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Resume La radiographie du sein ou mammographie est de nos jours la methode la plus sensible pour detecter et diagnostiquer le cancer du sein. Pour obtenir un cliche de la meilleure qualite possible, un controle de qualite de la chaine de production mammographique est periodiquement effectue. Ce controle est actuellement fonde sur la lecture visuelle d'un cliche representant un sein artificiel. L'avenement du mammographe numerique et la necessite de s'affranchir du caractere subjectif et manuel de ce controle, conduisent a s'interesser a l'integration de methodes numeriques de traitement du signal et de l'image afin de rendre ce controle moins contraignant et plus objectif. Cet article presente une approche, fondee sur le traitement d’image, de lecture automatisee de cliches de fantomes. Il s'est agi dans un premier temps de numeriser les cliches d'un fantome du sein puis d'en extraire des images relatives aux principales inclusions simulant des amas de microcalcifications, des masses et des fibres. Ces images fortement bruitees et peu contrastees ont fait l'objet d'un pretraitement fonde sur une methode adaptative de rehaussement de contraste. Les images debruitees et rehaussees ainsi obtenues ont ete segmentees afin d'extraire les objets contenus dans le fantome. Les resultats obtenus concernent neuf cliches de fantomes et montrent que la lecture de tels cliches intervenant dans le controle de qualite des installations mammographiques pourrait etre effectuee de facon plus objective en utilisant les techniques de traitement d'image.

Graph theory through the minimal spanning tree is used to study the so-called long-range percolation (LRP). The percolation thresholds are determined for the ten nearest-neighbour connections related to the eleven mosaics permitted in the plane. It is shown that LRP makes it possible to retrieve the behaviour of continuum percolation.

Graph theory, through the minimal spanning tree (MST), is used to determine site percolation thresholds related to 2D regular lattices. It is shown that there is a direct relation between and a geometrical parameter characterizing the lattices. Moreover, the methodology developed in this paper makes it possible to study long-range percolation in an efficient way.

A quite new appoach based on the graph theory through the minimal spanning tree analysis is applied to the study of site percolation transitions in 2D regular lattices. The critical probability thresholds p c are computed for regular and semi-regular mosaics allowed in the plane. It is shown that there is a direct relation between p c and a geometrical parameter characterizing the mosaics.

The distribution of zero crossings for the profile of a statistically rough surface of a silver thin film is determined and compared with a Poisson distribution. It is shown that the density of zero crossings may be related to the autocorrelation length and might be a useful parameter for characterizing spatial information of statistically rough surfaces.

This paper deals with the accurate determination of height and slope distributions for surfaces of rough metallic deposits (magnesium, copper, silver, and gold). These distributions are computed using a microdensitometer analysis of electron micrographs of surface replicas. It is shown that most of the surfaces examined have reasonable Gaussian height and slope distributions. Apart from magnesium surfaces, the rms roughnesses determined from these distributions agree (within the accuracy range of their measurements) with rms roughnesses deduced from the autocovariance functions computed previously. Within the framework of scalar scattering theory, some emphasis is laid on the value of slopes to draw certain conclusions about the validity of the assumptions under which the scalar scattering theory is derived.

Linear structures such as blood vessels in medical images are important features for computer-aided diagnosis and follow-up of many diseases. In this letter a new tracking-based segmentation method is proposed to detect blood vessels in retinal angiorams. Bayesian segmentation with the Maximum a posteriori (MAP) Probability criterion is used for that purpose. First promising results are presented and discussed.

This paper deals with segmentation of breast anatomical regions, pectoral muscle, fatty and fibroglandular regions, using a Bayesian approach. This work is a part of a computer aided diagnosis project aiming at evaluating breast cancer risk and its association with characteristics (density, texture, etc.) of regions of interest on digitized mammograms. Novelty in this paper consists in applying and adapting Markov random field for detecting breast anatomical regions on digitized mammograms whereas most of previous works were focused on masses and microcalcifications. The developed method was tested on 50 digitized mammograms of the mini-MIAS database. Computer segmentation is compared to manual one made by a radiologist. A good agreement is obtained on 68% of the mini-MIAS mammographic image database used in this study. Given obtained segmentation results, the proposed method could be considered as a satisfying first approach for segmenting regions of interest in a breast.

