画像処理のための複素数離散ウェーブレット変換の設計と応用に関する研究

Abstract

近年，カメラ等の撮像デバイスや計算機の高度化により，画像処理技術が広く普及している．画像処理技術によって，人間が視覚で行う検査，診断，監視等の様々な作業支援や作業の代替が期待されている．これらの技術の実現には，画像に映る物体等の特徴的な情報を抽出する特徴抽出という処理が必要となる．特徴抽出手法の一つにウェーブレット変換(WaveletTransform, WT)がある．これは画像の様々な周波数成分を計算し，多くの特徴を抽出できる．そのため従来から特徴抽出手法として多くの画像に対し利用されてきた．近年，画像の方向性エッジを特徴として計算出来る．2D-CDWT(2-Dimensional ComplexDiscrete Wavelet Transform, 2D-CDWT)が注目されている．この機能を方向選択性と呼び，物体の形状情報を得る手法として期待されているが，2D-CDWT から得られる方向性エッジは，抽出する特徴の種類が少なく，大まかな形状情報しか得られない．そこで，2D-CDWT 等を基に，詳細な方向性エッジを抽出する新たなウェーブレット変換を提案する．始めに，方向選択性の原理の基礎検討を行った．その結果，ヒルベルト変換ペアの実数部と虚数部のウェーブレットが，方向性の波形を構成することが確認された．また，ウェーブレットの周波数特性と方向に一意の関係があることを確認した．その関係を基に，方向性エッジの方向・角度範囲の評価手法を提案した．それにより，2D-CDWT 等の方向選択性の抽出機能を定量的に評価可能にした．次に，2D-CDWT の発展形である2 次元複素数離散ウェーブレットパケット変換(2-Dimensional Complex Discrete Wavelet Packet Transform, 2D-CWPT)に方向調節フィルタを付与し，2D-CWPT が計算する方向成分を変化させ，任意の方向性エッジを抽出する手法を提案した．またこの手法から詳細な方向性エッジの抽出を可能にした．この提案手法を半導体ウェーハの画像欠陥検査に応用し，K-measn 法と組み合わせた欠陥検査手法を提案した．その結果，画像欠陥を従来の2D-CDWT等の手法よりも高精度に認識できることを確認した．さらに，直接，方向成分に合わせて周波数特性を設計した方向性フィルタを提案した．そして，方向性フィルタによる新たな方向性ウェーブレット変換を提案した．この手法においても，画像から任意の方向性エッジを抽出可能であることを確認した．またこの手法を医用画像処理に応用した．CT(Computed Tomography)画像内に映る腫瘤の自動検出について検討し，サポートベクターマシン(Support Vector Machine, SVM)と併用すると，腫瘤を高精度に検出可能であった．また，従来手法である2D-CDWT，ガボールフィルタと比較し，方向性ウェーブレット変換が最も高い検出率を示した．また，2 次元画像から3 次元CT，MRI(Magnetic Resonance Imaging)を解析可能な3D-CDWT を開発している．これらの結果から，方向性ウェーブレット変換や2D-CWPT を基にした提案手法が画像の特徴抽出手法として有効であることを確認した．

In recent years, due to the improvement of the imaging devices and computers, the image processing techniques are widely spread industries, agricultures and medical fields. The image processing techniques are expected to achieve the inspection, diagnosis and monitoring which are previously carried out by people. These techniques require the process which extracts the characteristic information. This process is called ‘Feature Extraction’ and one of the feature extraction methods is a Wavelet Transform. The Wavelet Transform extracts the multiple frequency components from the image by using mother wavelet and filters. Therefore, the Wavelet Transform was used for variable image processing applications. The 2-D Complex Discrete Wavelet Transform (2D-CDWT) is especially interested. The 2D-CDWT can extract the singularities different with orientations (directional edges). Here, singularities mean the edge, border, lines and ridges in the image. This property is called directional selection and this property expected as the method to obtain the shape information from each directional edge. However, the number of directional edges is little and we can’t get detail features about directionalities. For instance when we use the directional information for the image recognition and object detection, we calculate more than 8 directional components. In this paper, we propose the novel 2D-CDWT which can extract the many directional edges and detail features. At first, the principle of directional selection is considered. We confirmed that the Hilbert Transform pair of the real part of wavelet and the imaginary part of wavelet which has the phase difference makes the specified waveforms. This waveform has the amplitude only the specified direction and we confirmed that this waveform extracts the directional edges. Moreover the frequency characteristics of this waveform and its direction have the unique relationship. Based on this relationship, we construct the evaluation method for the direction and the angular range of directional edges. According to the evaluation method, we can estimate the extracting ability of the directional selection quantitatively. Secondary, we focused on the 2-D Complex Discrete Wavelet Packet Transform (2D-CWPT) which is the advanced Wavelet Transform from the 2D-CDWT. Based on the 2D-CWPT, we propose the novel 2D-CWPT that can extract the arbitrary direction and angular range. The novel 2D-CWPT is added the modified filter to adjust the directional edges. We confirmed that we can get the desirable directional component using this method. But we also confirmed that there are error between the result and requested angular range. We apply the novel 2D-CWPT to the semiconductor wafer image for the automated defect detection. We used the novel 2D-CWPT as the feature extraction and K-means method as the pattern recognition method for the defect detection. As the detection result, the novel 2D-CWPT can detect the defect precisely rather than previous 2D-CDWT, 2D-CDWT, 2D-DWT, 2D-STFT (Short Time Fourier Transform). Thirdly, we propose the novel directional wavelet transform by using designed directional filter. The directional filter is designed based on the relationship the direction of wavelet and its frequency characteristics. The directional wavelet transform also can detect the desirable directional edges without the error between the desirable angular range and the result. As the application, we apply the directional wavelet transform to medical image processing. We consider the tumor detection from CT (Computed Tomography) image by using the directional wavelet transform and support vector machine. As the result the directional wavelet transform has the most accurate detection rate rather than previous 2D-CDWT and Gabor filters. Besides the 2D methods, we developed the 3D-CDWT which can be used for 3D-CT and 3D-MRI images. Previously the directional selection for the 3D images has not achieved yet. We construct the 3D directional selection based on the principle of the directional selection. The 3D directional selection extracts the 3D directional edges that have orientation and angular range in 3D space domain. We confirmed that the 3D directional edges show the features of 3D images. Moreover in the 3D CT image, we can detect and recognize the tumor using 3D-CDWT and SVM. Finally in this paper, we confirmed the validation of the novel 2D-CWPT and the directional wavelet transform as the image feature extraction method by using wafer images and medical CT images. Also we can show that the 3D directional selection can get 3D image features.