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

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

Unsupervised morphological segmentation for images

This paper deals with a morphological approach to unsupervised image segmentation. The proposed technique relies on a multiscale Top-Down approach allowing a hierarchical processing of the data ranging from the most global scale to the most detailed one. At each scale, the algorithm consists of four steps: image simplification, feature extraction, contour localization and quality estimation. The main emphasis of this paper is to discuss the selection of a simplification filter for segmentation. Morphological filters based on reconstruction proved to be very efficient for this purpose. The resulting unsupervised algorithm is very robust and can deal with very different type of images.Peer ReviewedPostprint (published version

Electrocardiogram Baseline Wander Suppression Based on the Combination of Morphological and Wavelet Transformation Based Filtering

One of the major noise components in electrocardiogram (ECG) is the baseline wander (BW). Effective methods for suppressing BW include the wavelet-based (WT) and the mathematical morphological filtering-based (MMF)algorithms. However, the T waveform distortions introduced by the WTand the rectangular/trapezoidal distortions introduced by MMF degrade the quality of the output signal. Hence, in this study, we introduce a method by combining the MMF and WTto overcome the shortcomings of both existing methods. To demonstrate the effectiveness of the proposed method, artificial ECG signals containing a clinicalBW are used for numerical simulation, and we also create a realistic model of baseline wander to compare the proposed method with other state-of-the-art methods commonly used in the literature. /e results show that the BW suppression effect of the proposed method is better than that of the others. Also, the new method is capable of preserving the outline of the BW and avoiding waveform distortions caused by the morphology filter, thereby obtaining an enhanced quality of ECG

A reconfigurable real-time morphological system for augmented vision

There is a significant number of visually impaired individuals who suffer sensitivity loss to high spatial frequencies, for whom current optical devices are limited in degree of visual aid and practical application. Digital image and video processing offers a variety of effective visual enhancement methods that can be utilised to obtain a practical augmented vision head-mounted display device. The high spatial frequencies of an image can be extracted by edge detection techniques and overlaid on top of the original image to improve visual perception among the visually impaired. Augmented visual aid devices require highly user-customisable algorithm designs for subjective configuration per task, where current digital image processing visual aids offer very little user-configurable options. This paper presents a highly user-reconfigurable morphological edge enhancement system on field-programmable gate array, where the morphological, internal and external edge gradients can be selected from the presented architecture with specified edge thickness and magnitude. In addition, the morphology architecture supports reconfigurable shape structuring elements and configurable morphological operations. The proposed morphology-based visual enhancement system introduces a high degree of user flexibility in addition to meeting real-time constraints capable of obtaining 93 fps for high-definition image resolution

On morphological hierarchical representations for image processing and spatial data clustering

Hierarchical data representations in the context of classi cation and data clustering were put forward during the fties. Recently, hierarchical image representations have gained renewed interest for segmentation purposes. In this paper, we briefly survey fundamental results on hierarchical clustering and then detail recent paradigms developed for the hierarchical representation of images in the framework of mathematical morphology: constrained connectivity and ultrametric watersheds. Constrained connectivity can be viewed as a way to constrain an initial hierarchy in such a way that a set of desired constraints are satis ed. The framework of ultrametric watersheds provides a generic scheme for computing any hierarchical connected clustering, in particular when such a hierarchy is constrained. The suitability of this framework for solving practical problems is illustrated with applications in remote sensing

Convex Structuring Element Decomposition for Single Scan Binary Mathematical Morphology

International audienceThis paper presents a structuring element decomposition method and a corresponding morphological erosion algorithm able to compute the binary erosion of an image using a single regular pass whatever the size of the convex structuring element. Similarly to classical dilation-based methods, the proposed decomposition is iterative and builds a growing set of structuring elements. The novelty consists in using the set union instead of the Minkowski sum as the elementary structuring element construction operator. At each step of the construction, already-built elements can be joined together in any combination of translations and set unions. There is no restrictions on the shape of the structuring element that can be built. Arbitrary shape decompositions can be obtained with existing genetic algorithms with an homogeneous construction method. This paper, however, addresses the problem of convex shape decomposition with a deterministic method

Image watermarking, steganography, and morphological processing

With the fast development of computer technology, research in the fields of multimedia security, image processing, and robot vision have recently become popular. Image watermarking, steganogrphic system, morphological processing and shortest path planning are important subjects among them. In this dissertation, the fundamental techniques are reviewed first followed by the presentation of novel algorithms and theorems for these three subjects. The research on multimedia security consists of two parts, image watermarking and steganographic system. In image watermarking, several algorithms are developed to achieve different goals as shown below. In order to embed more watermarks and to minimize distortion of watermarked images, a novel watermarking technique using combinational spatial and frequency domains is presented. In order to correct rounding errors, a novel technique based on the genetic algorithm (GA) is developed. By separating medical images into Region of Interest (ROI) and non-ROI parts, higher compression rates can be achieved where the ROI is compressed by lossless compression and the non-ROI by lossy compression. The GA-based watermarking technique can also be considered as a fundamental platform for other fragile watermarking techniques. In order to simplify the selection and integrate different watermarking techniques, a novel adjusted-purpose digital watermarking is developed. In order to enlarge the capacity of robust watermarking, a novel robust high-capacity watermarking is developed. In steganographic system, a novel steganographic algorithm is developed by using GA to break the inspection of steganalytic system. In morphological processing, the GA-based techniques are developed to decompose arbitrary shapes of big binary structuring elements and arbitrary values of big grayscale structuring elements into small ones. The decomposition is suited for a parallel-pipelined architecture. The techniques can speed up the morphological processing and allow full freedom for users to design any type and any size of binary and grayscale structuring elements. In applications such as shortest path planning, a novel method is first presented to obtaining Euclidean distance transformation (EDT) in just two scans of image. The shortest path can be extracted based on distance maps by tracking minimum values. In order to record the motion path, a new chain-code representation is developed to allow forward and backward movements. By placing the smooth turning-angle constraint, it is possible to mimic realistic motions of cars. By using dynamically rotational morphology, it is not only guarantee collision-free in the shortest path, but also reduce time complexity dramatically. As soon as the distance map of a destination and collision-free codes have been established off-line, shortest paths of cars given any starting location toward the destination can be promptly obtained on-line