very close to zero. The “average image” from a set of similar images can be used to predict the pixel values in each image of the set. A simple model for

The application of the Centroid method to medical images

Medical imaging is an area in which the Enhanced Compression Model can be used very effectively. The reason is that medical images always depict parts of the same subject: the human body. Moreover, the standard procedures used in radiology result in images very similar to one another. For example, for every chest X-ray the position of the patient, the orientation of the imaging device, and the parameters used are standard. A collection of 1000 chest X-rays is significantly more serf-correlated,

Conclusion

Image compression is possible because of the existence of different types of redundancy in digital images. Current compression methods usually target the intra-image redundancies; however, sets of similar images contain significant amounts of inter-image redundancy, the set redundancy. Set redundancy can be used to improve compression in sets of similar images. This paper describes the Enhanced Compression Model that extends the current theoretical compression model by including a set mapping

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