Wavelet transform methods for object detection and recovery

We show that a biorthogonal spline wavelet closely approximates the prewhitening matched filter for detecting Gaussian objects in Markov noise. The filterbank implementation of the wavelet transform acts as a hierarchy of such detectors operating at discrete object scales. If the object to be detected is Gaussian and its scale happens to coincide with one of those computed by the wavelet transform, and if the background noise is truly Markov, then optimum detection is realized by thresholding the appropriate subband image. In reality, the Gaussian may be a rather coarse approximation of the object, and the background noise may deviate from the Markov assumption. In this case, we may view the wavelet decomposition as a means for computing an orthogonal feature set for input to a classifier. We use a supervised linear classifier applied to feature vectors comprised of samples taken from the subbands of an N-octave, undecimated wavelet transform. The resulting map of test statistic values indicates the presence and location of objects. The object itself is reconstructed by using the test statistic to emphasize wavelet subbands, followed by computing the inverse wavelet transform. We show two contrasting applications of the wavelets-based object recovery algorithm. For detecting microcalcifications in digitized mammograms, the object and noise models closely match the real image data, and the multiscale matched filter paradigm is highly appropriate. The second application, extracting ship outlines in noisy forward-looking infrared images, is presented as a case where good results are achieved despite the data models being less well matched to the assumptions of the algorithm.     

Peak transform for efficient image representation and coding.

In this work, we introduce a nonlinear geometric transform, called peak transform (PT), for efficient image representation and coding. The proposed PT is able to convert high-frequency signals into low-frequency ones, making them much easier to be compressed. Coupled with wavelet transform and subband decomposition, the PT is able to significantly reduce signal energy in high-frequency subbands and achieve a significant transform coding gain. This has important applications in efficient data representation and compression. To maximize the transform coding gain, we develop a dynamic programming solution for optimum PT design. Based on PT, we design an image encoder, called the PT encoder, for efficient image compression. Our extensive experimental results demonstrate that, in wavelet-based subband decomposition, the signal energy in high-frequency subbands can be reduced by up to 60% if a PT is applied. The PT image encoder outperforms state-of-the-art JPEG2000 and H.264 (INTRA) encoders by up to 2-3 dB in peak signal-to-noise ratio (PSNR), especially for images with a significant amount of high-frequency components. Our experimental results also show that the proposed PT is able to efficiently capture and preserve high-frequency image features (e.g., edges) and yields significantly improved visual quality. We believe that the concept explored in this work, designing a nonlinear transform to convert hard-to-compress signals into easy ones, is very useful. We hope this work would motivate more research work along this direction.     

Wavelet transforms for detecting microcalcifications in mammograms

Clusters of fine, granular microcalcifications in mammograms may be an early sign of disease. Individual grains are difficult to detect and segment due to size and shape variability and because the background mammogram texture is typically inhomogeneous. The authors develop a 2-stage method based on wavelet transforms for detecting and segmenting calcifications. The first stage is based on an undecimated wavelet transform, which is simply the conventional filter bank implementation without downsampling, so that the low-low (LL), low-high (LH), high-low (HL), and high-high (HH) sub-bands remain at full size. Detection takes place in HH and the combination LH+HL. Four octaves are computed with 2 inter-octave voices for finer scale resolution. By appropriate selection of the wavelet basis the detection of microcalcifications in the relevant size range can be nearly optimized. In fact, the filters which transform the input image into HH and LH+HL are closely related to prewhitening matched filters for detecting Gaussian objects (idealized microcalcifications) in 2 common forms of Markov (background) noise. The second stage is designed to overcome the limitations of the simplistic Gaussian assumption and provides an accurate segmentation of calcification boundaries. Detected pixel sites in HH and LH+HL are dilated then weighted before computing the inverse wavelet transform. Individual microcalcifications are greatly enhanced in the output image, to the point where straightforward thresholding can be applied to segment them. FROG curves are computed from tests using a freely distributed database of digitized mammograms.     

