適用於對稱和規律影像分析之計算模型

A Computational Model for Image Analysis Based on Symmetry and Regularity

蔡馨瑩(Hsin-Ying Tsai)

指導教授 ： 貝蘇章

國立臺灣大學/電機資訊學院/電信工程學研究所/碩士(2017年)

https://doi.org/10.6342/NTU201701670

摘要

人們具有先天的能力來辨認一個影像的對稱性和規律性，但如何能透過電腦自動化地辨認影像，卻值得我們去深思，在我們的研究中，我們以奇偶對稱性，Wallpaper Groups以及規律性來進行辨認影像。
在第二章中，我們透過奇偶能量比將影像切割成許多未重疊的區塊，而在這些切割後的區塊具有強烈的對稱性。接著，透過影像的對稱性，區塊位置以及大小等特徵進行影像之壓縮，並且求得此種影像壓縮方法的峰值訊雜比和壓縮比。
在第三章中，我們基於Wallpaper Groups進行影像之辨認，產生以及分解等三項工作。而這些方法分別為以下三項，第一項是辨認任何一張影像的Wallpaper Groups，第二項是透過一個基本的Wallpaper圖像來產生一幅彩色的影像，最後一項是將一張影像依據Wallpaper色彩做分解。此外，我們對奇偶對稱性與Wallpaper Groups的關係做了進一步的研討。
在第四章中，我們針對具有以下共通點:即是針對規律與接近規律性的自然影像偵測的演算法進行探討。在自然影像中，有一些規律的影像常被破壞。因此，我們分別介紹兩種方式來克服此問題:第一個方法為聚類傳播算法而第二個方法為視覺環境辨識。由於接近規律的材質在自然影像中無所不在，因而在本文的最後我們介紹一個有關接近規律材質的分析和合成的計算模型，作為本論文的結尾。

關鍵字

對稱性 ； 局部對稱性 ； Wallpaper Groups ； 規律性 ； 接近規律性

並列摘要

Contrary to the inaccurately computer-automated characteristics recognition, humans have an innate ability to perceive symmetry. In order to quantize the detection model, we address a novel detection approach consisting of even or odd symmetry, wallpaper groups, and regularity extraction methods in three chapters respectively.
In Chapter 2, an image is segmented into the variable-sized blocks with strong symmetrical characteristics extracted through either even or odd energy portions by optimally placing the center of symmetry. The experimental result shows excellent performance of PSNR and compression ratio performance of the testing images.
In Chapter 3, three kinds of distinct analyses are applied to examine the wallpaper group approach, including classification, generation, and decomposition. With these three kinds of analysis, we can identify any wallpaper by different wallpaper groups, generate a colorful wallpaper from basic patterns and decompose a wallpaper into the segmented wallpapers with different colors, accordingly. In addition, the relationship between the even or odd symmetry and wallpaper groups is investigated.
The algorithm studied in Chapter 4 are to detect regular and near-regular patterns with a natural image. Due to the deformed regular patterns, two efficient methods are proposed to solve the above-mentioned problem: mean-shift belief propagation and visual place recognition way. There are near-regular textures in the natural world, so we addressed a model for realizing the near-regular texture analysis algorithms.

並列關鍵字

Symmetry ； Local Symmetry ； Wallpaper Groups ； Regularity ； Near Regularity

參考文獻

[1] A. Gnutti, F. Guerrini and R. Leonardi, “Representation of signals by local symmetry decomposition,” in Proceedings of Signal Processing Conference (EUSIPCO), pp. 983-987, 2015.

[3] D.K. Washburn and D.W. Crowe, Symmetries of Culture: Theory and Practice of Plane Pattern Analysis, University of Washington Press, 1991.

[5] A.R. Rao and G.L. Lohse, “Identifying high level features of texture perception,” in CVGIP: Graphical Models and Image Processing, pp. 218-233, 1993.

[6] A.D. Grossand and T.E. Boult, “Analyzing skewed symmetries,” in International Journal of Computer Vision, pp. 91-111, 1994.

[7] G. Marola, “On the detection of the axes of symmetry of symmetric and almost symmetric planar images,” IEEE Transactions on Pattern Analysis and Machine Intelligence, pp. 104-108, 1989.