Application of Wavelets and Principal Component Analysis in Image Query and Mammography

Breast cancer is currently one of the major causes of death for women in the U.S. Mammography is currently the most effective method for detection of breast cancer and early detection has proven to be an efficient tool to reduce the number of deaths. Mammography is the most demanding of all clinical imaging applications as it requires high contrast, high signal to noise ratio and resolution with minimal x-radiation. According to studies [36], 10% to 30% of women having breast cancer and undergoing mammography, have negative mammograms, i.e. are misdiagnosed. Furthermore, only 20%-40% of the women who undergo biopsy, have cancer. Biopsies are expensive, invasive and traumatic to the patient. The high rate of false positives is partly because of the difficulties in the diagnosis process and partly due to the fear of missing a cancer. These facts motivate research aimed to enhance the mammogram images (e.g. by enhancement of features such as clustered calcification regions which were found to be associated with breast cancer) , to provide CAD (Computer Aided Diagnostics) tools that can alert the radiologist to potentially malignant regions in the mammograms and to develope tools for automated classification of mammograms into benign and malignant classes. In this paper we apply wavelet and Principal Component analysis, including the approximate Karhunen Loeve aransform to mammographic images, to derive feature vectors used for classification of mammographic images from an early stage of malignancy. Another area where wavelet analysis was found useful, is the area of image query. Image query of large data bases must provide a fast and efficient search of the query image. Lately, a group of researchers developed an algorithm based on wavelet analysis that was found to provide fast and efficient search in large data bases. Their method overcomes some of the difficulties associated with previous approaches, but the search algorithm is sensitive to displacement and rotation of the query image due to the fact that wavelet analysis is not invariant under displacement and rotation. In this study we propose the integration of the Hotelling transform to improve on this sensitivity and provide some experimental results in the context of the standard alphabetic characters

Mathematical transforms and image compression: A review

It is well known that images, often used in a variety of computer and other scientific and engineering applications, are difficult to store and transmit due to their sizes. One possible solution to overcome this problem is to use an efficient digital image compression technique where an image is viewed as a matrix and then the operations are performed on the matrix. All the contemporary digital image compression systems use various mathematical transforms for compression. The compression performance is closely related to the performance by these mathematical transforms in terms of energy compaction and spatial frequency isolation by exploiting inter-pixel redundancies present in the image data. Through this paper, a comprehensive literature survey has been carried out and the pros and cons of various transform-based image compression models have also been discussed

Image processing algorithms employing two-dimensional Karhunen-Loeve Transform

In the fields of image processing and pattern recognition there is an important problem of acquiring, gathering, storing and processing large volumes of data. The most frequently used solution making these data reduced is a compression, which in many cases leads also to the speeding-up further computations. One of the most frequently employed approaches is an image handling by means of Principal Component Analysis and Karhunen-Loeve Transform, which are well known statistical tools used in many areas of applied science. Their main property is the possibility of reducing the volume of data required for its optimal representation while preserving its specific characteristics.The paper presents selected image processing algorithms such as compression, scrambling (coding) and information embedding (steganography) and their realizations employing the twodimensional Karhunen-Loeve Transform (2DKLT), which is superior to the standard, onedimensional KLT since it represents images respecting their spatial properties. The principles of KLT and 2DKLT as well as sample implementations and experiments performed on the standard benchmark datasets are presented. The results show that the 2DKLT employed in the above applications gives obvious advantages in comparison to certain standard algorithms, such as DCT, FFT and wavelets

Astronomical Image Compression Techniques Based on ACC and KLT Coder

This paper deals with a compression of image data in applications in astronomy. Astronomical images have typical specific properties — high grayscale bit depth, size, noise occurrence and special processing algorithms. They belong to the class of scientific images. Their processing and compression is quite different from the classical approach of multimedia image processing. The database of images from BOOTES (Burst Observer and Optical Transient Exploring System) has been chosen as a source of the testing signal. BOOTES is a Czech-Spanish robotic telescope for observing AGN (active galactic nuclei) and the optical transient of GRB (gamma ray bursts) searching. This paper discusses an approach based on an analysis of statistical properties of image data. A comparison of two irrelevancy reduction methods is presented from a scientific (astrometric and photometric) point of view. The first method is based on a statistical approach, using the Karhunen-Loeve transform (KLT) with uniform quantization in the spectral domain. The second technique is derived from wavelet decomposition with adaptive selection of used prediction coefficients. Finally, the comparison of three redundancy reduction methods is discussed. Multimedia format JPEG2000 and HCOMPRESS, designed especially for astronomical images, are compared with the new Astronomical Context Coder (ACC) coder based on adaptive median regression

Image processing algorithms employing two-dimensional Karhunen-Loeve Transform

In the fields of image processing and pattern recognition there is an important problem of acquiring, gathering, storing and processing large volumes of data. The most frequently used solution making these data reduced is a compression, which in many cases leads also to the speeding-up further computations. One of the most frequently employed approaches is an image handling by means of Principal Component Analysis and Karhunen-Loeve Transform, which are well known statistical tools used in many areas of applied science. Their main property is the possibility of reducing the volume of data required for its optimal representation while preserving its specific characteristics.The paper presents selected image processing algorithms such as compression, scrambling (coding) and information embedding (steganography) and their realizations employing the twodimensional Karhunen-Loeve Transform (2DKLT), which is superior to the standard, onedimensional KLT since it represents images respecting their spatial properties. The principles of KLT and 2DKLT as well as sample implementations and experiments performed on the standard benchmark datasets are presented. The results show that the 2DKLT employed in the above applications gives obvious advantages in comparison to certain standard algorithms, such as DCT, FFT and wavelets

Dominant run-length method for image classification

In this paper, we develop a new run-length texture feature extraction algorithm that significantly improves image classification accuracy over traditional techniques. By directly using part or all of the run-length matrix as a feature vector, much of the texture information is preserved. This approach is made possible by the introduction of a new multi-level dominant eigenvector estimation algorithm. It reduces the computational complexity of the Karhunen-Loeve Transform by several orders of magnitude. Combined with the Bhattacharya distance measure, they form an efficient feature selection algorithm. The advantage of this approach is demonstrated experimentally by the classification of two independent texture data sets. Perfect classification is achieved on the first data set of eight Brodatz textures. The 97% classification accuracy on the second data set of sixteen Vistex images further confirms the effectiveness of the algorithm. Based on the observation that most texture information is contained in the first few columns of the run-length matrix, especially in the first column, we develop a new fast, parallel run-length matrix computation scheme. Comparisons with the co-occurrence and wavelet methods demonstrate that the run-length matrices contain great discriminatory information and that a method of extracting such information is of paramount importance to successful classification.Funding was provided by the Office of Naval Research through Contract No. N00014-93-1-0602