US 20040071350 A1 Abstract Several embodiments in accordance with the invention are disclosed. An embodiment for compressing a gray scale image is described and an embodiment for decompressing the codebook produced by compressing the gray scale image is described. Of course, the invention is not limited to only gray scale images, however.
Claims(24) 1. A method of compressing an image, the image being having gray scale values, comprising:
(a) dividing the image into quadrants; (b) measuring the gray scale variation in each quadrant so that each quadrant is either a low variation_ quadrant or a high variation quadrant; (c) replacing any low variation quadrants with an estimate for the particular quadrant; (d) determining whether any high-variation quadrants can be estimated using a contractive map of the image; and if not, applying (a), (b), (c), and (d) to, the particular one or more high variation quadrants that cannot be estimated by a contractive map of the image. 2. The method of 3. The method of 4. The method of 5. The method of 6. The method of 7. The method of 8. The method of 9. An article comprising a storage medium having stored thereon instructions, that, when executed by a computing platform, results in compression of an image having gray scale values by:
(a) dividing the; image into quadrants; (b) measuring the gray scale variation in each quadrant so that each quadrant is either a low variation quadrant or a high variation quadrant; (c) replacing any low variation quadrants with an estimate for the particular quadrant; (d) determining whether any high variation quadrants can be estimated using a contractive map of the image; and if not, applying (a), (b), (c), and (d) to the particular one or more high variation quadrants that cannot be estimated by a contractive map of the image. 10. The article of 11. The article of 12. The article of 13. The article of 14. The article of 15. A method of decompressing a codebook for a compressed gray scale image comprising:
(a) forming a decompression estimate image from scalar multiples of a contractive map of a previous decompression estimate image, the scalar multiples being provided by the codebook; (b) if the decompression estimate image and the previous decompression estimate image are equal, then dividing the decompression estimate into quadrants and applying (a), (b), and (c) by treating the quadrants as the previous decompression estimate image until the codebook is empty of scalar multiples to apply; (c) if the decompression estimate image and the previous decompression estimate image are not equal, apply (a), (b), and (c) by treating the decompression estimate image as the previous decompression estimate image. 16. The method of after the codebook is empty of scalar multiples to apply to contractive maps: scaling the result image based, at least in part, in a mean gray scale value for the compressed gray scale image, and reconstructing those quadrants for which a mean gray scale level has been stored. 17. The method of 18. The method of 19. An article comprising: a storage medium having stored thereon instructions, that, when executed by a computing platform, results in decompression of codebook for a compressed gray scale image by:
(a) forming a decompression estimate image from scalar multiples of a contractive map of a previous decompression estimate image, the scalar multiples being provided by the codebook; (b) if the decompression estimate image and the previous decompression estimate image are equal, then dividing the decompression estimate into quadrants and applying (a), (b), and (c) by treating the quadrants as the previous decompression estimate image until the codebook is empty of scalar multiples to apply; (c) if the decompression estimate image and the previous decompression estimate image are not equal, apply (a), (b), and (c) by treating the decompression estimate image as the previous decompression estimate image. 20. The article of after the codebook is empty of scalar multiples to apply to contractive maps: scaling the result image based, at least in part, in a mean gray scale value for the compressed gray scale image, and reconstructing those quadrants for which a mean gray scale level has been stored. 21. The article of 22. The article of 23. A method of compressing an image, the image being having gray scale values, comprising:
(a) dividing the image into quadrants; (b) determining whether any quadrants can be estimated using a contractive map of the image; and if not, recursively applying (a) and (b) to the particular one or more quadrants that cannot be estimated by a contractive map of the image. 24. The method of measuring the gray scale variation in each quadrant so that each quadrant is either a low variation quadrant or a high variation quadrant; replacing any low variation quadrants with an estimate for the particular quadrant. Description [0001] The present disclosure is related to compressing images. [0002] As is well-known, image compression techniques are desirable for a variety of purposes. For example, without limitation, images are compressed for storage and/or for transmission across a communications medium. Desirable aspects of image compression techniques include: occupying less storage space; applicability to a wide variety of images; and/or computationally efficient or fast encoding/decoding. Improvements in image compression that include one or all of these aspects continue to be desirable. [0003] The subject matter regarded as the invention is particularly pointed out and distinctly claimed in the concluding portion of the specification. The invention, however, both as to organization and method of operation, together with objects, features, and advantages thereof, may best be understood by reference to the following detailed description when read with the accompanying drawings in which: [0004]FIG. 1 is a flowchart illustrating an embodiment of a method of compressing an image in accordance with the present invention; [0005]FIG. 2 is a flowchart illustrating an embodiment of a method of decompressing an image that corresponds to the embodiment of FIG. 1. [0006] In the following detailed description, numerous specific details are set forth in order to provide a thorough understanding of the invention. However, it will be understood by those