Image compression based on fuzzy algorithms for learning vectorquantization and wavelet image decomposition

This paper evaluates the performance of an image compression system based on wavelet-based subband decomposition and vector quantization. The images are decomposed using wavelet filters into a set of subbands with different resolutions corresponding to different frequency bands. The resulting subbands are vector quantized using the Linde-Buzo-Gray (1980) algorithm and various fuzzy algorithms for learning vector quantization (FALVQ). These algorithms perform vector quantization by updating all prototypes of a competitive neural network through an unsupervised learning process. The quality of the multiresolution codebooks designed by these algorithms is measured on the reconstructed images belonging to the training set used for multiresolution codebook design and the reconstructed images from a testing set.     

Contourlet-based image adaptive watermarking

In the contourlet transform (CT), the Laplacian pyramid (LP) decomposes an image into a low-frequency (LF) subband and a high-frequency (HF) subband. The LF subband is created by filtering the original image with 2-D low-pass filter. However, the HF subband is created by subtracting the synthesized LF subband from the original image but not by 2-D high-pass filtering the original image. In this paper, we propose a contourlet-based image adaptive watermarking (CIAW) scheme, in which the watermark is embedded into the contourlet coefficients of the largest detail subbands of the image. The transform structure of the LP makes the embedded watermark spread out into all subbands likely in which the LF subbands are included when we reconstruct the watermarked image based on the watermarked contourlet coefficients. Since both the LF subbands and the HF subbands contain watermarking components, our watermarking scheme is expected to be robust against both the LF image processing and the HF image processing attacks. The corresponding watermarking detection algorithm is proposed to decide whether the watermark is present or not by exploiting the unique transform structure of LP. With the new proposed concept of spread watermark, the watermark is detected by computing the correlation between the spread watermark and the watermarked image in all contourlet subbands fully. The proposed CIAW scheme is particularly superior to the conventional watermarking schemes when the watermarked image is attacked by some image processing methods, which destroy the HF subbands, thanks to the watermarking components preserved in the LF subbands. Experimental results show the validity of CIAW in terms of both the watermarking invisibility and the watermarking robustness. In addition, the comparison experiments prove the high-efficiency of CIAW again.     

Optimal filter-based detection of microcalcifications

This paper deals with the problem of texture feature extraction in digital mammograms. We use the extracted features to discriminate between texture representing clusters of microcalcifications and texture representing normal tissue. Having a two-class problem, we suggest a texture feature extraction method based on a single filter optimized with respect to the Fisher criterion. The advantage of this criterion is that it uses both the feature mean and the feature variance to achieve good feature separation. Image compression is desirable to facilitate electronic transmission and storage of digitized mammograms. In this paper, we also explore the effects of data compression on the performance of our proposed detection scheme. The mammograms in our test set were compressed at different ratios using the Joint Photographic Experts Group compression method. Results from an experimental study indicate that our scheme is very well suited for detecting clustered microcalcifications in both uncompressed and compressed mammograms. For the uncompressed mammograms, at a rate of 1.5 false positive clusters/image our method reaches a true positive rate of about 95%, which is comparable to the best results achieved so far. The detection performance for images compressed by a factor of about four is very similar to the performance for uncompressed images.     

Integrated wavelets for enhancement of microcalcifications in digital mammography

This paper presents a new algorithm for enhancement of microcalcifications in mammograms. The main novelty is the application of techniques we have developed for construction of filterbanks derived from the continuous wavelet transform. These discrete wavelet decompositions, called integrated wavelets, are optimally designed for enhancement of multiscale structures in images. Furthermore, we use a model based approach to refine existing methods for general enhancement of mammograms resulting in a more specific enhancement of microcalcifications. We present results of our method and compare them with known algorithms. Finally, we want to indicate how these techniques can also be applied to the detection of microcalcifications. Our algorithm was positively evaluated in a clinical study. It has been implemented in a mammography workstation designed for soft-copy reading of digital mammograms developed by IMAGETOOL, Germany.     

