Recursive operations in image algebra

The image algebra, developed by Ritter et al. at the University of Florida, is an algebraic structure for image processing. The three commonly used high-level image-template operations provided by the image algebra are the generalized convolution , the additive maximum or generalized lattice convolution {ie23-1}, and the multiplicative maximum {ie23-2}. These are used to realize various nonrecursive image transformations, including morphological transformations. Along with nonrecursive transformations, a class of recursive transformations, such as IIR filters, adaptive dithering, and predictive coding, are also widely used in signal and image processing. In this paper the notions of recursive templates and recursive template operations are introduced; these allow the image algebra to express a set of linear and nonlinear recursive transformations. Algebraic properties of these recursive operations are given, providing a mathematical basis for recursive template composition and decomposition. Finally, applications of recursive template operations in specifying some image processing algorithms are presented.     

Vector quantization, an image-template mapping

The relation between a scalar-quantized image and the same image after vector quantization is shown to be an image-template mapping. The implications of this observation for some image processing procedures are discussed.     

Generalizing Operations of Binary Autoassociative Morphological Memories Using Fuzzy Set Theory

Morphological neural networks (MNNs) are a class of artificial neural networks whose operations can be expressed in the mathematical theory of minimax algebra. In a morphological neural net, the usual sum of weighted inputs is replaced by a maximum or minimum of weighted inputs (in this context, the weighting is performed by summing the weight and the input). We speak of a max product, a min product respectively.In recent years, a number of different MNN models and applications have emerged. The emphasis of this paper is on morphological associative memories (MAMs), in particular on binary autoassociative morphological memories (AMMs). We give a new set theoretic interpretation of recording and recall in binary AMMs and provide a generalization using fuzzy set theory.     

大结构元素二值形态学基本操作改进算法

二值图像的数学形态学方法应用广泛,但当涉及的图像和结构元素较大时,操作速度变慢。针对结构元素参考点包括在结构元素中且为单一连通区域的大结构元素,提出了二值形态学膨胀操作的改进算法,首先提取待膨胀二值区域的轮廓,然后对轮廓进行膨胀,再将膨胀结果与原二值区域取并集得到总的膨胀结果;证明了改进膨胀算法与标准膨胀操作的等价性;基于膨胀与腐蚀操作的对偶关系给出了改进的腐蚀算法;给出了改进的开、闭运算算法。在80张高分辨率植物叶片二值图像上进行了腐蚀、膨胀、开运算和闭运算标准方法和改进算法的对比实验,结果表明改进算法可显著提高二值形态学处理的速度。     

Methods for fast morphological image transforms using bitmapped binary images

In this paper we present new implementations for morphological binary image processing on a general-purpose computer, using a bitmap representation of binary images instead of representing binary images as bitplanes inserted in gray value images. The bitmap data representation is a very efficient one, both in terms of memory requirements and in terms of algorithmic efficiency because of the CPU operates on 32 pixels in parallel. The algorithms described in this paper are capable of performing the basic morphological image transforms using structuring elements of arbitrary size and shape. In order to speed up morphological operations with respect to commonly used, large, convex structuring elements, the logarithmic decomposition of structuring elements is used. Experiments indicate that the new algorithms are more than 30 times faster for pixelwise operations and about an order of magnitude faster for the basic morphological transforms than the fastest known software implementations.     

复杂车辆图像中的车牌快速形态定位算法

针对复杂环境下的车牌定位问题,提出了一种基于形态学的快速车牌定位方法。该方法先对车牌图像进行预处理和二值化,然后用形态学方法对二值化后的图像进行系列形态运算,将车牌图像分割为一个个独立的小区域,根据车牌特性去掉较小的区域,并对保留的连通域进行标记,最后用车牌形状特性进行车牌快速定位。实验结果表明,该方法定位效果好,速度快,适于应用对现实的车牌图像进行定位。     

Computational Gray-scale Mathematical Morphology on Lattices (A Comparator-based Image Algebra) Part 1: Architecture

