Binary Pictures Research Articles

Jordan surfaces in simply connected digital spaces

Certain tasks in multidimensional digital image analysis, in particular surface detection and volume estimation, lead us to the study of “surfaces” in the digital environment. It is desirable that these surfaces should have a “Jordan” property analogous to that of simple closed curves in two dimensions-namely, that they should partition the underlying space into an inside and an outside which are disconnected from each other. A version of this property, called near-Jordanness, has been previously defined and has been shown to be useful within a general theory of surfaces in digital spaces. The definition of a near-Jordan surface is global: it demands that all paths from the interior to the exterior cross the surface. This makes it difficult in many practical applications to check whether surfaces are near-Jordan. The work reported in this paper is motivated by the desire for a “local” condition, such that if a surface satisfies this condition at each of its elements, then it is guaranteed to be near-Jordan. In the search for such a condition, we were led to a concept of “simple connectedness” of a digital space, which resembles simple connectedness in ordinary topological spaces. We were then able to formulate the desired local condition for simply connected digital spaces. Many digital spaces, in particular those based on the commonly-studied tessellations of n-dimensional Euclidean space, are shown to be simply connected and thus our theory yields general sufficient conditions for boundaries in binary pictures to be near-Jordan.

A Boolean characterization of three-dimensional simple points

A simple point in a binary digital picture is a point belonging to the object whose removal does not change the basic connectivity features of the image. In this paper, we propose a Boolean characterization of three-dimensional simple points in cubic grids. This characterization requires the checking of 5 basic configurations in the neighborhood of the point considered.

Pyramidal thinning algorithm for SIMD parallel machines

We propose a parallel thinning algorithm for binary pictures. Given an N × N binary image including an object, our algorithm computes in O( N 2) the skeleton of the object, using a pyramidal decomposition of the picture. The behavior of this algorithm is studied considering a family of digitalization of the same object at a different level of resolution. With the Exclusive Read Exclusive Write (EREW) Parallel Random Access Machine (PRAM), our algorithm runs in O(log N) time using O( N 2/log N) processors and it is work-optimal. The same result is obtained with high-connectivity distributed memory SIMD machines having strong hypercube and pyramid. We describe the basic operator, the pyramidal algorithm and some experimental results on the SIMD MasPar parallel machine.

Microcomputer processing the photograph of timber with hole knots

A reliable method non-destructive X-ray test of wood defects with computer digital image processing technique was presented in the paper which made the knot-hole in wood clear and easily recognized. It was the first time to use maximum entropy to determine the threshold of binary picture and the result was satisfying. The improved Robert was used in the paper in the paper to outline the knot-hole so that the processing was almost on real time.

Jordan Pairs of Adjacency Relations in Digital Spaces

ABSTRACT: We define a digital space to be a pair consisting of an arbitrary nonempty set V and a symmetric binary relation π on V with respect to which V is connected. Our intent is to capture and investigate the notion of a boundary in this extremely general environment. Our motivation comes from practical applications, where boundaries need to be identified in multidimensional data sets with the further aim of displaying them on a computer screen. Our definitions are biased towards such applications. In particular, we refer to elements of V as spels (short for “spatial elements”). We call an arbitrary nonempty subset of a π surface and we define the notions of the interior and the exterior of a surface. We also introduce the notion of a near‐Jordan surface; its interior and exterior partition V. We call a symmetric binary relations on V that contains π a spel‐adjacency. For spel‐adjacencies κ and λ, we call a surface κλ‐Jordan if it is near‐Jordan, its interior is κ‐connected and its exterior is λ‐connected. Our first main result is that the surface between a κ‐connected set and any λ‐component of its complement is κλ‐Jordan. We introduce the notion of a binary picture in which there is an assignment of a 1 or a 0 to elements of V. A κλ‐boundary is defined as the surface between a λ‐component of 1‐spels and a λ‐component of 0‐spels. We discuss the notion of tightness for spel‐adjacencies. Our next main result is that for tight spel‐adjacencies κ and λ, the interior of a κλ‐boundary is κ‐connected, while its exterior is λ‐connected. We say that {κ, λ} is a Jordan pair, if κ and λ are tight spel‐adjacencies and every κλ‐boundary (equivalently, every λκ‐boundary) is near‐Jordan. It therefore follows from the previously stated result that if {κ, λ} is a Jordan pair, then a κλ‐boundary is κλ‐Jordan. We also show that if {κ, λ} is a Jordan pair and κ′ and λ′ are tight spel adjacencies containing κ and λ, respectively, then {κ′, λ′} is also a Jordan pair.

