A Parallel Algorithmic Pattern

Journal of Computer Science, 2006

The tools of mathematical morphology developed within the framework of the image processing, require of big capacity of data and the very high costs of execution. So today, the limits of the sequential machines are not to be any more to show, the passage in the new parallel machines of type Simd, Mimd, clusters or grids is imperative. This paper deals with problems related to the parallelisation of the algorithm of mathematical morphology and highlights the resources influencing over the computing time. This study leans on the various levels of parallelisable calculation to evaluate the awaited profits then in term of processing time. An implementation of a whole of algorithms of reference is carried out on a cluster and a simd computer.

From Theory to Applications, 2013

Since the Babylonians and more recently since Lovelace [STU 87], an algorithm has been formally defined as a series operations sequenced to solve a problem by a calculation. morphology, filters or operators usually operate on sets or functions and are defined in formal mathematical terms. An algorithm is therefore the expression of an efficient solution leading to the same result as the mathematical operator applied to input data. This translation process in a mathematical algorithm aims to facilitate the implementation of an operator on a computer as a program regardless of the chosen programming language. Consequently, the algorithmic description should be expressed in general and abstract terms in order to allow implementations in any environment (platform, language, toolbox, library, etc.). Computer scientists are familiar with the formalization of the concept of an algorithm and computation on a real computer with the Turing machine [TUR 36]. This formalization enables any correct algorithm to be implemented, although not in a tractable form. Rather than describing algorithms with this formalism, we use a more intuitive notation that, in particular, relies on non-trivial data structures. This chapter is organized as follows. In section 12.2, we first discuss the translation process of data structures and mathematical morphology definitions in computational terms. In section 12.3, we deal with different aspects related to algorithms in the scope of mathematical morphology. In particular, we propose a taxonomy, discuss possible tradeoffs, and present algorithmic classes. These aspects are put into perspective for the particular case of the morphological reconstruction operator in section 12.4. Finally, historical perspectives and bibliographic notes are presented in section 12.5. 12.2. Translation of definitions and algorithms 12.2.1. Data structures Before discussing an algorithm, we have to describe the data to be processed and how they materialize once they are no longer pure mathematical objects.

2000

Multichannel images are characteristic of certain applications, such as medical imaging or remotely sensed data analysis. In such images, each pixel is given by a vector of values. Due to the large data volumes often associated with multichannel imagery, there is a need for parallel algorithms able to process those data quickly enough for practical use. This paper describes a

Journal of Real-Time Image Processing, 2011

Many useful morphological filters are built as more or less long concatenations of erosions and dilations: openings, closings, size distributions, sequential filters, etc. An efficient implementation of such concatenation would allow all the sequentially concatenated operators run simultaneously, on the time-delayed data. A recent algorithm (see below) for the morphological dilation/erosion allows such inter-operator parallelism. This paper introduces an additional, intra-operator level of parallelism in this dilation/erosion algorithm. Realized in a dedicated hardware, for rectangular structuring elements with programmable size, such an implementation allows to obtain previously unachievable, real-time performances for these traditionally costly operators. Low latency and memory requirements are the main benefits when the performance is not deteriorated even for long concatenations or high-resolution images.

Proceedings 14th International Parallel and Distributed Processing Symposium. IPDPS 2000, 2000

One of the most important features in image analysis and understanding is shape. Mathematical morphology is the image processing branch that deals with shape analysis. The definition of all morphological transformations is based on two primitive operations, i.e. dilation and erosion. Since many applications require the solution of morphological problems in real time, researching time efficient algorithms for these two operations is crucial. In this paper, efficient parallel algorithms for the binary dilation and erosion are presented and evaluated for an advanced associative processor. Simulation results indicate that the achieved speedup is linear.

Journal of Electronic Imaging, 2001

One of the most important features in image analysis and understanding is shape. Mathematical morphology is the image processing branch that deals with shape analysis. The definition of all morphological transformations is based on two primitive operations, i.e. dilation and erosion. Since many applications require the solution of morphological problems in real time, researching time efficient algorithms for these two operations is crucial. In this paper, efficient parallel algorithms for the binary dilation and erosion are presented and evaluated for an advanced associative processor. Simulation results indicate that the achieved speedup is linear.

2004

In this book chapter (for the forthcoming Oxford Handbook of Morphological Theory, edited by Audring & Masini) we develop an account of morphology, couched in the framework of the Parallel Architecture.

Proceedings of the IEEE, 2002

Many works have been done for parallelizing low-level image analysis computations. However, the task is harder for higher levels, as the data manipulations are complex, and there is a wide range of algorithms to encompass. To allow concurently speed and programmability, a high-level programming model that can be efficiently implemented on parallel architectures is required. To achieve this goal, we propose the associative nets model, a parallel computing model for image analysis based on simple data-parallelism paradigms, providing special features, such as graph-based data structures to handle irregular data, virtual data-structures to ease hierarchical image descriptions, and specific primitives (dirassoc) to compute on the interpixels relation graph. For implementation purposes, the dirassoc computing primitive performs asynchronous local computations until it reaches stability. Asynchronism has many advantages for hardware (speed, power consumptions, and chip size) as well as in software (less synchronization barriers). However, to insure completion of the asynchronous operation, the dirassoc must use a set of specific operators (r-operators) introduced by Ducourthial. In this paper, we emphasize on the interest of the r-operators and of the asynchronous computations for image analysis algorithms. We give applications in distance transforms, contour closing, Voronoï segmentation, watershed segmentation, and mathematical morphology. Hence, we show that asynchronous computations are powerful tools for image analysis on interpixel graphs.

Pattern Recognition Letters, 1996

This paper presents a general algorithm that performs basic mathematical morphology operations, like erosions and openings, with any arbitrary shaped structuring element in an efficient way. It is shown that our algorithm has a lower or equal complexity but better computing time than all comparable known methods.