Why Shape Coding? Asymptotic Analysis of the Entropy Rate for Digital Images
This paper focuses on the ultimate limit theory of image compression. It proves that for an image source, there exists a coding method with shapes that can achieve the entropy rate under a certain condition where the shape-pixel ratio in the encoder/decoder is <inline-formula><math xmlns=&q...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-12-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/25/1/48 |
| _version_ | 1797442997320679424 |
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| author | Gangtao Xin Pingyi Fan Khaled B. Letaief |
| author_facet | Gangtao Xin Pingyi Fan Khaled B. Letaief |
| author_sort | Gangtao Xin |
| collection | DOAJ |
| description | This paper focuses on the ultimate limit theory of image compression. It proves that for an image source, there exists a coding method with shapes that can achieve the entropy rate under a certain condition where the shape-pixel ratio in the encoder/decoder is <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">O</mi><mo>(</mo><mrow><mn>1</mn><mo>/</mo><mrow><mo form="prefix">log</mo><mi>t</mi></mrow></mrow><mo>)</mo></mrow></semantics></math></inline-formula>. Based on the new finding, an image coding framework with shapes is proposed and proved to be asymptotically optimal for stationary and ergodic processes. Moreover, the condition <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">O</mi><mo>(</mo><mrow><mn>1</mn><mo>/</mo><mrow><mo form="prefix">log</mo><mi>t</mi></mrow></mrow><mo>)</mo></mrow></semantics></math></inline-formula> of shape-pixel ratio in the encoder/decoder has been confirmed in the image database MNIST, which illustrates the soft compression with shape coding is a near-optimal scheme for lossless compression of images. |
| first_indexed | 2024-03-09T12:49:43Z |
| format | Article |
| id | doaj.art-264816375a874579ba7f811d7335550c |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-09T12:49:43Z |
| publishDate | 2022-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-264816375a874579ba7f811d7335550c2023-11-30T22:07:30ZengMDPI AGEntropy1099-43002022-12-012514810.3390/e25010048Why Shape Coding? Asymptotic Analysis of the Entropy Rate for Digital ImagesGangtao Xin0Pingyi Fan1Khaled B. Letaief2Department of Electronic Engineering, Tsinghua University, Beijing 100084, ChinaDepartment of Electronic Engineering, Tsinghua University, Beijing 100084, ChinaDepartment of Electrical and Computer Engineering, Hong Kong University of Science and Technology (HKUST), Hong KongThis paper focuses on the ultimate limit theory of image compression. It proves that for an image source, there exists a coding method with shapes that can achieve the entropy rate under a certain condition where the shape-pixel ratio in the encoder/decoder is <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">O</mi><mo>(</mo><mrow><mn>1</mn><mo>/</mo><mrow><mo form="prefix">log</mo><mi>t</mi></mrow></mrow><mo>)</mo></mrow></semantics></math></inline-formula>. Based on the new finding, an image coding framework with shapes is proposed and proved to be asymptotically optimal for stationary and ergodic processes. Moreover, the condition <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">O</mi><mo>(</mo><mrow><mn>1</mn><mo>/</mo><mrow><mo form="prefix">log</mo><mi>t</mi></mrow></mrow><mo>)</mo></mrow></semantics></math></inline-formula> of shape-pixel ratio in the encoder/decoder has been confirmed in the image database MNIST, which illustrates the soft compression with shape coding is a near-optimal scheme for lossless compression of images.https://www.mdpi.com/1099-4300/25/1/48image compressioninformation theoryentropy ratelimit theoremasymptotic bounds |
| spellingShingle | Gangtao Xin Pingyi Fan Khaled B. Letaief Why Shape Coding? Asymptotic Analysis of the Entropy Rate for Digital Images Entropy image compression information theory entropy rate limit theorem asymptotic bounds |
| title | Why Shape Coding? Asymptotic Analysis of the Entropy Rate for Digital Images |
| title_full | Why Shape Coding? Asymptotic Analysis of the Entropy Rate for Digital Images |
| title_fullStr | Why Shape Coding? Asymptotic Analysis of the Entropy Rate for Digital Images |
| title_full_unstemmed | Why Shape Coding? Asymptotic Analysis of the Entropy Rate for Digital Images |
| title_short | Why Shape Coding? Asymptotic Analysis of the Entropy Rate for Digital Images |
| title_sort | why shape coding asymptotic analysis of the entropy rate for digital images |
| topic | image compression information theory entropy rate limit theorem asymptotic bounds |
| url | https://www.mdpi.com/1099-4300/25/1/48 |
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