Ultra-fast parallel contour tracking, with applications to thinning

This paper proposes a parallel algorithm for contour tracking of binary pictures. Given an object contour composed by O(N) pixels, our algorithm computes in constant time the next layer of the contour of that object, using the weakest parallel model, i.e. an Exclusive Read Exclusive Write (EREW) Parallel Random Access Machine (PRAM). As an application of the technique we show a work-optimal parallel thinning algorithm for binary pictures, based on Pavlidis' characterization of a skeleton. Our algorithm improves on previous solutions by producing a list of coordinates corresponding to the skeleton contour in O(N) time with O(N) processors in an EREW PRAM, where N is the width of the picture.

Oriented Surfaces in Digital Spaces

We define a digital space to be a pair consisting of an arbitrary nonempty set V and a symmetric binary relation π on V with respect to which V is connected. Our intent is to investigate the notion of an oriented surface in this general environment. Our terminology reflects this: we refer to elements of V as spels (short for "spatial elements"), to artibrary nonempty subsets of π as surfaces, and we define the notions of the interior and the exterior of a surface. We introduce the notion of a near-Jordan surface, its interior and exterior partition V. We call a symmetric binary relation on V that contains π a spel-adjacency. For spel-adjacencies κ and λ, we call a surface κλ-Jordan if it is near-Jordan, its interior is κ-connected, and its exterior is λ-connected. We prove a number of results which characterize κλ-Jordan surfaces in general digital spaces and in binary pictures (in which there is an assignment of a 1 or a 0 to elements of V).

Oriented Surfaces in Digital Spaces

We define a digital space to be a pair consisting of an arbitrary nonempty set V and a symmetric binary relation π on V with respect to which V is connected. Our intent is to investigate the notion of an oriented surface in this general environment. Our terminology reflects this: we refer to elements of V as spels (short for "spatial elements"), to artibrary nonempty subsets of π as surfaces, and we define the notions of the interior and the exterior of a surface. We introduce the notion of a near-Jordan surface, its interior and exterior partition V. We call a symmetric binary relation on V that contains π a spel-adjacency. For spel-adjacencies κ and λ, we call a surface κλ-Jordan if it is near-Jordan, its interior is κ-connected, and its exterior is λ-connected. We prove a number of results which characterize κλ-Jordan surfaces in general digital spaces and in binary pictures (in which there is an assignment of a 1 or a 0 to elements of V).

A giant X-ray flare on Lambda Eridani (B2e)

A 30 ks observation with the ROSAT PSPC distributed over 39 hr shows that the putatively single, mild B2e star Lambda Eri emits at most times a soft X-ray flux at a rate and temperature consistent with other B stars. However, during the middle of our observations, this star's X-ray flux increased by a factor of 6 before returning to the basal level. This brightening, due entirely to photon energies of 0.7 keV or greater, can be fitted well to a Raymond-Smith temperature parameter of 14 MK and luminosity 4 x 10 exp 31 ergs/s; these are characteristics of giant stellar flares. With an estimated duration of about 50,000 s, this event is arguably the strongest X-ray flare yet observed. We consider several possible scenarios for the site of the flare, including several with an active cool secondary or degenerate companion. We find that IUE and optical spectra do not support a binary picture and that it is most probable that the flare site is on or related to Lambda Eri itself. This supports other evidence for violent magnetic activity on some B-type stars.