基于奇异值分解的Contourlet域图像水印算法

针对小波变换由于方向性缺乏而无法有效稀疏地表示图像本身几何结构的问题,结合Contourlet变换和奇异值分解的优点,提出了一种Contourlet变换域内基于奇异值分解的数字水印算法。宿主图像经过两层Contourlet分解后,生成一系列多尺度多方向的子带,选取第二层分解中能量最大的子带进行大小为4×4的互不重叠的分块,并进行奇异值分解,再将置乱后的原始二值水印信息嵌入到奇异值矩阵中。实验结果表明,该算法实现简单,透明性良好,对常规攻击和几何攻击具有较强的鲁棒性,且优于一般的小波域算法。     

Region adaptive subband image coding

We present a region adaptive subband image coding scheme using the statistical properties of image subbands for various subband decompositions. Motivated by analytical results obtained when the input signal to the subband decomposition is a unit step function, we analyze the energy packing properties toward the lower frequency subbands, edges, and the dependency of energy distribution on the orientation of the edges, in subband decomposed images. Based on these investigations and ideal analysis/synthesis filtering done in the frequency domain, the region adaptive subband image coding scheme extracts suitably shaped regions in each subband and then uses adaptive entropy-constrained quantizers for different regions under the assumption of a generalized Gaussian distribution for the image subbands. We also address the problem of determining an optimal subband decomposition among all possible decompositions. Experimental results show that visual degradations in the reconstructed image are negligible at a bit rate of 1.0 b/pel and reasonable quality images are obtainable at rates as low as 0.25 b/pel.     

A novel approach to microcalcification detection using fuzzy logictechnique

Breast cancer continues to be a significant public health problem in the United States. Approximately, 182,000 new cases of breast cancer are diagnosed and 46,000 women die of breast cancer each year. Even more disturbing is the fact that one out of eight women in the United States will develop breast cancer at some point during her lifetime. Since the cause of breast cancer remains unknown, primary prevention becomes impossible. Computer-aided mammography is an important and challenging task in automated diagnosis. It has great potential over traditional interpretation of film-screen mammography in terms of efficiency and accuracy. Microcalcifications are the earliest sign of breast carcinomas and their detection is one of the key issues for breast cancer control. In this study, a novel approach to microcalcification detection based on fuzzy logic technique is presented. Microcalcifications are first enhanced based on their brightness and nonuniformity. Then, the irrelevant breast structures are excluded by a curve detector. Finally, microcalcifications are located using an iterative threshold selection method. The shapes of microcalcifications are reconstructed and the isolated pixels are removed by employing the mathematical morphology technique. The essential idea of the proposed approach is to apply a fuzzified image of a mammogram to locate the suspicious regions and to interact the fuzzified image with the original image to preserve fidelity. The major advantage of the proposed method is its ability to detect microcalcifications even in very dense breast mammograms. A series of clinical mammograms are employed to test the proposed algorithm and the performance is evaluated by the free-response receiver operating characteristic curve. The experiments aptly show that the microcalcifications can be accurately detected even in very dense mammograms using the proposed approach     

基于二维APDCSF的列率子带特征编码方法

提出了一种子带编码的新方法。该方法利用二维全相位离散反余弦列率滤波器（APDCSF）对图像进行子带分解;对于低频子带图像采用直接斜交多重亚采样和基于全相位离散反余弦列牢滤波器（APDICsF）的多重旋转内插恢复．而对高频子带图像利用直方图自动阈值化提取如边缘和线等特征的图像元;根据各个子带的图像元的特征分别进行编码压缩,解压缩后利用凸集投影重建原始图像。该方法消除了传统的离散余弦变换（DCT）编码的方块化效应,与基于小波变换的子带特征编码方法相比,计算复杂度小,压缩率高,主观视觉性能好,对于灰阶图像可达到0．1～0．3bpp,特别适用于低比特率图像压缩。     

Detection of Clustered Microcalcifications on Mammograms Using Surrounding Region Dependence Method and Artificial Neural Network

Clustered microcalcifications on X-ray mammograms are an important sign in the detection of breast cancer. A statistical texture analysis method, called the surrounding region dependence method (SRDM), is proposed for the detection of clustered microcalcifications on digitized mammograms. The SRDM is based on the second-order histogram in two surrounding regions. This method defines four textural features to classify region of interests (ROIs) into positive ROIs containing clustered microcalcifications and negative ROIs of normal tissues. The database is composed of 64 positive and 76 negative ROI images, which are selected from digitized mammograms with a pixel size of 100 × 100 m² and 12 bits per pixel. An ROI is selected as an area of 128 × 128 pixels on the digitized mammograms. In order to classify ROIs into the two types, a three-layer backpropagation neural network is employed as a classifier. A segmentation of individual microcalcifications is also proposed to show their morphologies. The classification performance of the proposed method is evaluated by using the round-robin method and a free-response receiver operating-characteristics (FROC) analysis. A receiver operating-characteristics (ROC) analysis is employed to present the results of the round-robin testing for the case of several hidden neurons. The area under the ROC curve, A _z, is 0.997, which is achieved in the case of 4 hidden neurons. The FROC analysis is performed on 20 cropped images. A cropped image is selected as an area of 512 × 512 pixels on the digitized mammograms. In terms of the FROC, a sensitivity of more than 90% is obtained with a low false-positive (FP) detection rate of 0.67 per cropped image.     

