Adaptive Context-Tree-Based Statistical Filtering for Raster Map Image Denoising

Abstract

Filtering of raster map images is chosen as a case study of a more general class of palette-indexed images for the denoising problem of images with a discrete number of output colors. Statistical features of local context are analyzed to avoid damage to pixel-level patterns, which is frequently caused by conventional filters. We apply a universal statistical filter using context-tree modeling via a selective context expansion capturing those pixel combinations that are present in the image. The selective context expansion makes it possible to use a much larger spatial neighborhood, with a feasible time and memory complexity, than fixed-size templates. We improve the existing context-tree approaches in two aspects: Firstly, in order to circumvent the context contamination problem, a context-merging strategy is applied where multiple similar contexts are considered in the conditional probability estimation procedure. Secondly, we study a specific continuous-input-finite-output problem in which the map images are corrupted by additive Gaussian noise. Performance comparisons with competitive filters demonstrate that the proposed algorithm provides robust noise filtering performance and good structure preservation in all test cases without any a priori information on the statistical properties of the noise. Index Terms-Context-tree modeling, raster map image, statistical filtering. I. INTRODUCTION G EOGRAPHICAL map images are classified into two formats: raster and vector. Vector format is suitable for large databases, providing excellent flexibility for display and compact storage size. A raster image, on the other hand, is encoded in a regular grid of pixel colors in which each color represents a different class of semantic map object. It consists of pixel-level detailed structures and sharp edges but lacks smooth color transitions that are typical for photographic images. It does not require any additional image processing and is suitable for delivery to multimedia applications as such.

Adversarial attacks and defenses for visual signals

“…This step also renders the preprocessing stage non-differentiable, which makes it non-trivial for an adversary to optimize against, allowing only estimations to be made of the transformation [31]. We show in our evaluation (Section 4.2) that JPEG compression effectively removes adversarial perturbation Many classic methods address image denoising as a statistics problem using analytical priors [97][98][99]. BM3D [15], one of the most widely used algorithms tries to estimate the true signal by collaboratively filtering several similar image fragments and enhancing their sparsity in the frequency domain.…”