Optimum non linear binary image restoration through linear grey-scale operations

Non-linear image processing operators give excellent results in a number of image processing tasks such as restoration and object recognition. However they are frequently excluded from use in solutions because the system designer does not wish to introduce additional hardware or algorithms and because their design can appear to be ad hoc. In practice the median filter is often used though it is rarely optimal. This paper explains how various non-linear image processing operators may be implemented on a basic linear image processing system using only convolution and thresholding operations. The paper is aimed at image processing system developers wishing to include some non-linear processing operators without introducing additional system capabilities such as extra hardware components or software toolboxes. It may also be of benefit to the interested reader wishing to learn more about non-linear operators and alternative methods of design and implementation. The non-linear tools include various components of mathematical morphology, median and weighted median operators and various order statistic filters. As well as describing novel algorithms for implementation within a linear system the paper also explains how the optimum filter parameters may be estimated for a given image processing task. This novel approach is based on the weight monotonic property and is a direct rather than iterated method

A Learning Framework for Morphological Operators using Counter-Harmonic Mean

We present a novel framework for learning morphological operators using counter-harmonic mean. It combines concepts from morphology and convolutional neural networks. A thorough experimental validation analyzes basic morphological operators dilation and erosion, opening and closing, as well as the much more complex top-hat transform, for which we report a real-world application from the steel industry. Using online learning and stochastic gradient descent, our system learns both the structuring element and the composition of operators. It scales well to large datasets and online settings.Comment: Submitted to ISMM'1

Hierarchical stack filtering : a bitplane-based algorithm for massively parallel processors

With the development of novel parallel architectures for image processing, the implementation of well-known image operators needs to be reformulated to take advantage of the so-called massive parallelism. In this work, we propose a general algorithm that implements a large class of nonlinear filters, called stack filters, with a 2D-array processor. The proposed method consists of decomposing an image into bitplanes with the bitwise decomposition, and then process every bitplane hierarchically. The filtered image is reconstructed by simply stacking the filtered bitplanes according to their order of significance. Owing to its hierarchical structure, our algorithm allows us to trade-off between image quality and processing time, and to significantly reduce the computation time of low-entropy images. Also, experimental tests show that the processing time of our method is substantially lower than that of classical methods when using large structuring elements. All these features are of interest to a variety of real-time applications based on morphological operations such as video segmentation and video enhancement

Medical image enhancement using threshold decomposition driven adaptive morphological filter

One of the most common degradations in medical images is their poor contrast quality. This suggests the use of contrast enhancement methods as an attempt to modify the intensity distribution of the image. In this paper, a new edge detected morphological filter is proposed to sharpen digital medical images. This is done by detecting the positions of the edges and then applying a class of morphological filtering. Motivated by the success of threshold decomposition, gradientbased operators are used to detect the locations of the edges. A morphological filter is used to sharpen these detected edges. Experimental results demonstrate that the detected edge deblurring filter improved the visibility and perceptibility of various embedded structures in digital medical images. Moreover, the performance of the proposed filter is superior to that of other sharpener-type filters

The output distribution of important LULU-operators

Two procedures to compute the output distribution phi_S of certain stack filters S (so called erosion-dilation cascades) are given. One rests on the disjunctive normal form of S and also yields the rank selection probabilities. The other is based on inclusion-exclusion and e.g. yields phi_S for some important LULU-operators S. Properties of phi_S can be used to characterize smoothing properties of S. One of the methods discussed also allows for the calculation of the reliability polynomial of any positive Boolean function (e.g. one derived from a connected graph).Comment: 20 pages, up to trivial differences this is the final version to be published in Quaestiones Mathematicae 201

A fast method for computing the output of rank order filters within arbitrarily shaped windows

Rank order filters are used in a multitude of image processing tasks. Their application can range from simple preprocessing tasks which aim to reduce/remove noise, to more complex problems where such filters can be used to detect and segment image features. There is, therefore, a need to develop fast algorithms to compute the output of this class of filter. A number of methods for efficiently computing the output of specific rank order filters have been proposed [1]. For example, numerous fast algorithms exist that can be used for calculating the output of the median filter. Fast algorithms for calculating morphological erosions and dilations - which are also a special case of the more general rank order filter - have also been proposed. In this paper we present an extension of a recently introduced method for computing fast morphological operators to the more general case of rank order filters. Using our method, we are able to efficiently compute any rank, using any arbitrarily shaped window, such that it is possible to quickly compute the output of any rank order filter. We demonstrate the usefulness and efficiency of our technique by implementing a fast method for computing a recent generalisation of the morphological Hit-or-Miss Transform which makes it more robust in the presence of noise. We also compare the speed and efficiency of this routine with similar techniques that have been proposed in the literature