基于小波正交变换的图像数字信息隐写算法

本文介绍了基于小波正交变换下将数字印章信息嵌入到图像中的信息隐写算法.图像经离散小波正交变换,分解成4个四分之一大小子图:水平方向、垂直方向和对角线方向的细节子图和低频逼近子图,三个细节子图构成一个矢量,而矢量间又是相互关联的.在此原理上可以得到矢量中每个细节子图中像素的最大值和最小值,从而求得它们差值的绝对值,这样可用其来控制印章信息的嵌入.当需要印章的相关信息时,可以从图像中提取出来.从实验结果分析,写入信息的图像,可以达到不影响视觉效果.     

A CAD system for the automatic detection of clustered microcalcifications in digitized mammogram films

Clusters of microcalcifications in mammograms are an important early sign of breast cancer. This paper presents a computer-aided diagnosis (CAD) system for the automatic detection of clustered microcalcifications in digitized mammograms. The proposed system consists of two main steps. First, potential microcalcification pixels in the mammograms are segmented out by using mixed features consisting of wavelet features and gray level statistical features, and labeled into potential individual microcalcification objects by their spatial connectivity. Second, individual microcalcifications are detected by using a set of 31 features extracted from the potential individual microcalcification objects. The discriminatory power of these features is analyzed using general regression neural networks via sequential forward and sequential backward selection methods. The classifiers used in these two steps are both multilayer feedforward neural networks. The method is applied to a database of 40 mammograms (Nijmegen database) containing 105 clusters of microcalcifications. A free-response operating characteristics (FROC) curve is used to evaluate the performance. Results show that the proposed system gives quite satisfactory detection performance. In particular, a 90% mean true positive detection rate is achieved at the cost of 0.5 false positive per image when mixed features are used in the first step and 15 features selected by the sequential backward selection method are used in the second step. However, we must be cautious when interpreting the results, since the 20 training samples are also used in the testing step.     

Subband coding of images using vector quantization

A novel two-dimensional subband coding technique is presented that can be applied to images as well as speech. A frequency-band decomposition of the image is carried out by means of 2D separable quadrature mirror filters, which split the image spectrum into 16 equal-rate subbands. These 16 parallel subband signals are regarded as a 16-dimensional vector source and coded as such using vector quantization. In the asymptotic case of high bit rates, a theoretical analysis yields that a lower bound to the gain is attainable by choosing this approach over scalar quantization of each subband with an optimal bit allocation. It is shown that vector quantization in this scheme has several advantages over coding the subbands separately. Experimental results are given, and it is shown the scheme has a performance that is comparable to that of more complex coding techniques     

Optimization of wavelet decomposition for image compression and feature preservation

A neural-network-based framework has been developed to search for an optimal wavelet kernel that can be used for a specific image processing task. In this paper, a linear convolution neural network was employed to seek a wavelet that minimizes errors and maximizes compression efficiency for an image or a defined image pattern such as microcalcifications in mammograms and bone in computed tomography (CT) head images. We have used this method to evaluate the performance of tap-4 wavelets on mammograms, CTs, magnetic resonance images, and Lena images. We found that the Daubechies wavelet or those wavelets with similar filtering characteristics can produce the highest compression efficiency with the smallest mean-square-error for many image patterns including general image textures as well as microcalcifications in digital mammograms. However, the Haar wavelet produces the best results on sharp edges and low-noise smooth areas. We also found that a special wavelet whose low-pass filter coefficients are 0.32252136, 0.85258927, 1.38458542, and -0.14548269) produces the best preservation outcomes in all tested microcalcification features including the peak signal-to-noise ratio, the contrast and the figure of merit in the wavelet lossy compression scheme. Having analyzed the spectrum of the wavelet filters, we can find the compression outcomes and feature preservation characteristics as a function of wavelets. This newly developed optimization approach can be generalized to other image analysis applications where a wavelet decomposition is employed.     