Concepts of digital topology

In an earlier paper written for a different readership [ Computers and Graphics 13(2) (1989) 159–166] the first author defined a digital fundamental group—an analog, for binary digital pictures, of the fundamental group. In general the definition of the digital fundamental group involves continuous deformation. But an alternative, discrete, definition of the digital fundamental group was proposed for the strongly normal digital picture spaces defined in the same paper. The above-mentioned paper also defined a “continuous analog” C( P ) for each binary digital picture P on such a DPS (DPS=digital picture space). C( P ) is a polyhedron constructed by “filling in the gaps” between black points (1's) of the binary digital picture P in a specific way. Other kinds of continuous analog had previously been used by the first two authors. In seeking the simplest and most efficient algorithms for performing image processing operations, researchers have considered many different combinations of grids and adjacency relations. Almost all of those combinations are isomorphic to special cases of the concept of a strongly normal DPS. The main contribution of the present paper is a proof that the digital fundamental groups of binary digital pictures on a strongly normal DPS are naturally isomorphic to the fundamental groups of the digital pictures' continuous analogs. We use this result to establish that on a strongly normal DPS the discrete and continuous definitions of the digital fundamental group are equivalent, up to a natural group isomorphism. We also show that many topological results which hold in the Euclidean plane or Euclidean 3-space have analogs that hold in every strongly normal DPS. Our results suggest that a strongly normal DPS is a suitable domain for studying topology-related image processing operations such as thinning, border tracking and contour filling. The definitions of digital fundamental group, strongly normal DPS and continuous analog are included in this paper so as to make it self-contained.

The topology of digital images

A fenestration of the topological space S is a collection of disjoint open sets whose union is dense in S. Every fenestration E determines a digitalization of S—a rule for assigning a partition ( A, B) of E to each partition ( P, Q) of S— and a family of quotient spaces of S, called grids, each of which contains E as a discrete subspace. The embedding of E in a grid allows topological properties of P and Q (modelling an object and its background) to be deduced from the attributes of the discrete sets A and B (modelling their digital images in an array of binary picture elements represented by E ). A grid is a trace space: a space with a dense set of isolated points. The paper uses the properties of such spaces to develop the elements of a topology of digital images.

Estimation of Ca2+-Induced Surface Structural Changes of Artificial Lipid Membrane.

The surface structure of an artificial membrane composed of a Millipore filter and a synthetic lipid analogue, dioleylphosphate (DOPH), changes from a highly reflective hydrophilic state to a poorly reflective hydrophobic state in KCl solution with increasing calcium ion concentration in the solution. Using a microscopic digital image processing system the structural changes can be characterized quantitatively, in a histogram of the brightness level and a binary black-and-white picture. The gross area of hydrophilic domains and the mean diameter of hydrophilic particles were measured by processing the binary picture.

A neural net based architecture for the segmentation of mixed gray-level and binary pictures

A neural-net-based architecture is proposed to perform segmentation in real time for mixed gray-level and binary pictures. In this approach, the composite picture is divided into 16*16 pixel blocks, which are identified as character blocks or image blocks on the basis of a dichotomy measure computed by an adaptive 16*16 neural net. For compression purposes, each image block is further divided into 4*4 subblocks and, similar to the classical block truncation coding (BTC) scheme, a one-bit nonparametric quantizer is used to encode 16*16 character and 4*4 image blocks. In this case, however, the binary map and quantizer levels are obtained through a neural net segmentor over each block. The efficiency of the neural segmentation in terms of computational speed, data compression, and quality of the compressed picture is demonstrated. The effect of weight quantization is also discussed. VLSI implementations of such adaptive neural nets in CMOS technology are described and simulated in real time for a maximum block size of 256 pixels.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Width-independent fast skeletonization algorithm for binary pictures

An effective algorithm of skeletonization for digital binary pictures based on input-time-tracing principle and sequential decomposition of input picture into simple parts is described. The proposed algorithm is fast and requires no image memory. Its computing complexity does not depend on the thickness of picture patterns and is determined not by the number of picture pixels but by the essentially small number of horizontal and vertical lines constituting the contour of the picture.