A new design tool for feature extraction in noisy images based on grayscale hit-or-miss transforms

The Hit-or-Miss transform (HMT) is a well known morphological transform capable of identifying features in digital images. When image features contain noise, texture or some other distortion, the HMT may fail. Various researchers have extended the HMT in different ways to make it more robust to noise. The most successful, and most recent extensions of the HMT for noise robustness, use rank order operators in place of standard morphological erosions and dilations. A major issue with the proposed methods is that no technique is provided for calculating the parameters that are introduced to generalize the HMT, and, in most cases, these parameters are determined empirically. We present here, a new conceptual interpretation of the HMT which uses a percentage occupancy (PO) function to implement the erosion and dilation operators in a single pass of the image. Further, we present a novel design tool, derived from this PO function that can be used to determine the only parameter for our routine and for other generalizations of the HMT proposed in the literature. We demonstrate the power of our technique using a set of very noisy images and draw a comparison between our method and the most recent extensions of the HMT

Flat zones filtering, connected operators, and filters by reconstruction

This correspondence deals with the notion of connected operators. Starting from the definition for operator acting on sets, it is shown how to extend it to operators acting on function. Typically, a connected operator acting on a function is a transformation that enlarges the partition of the space created by the flat zones of the functions. It is shown that from any connected operator acting on sets, one can construct a connected operator for functions (however, it is not the unique way of generating connected operators for functions). Moreover, the concept of pyramid is introduced in a formal way. It is shown that, if a pyramid is based on connected operators, the flat zones of the functions increase with the level of the pyramid. In other words, the flat zones are nested. Filters by reconstruction are defined and their main properties are presented. Finally, some examples of application of connected operators and use of flat zones are described.Peer ReviewedPostprint (published version

Detection of dirt impairments from archived film sequences : survey and evaluations

Film dirt is the most commonly encountered artifact in archive restoration applications. Since dirt usually appears as a temporally impulsive event, motion-compensated interframe processing is widely applied for its detection. However, motion-compensated prediction requires a high degree of complexity and can be unreliable when motion estimation fails. Consequently, many techniques using spatial or spatiotemporal filtering without motion were also been proposed as alternatives. A comprehensive survey and evaluation of existing methods is presented, in which both qualitative and quantitative performances are compared in terms of accuracy, robustness, and complexity. After analyzing these algorithms and identifying their limitations, we conclude with guidance in choosing from these algorithms and promising directions for future research

A Cosmic Watershed: the WVF Void Detection Technique

On megaparsec scales the Universe is permeated by an intricate filigree of clusters, filaments, sheets and voids, the Cosmic Web. For the understanding of its dynamical and hierarchical history it is crucial to identify objectively its complex morphological components. One of the most characteristic aspects is that of the dominant underdense Voids, the product of a hierarchical process driven by the collapse of minor voids in addition to the merging of large ones. In this study we present an objective void finder technique which involves a minimum of assumptions about the scale, structure and shape of voids. Our void finding method, the Watershed Void Finder (WVF), is based upon the Watershed Transform, a well-known technique for the segmentation of images. Importantly, the technique has the potential to trace the existing manifestations of a void hierarchy. The basic watershed transform is augmented by a variety of correction procedures to remove spurious structure resulting from sampling noise. This study contains a detailed description of the WVF. We demonstrate how it is able to trace and identify, relatively parameter free, voids and their surrounding (filamentary and planar) boundaries. We test the technique on a set of Kinematic Voronoi models, heuristic spatial models for a cellular distribution of matter. Comparison of the WVF segmentations of low noise and high noise Voronoi models with the quantitatively known spatial characteristics of the intrinsic Voronoi tessellation shows that the size and shape of the voids are succesfully retrieved. WVF manages to even reproduce the full void size distribution function.Comment: 24 pages, 15 figures, MNRAS accepted, for full resolution, see http://www.astro.rug.nl/~weygaert/tim1publication/watershed.pd