Morphological filters for image enhancement
Digital images are subjected to filtering processes during the operations of noise reduction and lossy compression. Fine details are often lost or severely altered in these filtering processes. Connectivity preserving morphological filters haven been proposed in the past to remove noise while preserving thin but connected regions However, these filters preserved regional connectivity only in restricted orientations The present work has developed morphological filters that may be used for fast and efficient removal of noise while completely preserving connectivity information in gray scale images. These filters are shown to satisfy the requirements of well behaved abstract operations of algebraic opening and closing. When applied to the problem of speckle noise reduction from synthetic aperture radar images, the new filters performed significantly better than conventional linear and non-linear filters. The present work has also developed an image representation approach that may be used for developing high quality lossy image compression techniques based on morphological muhiresolution pyramid decomposition of images. A pyramid decomposition technique represents an image as a pyramid of differential images which store incremental information at various resolutions The lossy compression techniques based on pyramid decomposition often discard the first differential image component which usually consists of a substantial amount of high frequency noise. Complete omission of this image component can result in the loss of fine image details. The present work has developed an approach to approximately reconstruct the first differential image from its two components consisting of directional information. The simplification process is shown to be equivalent to connectivity preserving filtering. For various standard images, the entropies of the differential images were shown to decrease by 35% to 40% for approximately 10% mean square error between the original and the reconstructed differential images.