Fusion of multiparametric SAR images based on SW-nonsubsampled contourlet and PCNN

In this paper, a new fusion rule based on a pulse coupled neural network (PCNN) and the clarity of images is proposed for multi-band synthetic aperture radar (SAR) image fusion. By using a stationary wavelet-based nonsubsampled contourlet transform (SW-NSCT), we can calculate a flexible multiscale, multidirectional, anisotropy and shift-invariant representation of registered SAR images. A weighted fusion rule is performed on the low frequency subbands to calculate the fused lowpass band. For the fusion of high frequency directional subband images, a PCNN model is constructed, where the linking strength of each neuron is determined by the clarity of the decomposed subband images. The fusion approach exploits the advantages of both SW-NSCT in multiscale geometric representations and that of PCNN in the determination of fusion rules; as predicted, the obtained fusion image can preserve much more information regarding textures and edges of the images, compared to its counterparts. Some experiments are performed by comparing the new algorithm with other existing fusion rules and methods. The experimental results show that the proposed fusion approach is effective and can provide better performance in fusing multi-band SAR images than some current methods.     

基于RDU-PCNN和NSST的红外和可见图像融合算法

针对可见光和红外图像的融合容易出现块状噪声 、边缘有振铃现象等不足,提出了一种基于区 域双通道脉冲耦合神经网络(RDU-PCNN)和非下采样剪切波变换(NSST)的红外和见光图像融 合算法。首先 对待融合的可见光和红外图像进行NSST分解得到低频系数和高频方向系数,低频系数采用R DU-PCNN的 规则融合,高频方向系数采用离散余弦变换(DCT)的融合规则,对融合后的系数进行逆NSST ,从而得到融合后 的图像。仿真结果表明,与其他5种目前流行或者较为先进的算法相比,本文的算法在视觉 和客观评价指标上优于其他算法。     

Two-dimensional subband transforms: theory and applications

The one-dimensional subband FFT (SB-FFT) and one-dimensional SB-DCT were extended to the two-dimensional (2-D) case to obtain the 2-D SB-FFT and the 2-D SB-DCT. The two-dimensional subband transforms are based on subband decomposition of the input sequence in both dimensions. They use knowledge about the input signal to obtain an approximation to their transform by discarding the computations in bands that have little energy in both dimensions. Computational savings can be obtained from calculating only the remaining subbands. In many applications the computational speed is so important that some error in the calculated transform can be accepted. In image processing, due to the nature of most natural scenes, most of the energy content of the corresponding digitised images is concentrated predominantly in the low-low spatial frequency domain. The concentration of the energy in a localised region of the transform domain makes the approximate subband transform computation quite suitable for the calculation of the 2-D image spectra. The complexity and accuracy of both 2-D transforms are studied in detail in the paper. The approximation errors in both transforms are derived for a general case, in which any band out of M bands is to be computed. Both transforms are modified to be fully adaptive to select the band of interest to be computed. Image transform application examples are included. Savings in computational complexity of image transforms are shown. The efficiency of subband transforms of different images is indicated by computing the signal-to-noise ratio in the reconstructed images.     

Normalization of local contrast in mammograms

Equalizing image noise has been shown to be an important step in automatic detection of microcalcifications in digital mammograms. In this study, an accurate adaptive approach for noise equalization is presented and investigated. No additional information obtained from phantom recordings is involved in the method, which makes the approach robust and independent of film type and film development characteristics. Furthermore, it is possible to apply the method on direct digital mammograms as well. In this study, the adaptive approach is optimized by investigating a number of alternative approaches to estimate the image noise. The estimation of high-frequency noise as a function of the grayscale is improved by a new technique for dividing the grayscale in sample intervals and by using a model for additive high-frequency noise. It is shown that the adaptive noise equalization gives substantially better detection results than does a fixed noise equalization. A large database of 245 digitized mammograms with 341 clusters was used for evaluation of the method.