Morphological transformations of binary images with arbitrary structuring elements

This paper proposes a versatile algorithm for computing dilations and erosions of digital binary pictures with structuring elements of arbitrary size and shape. The first step consists in a tracking of the contours of the image under study and their encoding as loops. In a second step, the structuring element is efficiently propagated along the different loops thanks to its encoding in a customized data structure. The algorithm turns out to be extremely fast whatever the utilized elements. Moreover, even when simple shapes like squares or hexagons are considered, it is faster than most existing implementations. Finally, the present paper provides some examples of application, which highlight the practical interest of arbitrary structuring elements in the field of mathematical morphology.

Moment preserving detection of elliptical shapes in gray-scale images

A new method for elliptical shape detection based on the principle of gray and mass moment preserving is proposed. For each elliptical region in a gray-scale image, automatic bilevel thresholding based on gray moment preserving is used first to transform the blurred image in the region into a binary picture. The five parameters of the elliptical shape are then computed using the mass moment preserving principle. A major merit of the method is that these parameters can be uniquely and analytically determined without iterative computation. By the proposed method, other shapes like rectangles, circles, semi-circle running tracks, etc. can also be detected. Experimental results show the effectiveness of the proposed method.

Some geometric operations on binary pictures and their shape preserving properties

Shape preserving algorithms for magnification by arbitrary factors and rotation by arbitrary angles of binary pictures in two dimensions are presented. These algorithms may be useful for shape matching. How the proposed algorithms preserve the shape of the input picture is described.

Moment-preserving corner detection

A new corner detection method based on the principle of preserving gray and mass moments is proposed. For each circular region in a digital image, bilevel thresholding based on gray moment preserving is used first to transform the blurred subimage in the region into a binary picture. Two approximate boundary points on the circumference of the thresholded circular region are obtained next by simple traversal. An approximate corner point is estimated from the geometric relation between the centroid and the three vertices of the triangular lamina formed by the corner pattern within the circular region. These points are then used as an initial guess for solving a system of nonlinear equations that are constructed by preserving the area and the three mass moments of the partial object lamina within the circular region. More accurate corner boundary points can finally be determined, from which not only the location but also the orientation as well as the angle of the corner can be computed. Experimental results show the effectiveness of the proposed method.

The Pulse Extension Method for the Variable Neighborhood Distance Transformation of 2‐ and 3‐Dimensional Digitized Pictures

AbstractThis paper proposes a variable neighborhood distance transformation algorithm for two‐ and three‐dimensional (2‐D and 3‐D) digital binary pictures which is based on a new concept called path extension. The properties and performance of the method are experimentally evaluated. An algorithm was constructed using path extension which calculates the variable neighborhood distance for all one pixels in a 2‐D picture, using a sequence of four and eight neighborhoods composed in an appropriate way.In previous distance transformation algorithms, the distance for the central pixel under consideration is calculated uniquely from the distances of several neighborhood pixels, while the distance transformation in the path extension algorithm is executed by determining the distances of several neighborhood pixels from the distance of the central pixel under consideration.This paper proposes a serial path extension algorithm and two parallel path extension algorithms for both 2‐D and 3‐D pictures. For comparison of performance, one serial and one parallel algorithm, which are modifications of the traditional fixed neighborhood algorithms, are further analyzed. Finally, the results of an experimental evaluation are presented for computation time in the five proposed algorithms.

Gray scale pictures via Group 3 facsimile

The CCITT has developed a recommendation for Group 3 facsimile that is based on the transmission of binary picture elements (pels) having a brightness value that is either black or white. By introducing a minor modification into the basically bilevel facsimile system, dither coding delivers an output image that conveys gray-scale information. An analysis is made of three dither coding techniques: random dither, clumped dither and distributed dither. The comparison of random and clumped dither was also studied by simulation. The random dither simulation runs having the intermediate random number range (RNR=192) exhibited the best combination of maximum image quality and minimum number of transmitted bits, relative to the other random dither runs. The clumped dither images are superior to the best random dither image when both image quality and transmitted bits are considered. For clumped dither, the average compression ratio for the three images is only 1.39, which is significantly poorer than for the same images without dither coding. This compression ratio corresponds to a transmission time of 4.5 min over the public switched telephone network. Although this time is significantly longer than the 1 min typical for nondithered pictures, this performance may be most satisfactory for many requirements and applications. >