Computational mathematical-morphology has been developed to provide a directly computable alternative to classical gray-scale morphology that is range preserving and compatible with the design of statistically optimal filters based on morphological representation. It serves as an image algebra because of the expressive capability of its image-operator representations. Because representations are based on binary comparators used in conjunction with AND and OR operations, it provides a low-level, efficient computational environment that is a direct extension of the finite Boolean operational environment. The paper focuses on development of the comparator-based representation, providing the relevant representation theory for lattice operators and lattice-vector operators. Computational lattice-operator theory represents a comparator-based alternative to the classical morphological lattice theory, one that is directly implementable in logic. For totally ordered valuation spaces, the lattice theory reduces to a simplified form appropriate to straightforward optimization. The present paper treats architectural considerations and a second part considers the implications for latticevalued image operators.     

数学形态学在图象处理中的应用进展

数学形态学是一种非线性滤波方法,形态和差运算,即膨胀与腐蚀是数学形态学的基础,数学形态学已由二值形态学、灰度形态软数学形态学、模糊形态学发展到模糊软形态学,可用于抑制噪声、特征提取、边缘检测、图象分割、形状识别,纹理分析、图象恢复与重建等图象处理问题,在图象处理领域得到了越来越广泛的应用,本文结合目前的研究进展,对数学形态学的理论研究及其应用进展进行综述性阐述。     

Binary image operations using non-coherent optical techniques

Information can be extracted from two valued images (binary images) by performing logical operations in which a new image is created which is a function of the original image. To form this new image, shifting, storage, and logical operations are required. Cross-correlating an image with a “transfer function image” and thresholding the resultant cross-correlation image will perform the equivalent operations in a single step. Experiments demonstrating the technique have been performed.     

一个基于图像代数的并行图像处理环境

系统可用性和应用程序可移植性差是许多现有的并行图像处理计算结构难以获得实际应用的重要原因，基于Ritter提出的图像代数理论，研究、实现了一个并行图像处理环境．用户在并行计算结构上进行程序设计时，只需用图像处理环境提供的图像代数运算描述算法即可，处理环境能够根据用户算法的描述，依据一个时间开销模型，自动从并行实现函数库中提取出最优或近似最优的并行代码完成算法的运行，算法的并行实现和并行计算结构的硬件细节对用户透明。     

Implementation of morphological filters using coordinate logic operations

In this paper we present a methodology for performing morphological operations using coordinate logic operations. Coordinate logic operations are simple and fast because they are logic operations among the corresponding binary values of the image pixels. Coordinate logic (CL) filters are a family of fast non-increasing, non-linear filters, which are based on coordinate logic operations. CL filters exhibit analogous properties to those of the morphological filters but due to their different definition they display slightly different response. This is revoked in this paper by using appropriate image gray level quantization and mapping of the resulting levels to a specific set of decimal numbers. Based on this approach some fast efficient implementations of morphological filters using CL operators are proposed.     

An interval‐based temporal algebra based on binary encoding of point relations

This paper presents a method for representing temporal interval relations using a bit‐encoded form of the relationships between interval end points. The set of bit patterns for each interval relationship yields a unique, single‐byte signature that forms the basis of a binary temporal algebra. Also presented is a matrix multiplication algorithm for computing transitive relations based on the definition of sum and product operations for the bit‐encoded relation signatures. This bit‐encoding encompasses the representation of unknown relations between end points of two intervals and captures ambiguities within a temporal system while providing an efficient binary algebra. Finally, an algorithm to compute the transitive closure over a set of intervals forming a temporal system is presented. The algorithm's complexity is analyzed and is O(n³), worst case, where n is the number of temporal intervals within the system. Empirical observations indicate that the closure algorithm completes in O(n²) time, on average. The small memory footprint for the bit‐code, the algorithmic transitive relation calculation, and the closure algorithm, together, form an efficient method for providing machine‐based temporal reasoning capabilities. ©2000 John Wiley & Sons, Inc.     

