二維離散樣本熵: 一種穩定且快速的紋理分析方法

Abstract

信息理論已在各個領域廣泛應用，產生了用於分析時間序列數據的基於熵的度量。本文關注將這些度量擴展到更高維度，對於像圖像分析和分類這樣的任務至關重要。雖然二維樣本熵（SampEn2D）在生物醫學圖像分析中顯示了潛力，但其計算效率低下且無法處理大尺寸圖像的限制限制了其實用性。相反，二維離散熵（DispEn2D）提供了一種更快的替代方案，但在分類具有高不規則性的紋理方面存在困難。為了解決這些限制，本研究介紹了二維離散樣本熵（DispSampEn2D），充分利用了二維樣本熵和二維離散熵的優勢，同時彌補了它們的缺陷。通過使用合成圖像和真實紋理數據集進行驗證，展示了二維離散樣本熵在分類任務中的有效性。此外，本研究強調了利用不同嵌入維度的熵向量的優勢，由於它們的互補特性，導致了改善的分類準確性。

Information theory has found wide applications across diverse domains, giving rise to entropy-based metrics for analyzing time-series data. This thesis focuses on extending these metrics to higher dimensions, a necessity for tasks like image analysis and classification. While two-dimensional sample entropy (SampEn2D) holds promise in biomedical image analysis, its computational inefficiency and inability to handle large-size images limit its utility. Conversely, two-dimensional dispersion entropy (DispEn2D) offers a quicker alternative but struggles with classifying textures exhibiting high irregularity. To overcome these limitations, this study introduces two-dimensional dispersion sample entropy (DispSampEn2D), leveraging the strengths of SampEn2D and DispEn2D while mitigating their weaknesses. Experiments using synthetic images and real-world texture datasets demonstrate the effectiveness of DispSampEn2D in classification tasks. Furthermore, this research underscores the advantages of utilizing entropy vectors with diverse embedding dimensions, resulting in improved classification accuracy due to their complementary characteristics.