基于小波變換的圖像邊緣檢測算法研究

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摘 要
邊緣是圖像的最基本特征，圖像的大部分信息都存在于圖像的邊緣中。因此如何獲取圖像的邊緣，成為圖像處理與分析技術(shù)中的研究熱點(diǎn)。到目前為止，已有許多圖像邊緣檢測的算法，但由于邊緣檢測的復(fù)雜性和固有問題，在抗噪和邊緣定位上都沒有很好的解決。因?yàn)閳D像邊緣點(diǎn)和噪聲在頻域內(nèi)多為高頻信號(hào)，目前的算法大多不能解決從局部高頻信號(hào)中區(qū)分噪聲和邊緣的問題，小波變換的“時(shí)頻”多尺度分析技術(shù)，為圖像邊緣檢測提供了新的技術(shù)途徑。
小波分析是繼 Fourier 分析之后的新的時(shí)頻域分析工具。由于其良好的時(shí)頻局部化特點(diǎn)和多尺度特性，能有效地檢測和分析信號(hào)的奇異點(diǎn)，在檢測邊緣的同時(shí)能有效地抑制噪聲，成為研究非平穩(wěn)信號(hào)的有力工具，在信息處理領(lǐng)域中倍受重視，在圖像處理技術(shù)中得到廣泛應(yīng)用。
本文首先介紹了小波變換的發(fā)展和應(yīng)用前景，概述了圖像邊緣檢測技術(shù)的研究現(xiàn)狀，然后對(duì)經(jīng)典的圖像邊緣檢測算法進(jìn)行分析，研究各算子的特點(diǎn)，總結(jié)出各自的優(yōu)缺點(diǎn)，由此引出小波變換應(yīng)用于圖像邊緣檢測中的研究。多尺度邊緣表征了圖像中不同強(qiáng)度和大小結(jié)構(gòu)的邊緣，是圖像的重要特征。如果對(duì)變換后的整幅圖像取同一閾值，那么由微弱邊緣形成的局部極大值對(duì)隨著由灰度不均勻、噪聲等產(chǎn)生的模極大值將一并濾除。因此，本文采用分塊自適應(yīng)法選取閾值，即將圖像分成許多小塊，在這些小塊中求模極大值的平均值，將此平均值設(shè)為閾值，從而改變?nèi)斯す浪汩撝挡粔驕?zhǔn)確的問題。

關(guān)鍵詞：邊緣檢測；小波變換；多尺度邊緣；模極大值；分塊自適應(yīng)
Abstract
Edge is the most basic feature of images,which includes the most part information of images. So obtaining the edge image has turned into a hot spot in research on image processing and analysis technology.So far,many algorithms have been presented in edge detection field.But the problems in anti-noise and edge location were not well resolved because of the complexity and inherent problems of edge detection. The reason is that the noise and edge were both high-frequency signals and it was hardly solved to distinguish between noises and edges from local high-frequency signals using current algorithms. “Time-frequency” multi-scale analysis of wavelet transform brings new ways to image edge detection.
Wavelet analysis is a new tool of time-frequency analysis after Fourier analysis. It can effectively analyze signal singularity point and detect edges while restraining noise because of its good time-frequency local property and multi-scale characteristics. So, as a powerful tool of researching non-stationary signal,it is paid more attention in the field of information processing and is widely applied in image processing technology.
In this paper,the prospect for the development and application of wavelet transformation is introduced firstly and then the research status of image edge detection is given. After studying the characteristics of the classical edge detection algorithm,summing up the advantages and disadvantages of each,wavelet theory applied in edge detection is introduced.Multiscale edge characterization edge images of different intensity and size of the structure is an important characteristic of the image. If you take the same threshold value for the entire image after the conversion, then the local maxima formed by the faint edge of the modulus maxima with uneven gray and noise generated will be filtered out. Therefore, this method uses the selected block adaptive threshold,the image is divided into many small pieces, these pieces of modulus maxima averages, the average set this threshold, thereby changing the artificial threshold inaccurate estimation problem .
Keywords: Edge detection;Wavelet transformation;Multiscale edge;Modulus maxima; Block adaptive
目 錄
第一章 緒論 1
1.1研究背景及意義 1
1.2國內(nèi)外研究現(xiàn)狀 2
1.3課題的研究內(nèi)容及安排 3
第二章 小波變換 5
2.1小波定義 5
2.2連續(xù)小波變換 6
2.3離散小波變換 8
2.4小波變換的多分辨率分析和Mallat算法 9
2.4.1多分辨率分析概念 9
2.4.2 Mallet算法 12
2.5 本章小結(jié) 14
第三章 圖像邊緣檢測算法設(shè)計(jì) 15
3.1圖像與數(shù)字圖像 15
3.2圖像邊緣檢測 16
3.3圖像邊緣檢測的基本步驟 19
3.4經(jīng)典邊緣檢測算子的檢測結(jié)果與性能比較 19
3.5小波邊緣檢測算法 22
3.6本章小結(jié) 24
第四章 小波邊緣檢測程序設(shè)計(jì) 25
4.1Matlab實(shí)現(xiàn)小波變換 25
4.1.1一維小波變換的實(shí)現(xiàn) 25
4.1.2二維小波變換的實(shí)現(xiàn) 25
4.2小波邊緣檢測程序 26
4.3小波多尺度邊緣檢測的算法實(shí)現(xiàn) 27
4.4本章小結(jié) 30
第五章 實(shí)驗(yàn)結(jié)果分析 31
5.1實(shí)驗(yàn)結(jié)果及分析 31
5.2本章小結(jié) 33
第六章 總結(jié)與展望 34
6.1總結(jié) 34
6.2展望 34
致 謝 36
參考文獻(xiàn) 37