基于机器视觉的轴承防尘盖检测算法

为实现工业现场对轴承防尘盖的自动检测,对机器视觉检测的关键技术进行了研究,提出一套基于机器视觉对轴承防尘盖的检测,针对轴承图像的特点,采用了一种最小二乘法进行圆拟合圆检测算法,完成了轴承防尘盖区域的提取,对连通区域的特征进行了分析,再进行量化处理和判断.实验结果表明,该方法实时性好,准确率高,可以满足工业检测需求.     

Design and use of DIP-1: A fast, flexible and dynamically microprogrammable pipelined image processor

The design of a fast, flexible and dynamically microprogrammable pipelined image processor is presented. The machine is especially suited, though not completely devoted, to perform local operations (up to 16 × 16) of both logical and arithmetic character on pictures, stored in a random access image memory in a 256 level grey scale. Separate parts of the machine take care of data manipulation and address generation. The machine's functioning is illustrated by discussing the way in which arithmetic N × N neighbourhood operations and binary 3 × 3 neighbourhood operations were implemented and finally the software supporting microprogram development and debugging and the run-time support software is described.     

A binary operation on trees and an initial algebra characterization for finite tree types

Summary A binary operation on the class of trees is defined that generates a set B of finite trees form a trivial tree (one node) and B contains for every finite tree G exactly one element isomorphic to G. The binary operation defines an algebraic structure on B, and as a consequence the finite tree types are characterized as an initial algebra in the same way as the natural numbers are characterized as an initial algebra by the Peano-Lawvere axiom [2]. Simple and primitive recursion are defined and some applications of the initial algebra characterization are given.     

Medial axis transform on mesh-connected computers with hyperbus broadcasting

To represent a region of a digital image as the union of maximal upright squares contained in the region is called the medial axis transform. In this paper, we present anO(logn) time parallel algorithm for the medial axis transform of ann×n binary image on an SIMD mesh-connected computers with hyperbus broadcasting usingn ³ processors.     

基于稀疏特性的盲二值图像去模糊

通过分析二值图像发现其像素值具有稀疏特性,因此采用L₀梯度反卷积算法结合二值图像的组合特性来处理盲二值图像的复原问题。常见的图像复原方法均将二值图像看作灰度值图像来处理,当其考虑到二值图像的特殊性质时,将会针对这种特定类型的图像得到更好的复原效果。提出的盲复原算法基于一阶梯度空间L₀最小化问题的框架,利用L₀梯度图像平滑方法来获得明显的图像边缘以估计模糊核,并将二值图像的特有属性作为正则项加入目标函数。在图像的复原过程中,通过二值图像先验来强制复原结果趋于二值图像。根据提出的模型,给出了基于稀疏特性的盲二值图像复原算法。通过实验将该算法与传统的盲反卷积复原算法进行比较,结果表明所提算法具有良好的性能,对二值图像进行复原是有效的。     

基于形态学重建颗粒分析的微囊体测量方法

电子墨水的制作过程中,微囊体颗粒的大小及均匀性是衡量其质量的重要指标,尽管可通过形态学颗粒分析等手段统计出这些参数,但由于颗粒分析是基于形态学开运算的,在测量过程中,容易造成微囊体颗粒的形状和大小改变。为此提出了一种基于形态学重建颗粒分析的微囊体图像测量方法,首先将获取的彩色微囊体颗粒图像转化为灰度图像,然后利用形态学区域开滤除小噪声斑点后,采用双阈值进行二值化;通过分水岭变换分离相互粘连的微囊颗粒体,最后采用基于形态学开重建的颗粒分析,在有效保证微囊体颗粒形状和大小的前提下,准确统计出微囊体颗粒的大小分布情况。实验表明,该方法能准确有效地统计出微囊体颗粒的大小分布等指标。     

求解二值图像连通域的改进算法

介绍了一种改进的二值图像连通域快速标记方法。该算法首先找出二值图像中每行的像素直线段,接着利用链表来确定它们之间的连通关系,以此来克服同类算法中像素重复标记和标记归并需大量运算等缺陷,具有一定的使用价值。