Parameterized Logarithmic Image Processing for practical applications

Image processing is the system of mathematically transforming an image, either to modify some characteristics or extract some feature. Image processing systems are necessary for a range of applications, such as enhancement, object detection and recognition, and noise reduction. Such image processing systems form the components of higher level systems, and in turn are composed of a set of lower-level processing operations that are the foundation of the complete system. Current practice in image processing relies on linear operations to implement increasingly complex. However, these methods make little use of any standardized, mathematically rigorous arithmetical structure specifically designed for image manipulation.;A number of image processing specific frameworks have been proposed. The image algebra was first designed to give a core set of 14 arithmetical operations to facilitate the design and inter-operability of algorithms. A number of non-linear frameworks have been proposed, such as the log-ratio approach and multiplicative homomorphic system. Many of these are based on the logarithm, as it is the foundation for the well known Weber-Fechner Law of human visual response, including the Logarithmic Image Processing (LIP) model. LIP was introduced to address the four fundamental requirements of an image processing framework; (1) physically relevant image formation model, (2) operations consistent with physical images, (3) computationally effective operations, (4) practical application.;While the LIP model has been shown to address these issues, it still has some practical limitations. For example, when multiple images are combined they can quickly go to saturation, causing clipping and loss of information. Further, processed images are not always representative of their constituent images, necessitating a more meaningful form of fusion. One solution may be a parameterization of this model, allowing better control over the output range of the image, controlling overall brightness and contrast using a set of parameters tuned to any specific application using the training methods detailed. However, we will see that this leads to an under-constrained problem. For this purpose, we introduce a fifth fundamental requirement for an image processing framework; it must not damage either signal.;As edge detection is an important problem which is an ideal application for the PLIP model, this is first looked at as a practical application. The foundation for edge detection is accurate contrast detection, and LIP subtraction has been proved to be an accurate measure of contrast independent of illumination and small scale brightness changes. A number of PLIP based contrast detectors will be presented as well as a novel thresholding method based on the human visual system. Comparative results will be presented, showing the improved performance of PLIP on the basis of Pratt's Figure of Merit.;Pratt's Figure of Merit, however, can only assess a detected edge map when the true edge map is available for comparison. In general, this is only possible for synthetic images due to the high subjectivity of "ideal" edge detection for a natural scene. For this reason, a PLIP based edge detection measure which does not rely on known ground truth is investigated. As it has been proven that the intensity and gradient for all "ideal" edge pixels in an image form a complete basis for that image, an edge map can be tested by reconstructing the original from the intensity and gradient of only the detected edge pixels. This reconstructed image is then compared to the original on the basis of established similarity measures. Comparative results for the measure will be shown, using Pratt's Figure of Merit to compare, demonstrating improved performance for PLIP.;A number of image enhancement methods rely on accurate edge detection, such as anisotropic diffusion. For this reason, the edge detection system developed will be used in conjunction with the Low Contrast Image Simplifier (LCIS), a state-of-the-art anisotropic diffusion method. PLIP methods will be utilized throughout the system, forming the Parameterized LCIS (PLCIS). A simple image enhancement method proposed with the original LCIS will then be presented. Results for both PLIP and LIP for this enhancement algorithm will be presented, showing the improved performance of the PLIP on the basis of the EMEE, an objective measure of image enhancement.