skilled in the art that the present invention may be practiced without these specific details. In other instances, well-known methods, procedures, components and circuits have not been described in detail so as not to obscure the present invention. [0007] As previously discussed, image compression is desirable for a number of applications. Furthermore, it is desirable if such compression techniques occupy less storage space, are applicable to a wide variety of images, and/or have an encoding/decoding process that is computationally efficient or fast. [0008] One technique that is sometimes employed in compression, such as in connection with the wavelet transform, or fractal-based compression/decompression, as two examples, involves a multi-resolution decomposition or multi-level division of the image. An embodiment of the present invention, based at least in part on fractal image compression, using an Iterative Function System (IFS), guided by certain probability measures, shall be described in more detail hereinafter. A basic notion of fractal image compression lies in the usage of self-similarity embedded in a given image. Using a set of affine contractive maps, as shall be explained in more detail hereinafter, for example, portions of an image may be reproduced, and by taking a collage of these parts, the entire image may be regenerated. The set of affine contractive maps is referred to in this context as IFS. For a particular embodiment in accordance with the invention, although the invention is not limited in scope in this respect, probabilities are assigned to the maps, which in turn, affect the iteration process, and generate, in this embodiment, a close, approximation of the image, employing a manageable amount of computational complexity or computational burden. A way to conceptualize the multi-level division of the image, then, for this particular embodiment, is as a “divide-and-conquer” approach. Therefore, an image may be subdivided and then the subdivisions may be further subdivided in a recursive fashion to determine how to compress the image efficiently. [0009] An embodiment of compressing an image in accordance with the present invention is one such approach. FIG. 1 is a flowchart illustrating this particular embodiment. It is noted that the invention is not limited in scope to this particular embodiment and many variations are possible within the scope of the present invention. [0010] In this particular embodiment, the image, in this embodiment, a gray scale image, I, is divided into quadrants, here designated I [0011] Although the invention is not limited in scope to a particular approach to measuring the gray scale variation of a quadrant of an image, in this particular embodiment, the gray scale variation is measured using the statistical variance, v [0012] In one embodiment, a high variation quadrant is where the statistical variance is above or equal to the pre-determined threshold, and a low variation quadrant is otherwise. In another embodiment, a low variation quadrant is where the statistical variance is below or equal to the predetermined threshold, and a high variation quadrant is otherwise. [0013] Likewise, when replacing a low variation quadrant with an estimate of the gray, scale level for the particular quadrant, many approaches are possible and the invention is not limited in scope to a single approach. Nonetheless, in this particular embodiment, the statistical mean (m [0014] As indicated above, an attempt is made to estimate particular quadrants using a contractive map of the image along with the probability (p [0015] It is noted, of course, that alternative approaches to forming a contractive map maybe employed. For example, a window of size three-by-three or perhaps a window of a shape other than a square shape may be employed. Nonetheless, in addition to forming a contractive map, for the particular quadrant, the probability is calculated for the quadrant. In this embodiment, for a quadrant, the probability of the quadrant is the ratio of the sum of the pixel gray scale values over the quadrant to the sum of the pixel gray scale values over the image. This may be illustrated by the following equation. p [0016] where S Σp [0017] where K=1 to 4. [0018] A particular quadrant is then estimated by multiplying the probability of that quadrant times the contractive map of the image, the multiplication being a scalar multiplication of the contractive map. [0019] Once this is complete for-the quadrants of an image, an estimate, I [0020] Once an estimate, I [0021] Referring now to FIG. 1 and flowchart [0022] Blocks [0023]FIG. 2 is a flowchart illustrating an embodiment [0024] This embodiment begins with an arbitrary image, J, having the same dimensions as the image to be decompressed, this arbitrary image having at least one zero pixel gray scale value. Therefore, at block [0025] Otherwise, at blocks [0026] If two successive estimates are equal, then, at block [0027] It will, of course, be understood that, although particular embodiments have just been described, the invention is not limited in scope to a particular embodiment or implementation. For example, one embodiment may be in hardware, whereas another embodiment may be in software. Likewise, an embodiment may be in firmware, or any combination of hardware, software, or firmware, for example. Likewise, although the invention is not limited in scope in this respect, one embodiment may comprise an article, such as a storage medium. Such a storage medium, such as, for example, a CD-ROM, or a disk, may have stored thereon instructions, which when executed by a system, such as a host computer or computing system or platform, or an imaging system, may result in a method of compressing or decompressing an image, such as an image of gray scale values, in accordance with the invention, such as, for example, one of the embodiments previously described. [0028] While certain features of the invention have been illustrated and described herein, many modifications, substitutions, changes and equivalents will now occur to those skilled in the art. It is, therefore, to be understood that the appended claims are intended to cover all such modifications and changes as fall within the true spirit of the invention. Classifications
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