In this thesis we develop algorithms for the processing of textures and images using a ladder-based biorthogonal directional filter bank (DFB). This work is based on the DFB originally proposed by Bamberger and Smith. First we present a novel implementation of this filter bank using ladder structures. This new DFB provides non-trivial FIR perfect reconstruction systems which are computationally very efficient. Furthermore we address the lack of shift-invariance in the DFB by presenting a novel undecimated DFB that preserves the computational simplicity of its maximally decimated counterpart. Finally, we study the use of the DFB in combination with pyramidal structures to form polar-separable image decompositions. Using the proposed filter banks we develop and evaluate algorithms for texture classification, segmentation and synthesis. We perform a comparative study with other image representations and find that the DFB provides some of the best results reported on the data sets used. Using the proposed directional pyramids we adapt wavelet thresholding algorithms. We find that our decompositions provide better edge and contour preservation than the best results reported using the undecimated discrete wavelet transform. Finally, we apply the developed algorithms to the analysis and processing of synthetic aperture radar (SAR) imagery. SAR image analysis is impaired by the presence of speckle noise. Our first objective will be to study the removal of speckle to enhance the visual quality of the image. Additionally, we implement land cover segmentation and classification algorithms taking advantage of the textural characteristics of SAR images. Finally, we propose a model-based SAR image compression algorithm in which the speckle component is separated from the structural features of a scene. The speckle component is captured with a texture model and the scene component is coded with a wavelet coder at very low bit rates. The resulting decompressed images have a better perceptual quality than SAR images compressed without removing speckle.