A detection algorithm, aimed at separating the foveal avascular zone from the eye background in a numerical angiogram image, is developed. This method is based on the use of a test derived from signal statistical theory. Results show that our approach could be considered as a good computer-assisted tool for location and follow-up of retinal pathologies.

A method based on image processing of tumoral neighbourhood is described for studying masses. By using polar and pseudopolar representations for the tumor and its neighbourhood, it is possible to detect divergent structures around the lesion and to evidence fuzzy areas in the boundary of the tumor, which constitute two significant features of breast cancer. The degree of spiculation is deduced from a shape parameter that characterizes the irregularity of the boundary; the radial component of the gradient on the boundary provides a measurement of fuzzy appearance.

At constant enzyme concentration and with the full set of nucleotide substrates dictated by template sequence, the chain-length distribution of polymeric product varies with template concentration in reactions catalysed by wheat-germ RNA polymerase II. Under the same conditions, but in the presence of a single ribonucleoside triphosphate, the rate of condensation of the triphosphate substrate to a dinucleotide primer also exhibits a complex dependence with the template concentration. This effect is observed using poly[d(A-T)] as a template. For both reactions there are two extreme types of behaviour in each of which transcription appears to involve a single enzyme synthetic mode, characterized by either a high (at low template concentration) or a low (at high template concentration) probability of releasing the transcripts. A strong correlation is found between these two pathways, such that conditions favouring the abortive release of trinucleotide products in the single-step addition reaction are associated with the synthesis of short-length RNA species in productive elongation, and reciprocally. A model previously developed by Papanicolaou, Lecomte & Ninio [(1986) J. Mol. Biol. 189, 435-448] to account for the kinetics of polymerization/excision ratios with Escherichia coli DNA polymerase I, and by Job, Soulié, Job & Shire [(1988) J. Theor. Biol. 134, 273-289] for kinetics of RNA-chain elongation by wheat-germ RNA polymerase II provides an explanation for the observed behaviour with the plant transcriptase. The basic requirement of this model is a slow equilibrium between two states of the polymerization complex with distinct probabilities of releasing the product. In the presence of Mn2+, and under conditions allowing the synthesis of poly[r(A-U)], one of these states is involved in the formation of oligonucleotides shorter than 15 bases, whereas the other catalyses the polymerization of chains longer than 40 bases.

It is shown that rough surfaces of thin silver films deposited on LiF underlayers may be accurately described by a low-order autoregressive process. The autoregressive (AR) parameters are determined, and the advantages of describing statistically rough surfaces of thin deposits by linear models instead of with the traditional autocovariance function (ACF) or the profile power-spectral-density function (PPSDF) are discussed.

On etudie sous ultra vide statique, la conductivite optique et la structure des depots tres minces de lithium. On montre que la bande d'absorption situee au voisinage de 4 eV et dont la position ne depend pas de l'epaisseur des depots, est due a une transition interbande. Les bandes d'absorption anormales localisees dans la region d'absorption intrabande, sont dues a des oscillations collectives des electrons de conduction. On explique le deplacement de ces bandes d'absorption anormales avec l'epaisseur des depots, et leur largeur a mi hauteur importante, par un effet du a la forme des grains constituant le depot. On montre enfin qu'il existe une analogie etroite entre absorption d'un depot granulaire de lithium sur un support dielectrique, et absorption des centres colores colloidaux de lithium a l'interieur d'une matrice dielectrique.

In this paper, the very first results are reported about searching for the fractal nature of thin‐film top surfaces from the surface relief reconstructed by microdensitometer analysis of an electron micrograph of a shadowed replica of the surface. It is found that such a reconstruction could be very helpful when dealing with the fractal nature of a surface.

Profiles for the protoplasmic face of the freeze-fractured membrane from the root storage tissue of red beets are reconstructed by microdensitometry of electron micrographs of surface-shadowed platinum carbon replicas. Different distribution functions (heights, cross sections, volumes) related to the intramembrane particles are determined from the digitized profiles. Those distribution functions are used to obtain information about the size and shape of particles. Statistical functions such as autocovariance functions (ACFs) and roughness spectrum are also computed from quantized profiles. The initial portions of the ACFs have a Gaussian form whose parameters (root-mean-square surface roughness height δ and autocovariance length σ) are estimated. The parameter estimates deduced from ACFs are shown to be in good agreement with those retrieved from distribution functions. The method illustrated in this paper on plasma membrane particles from red beetroot cells is quite general and can be applied to any intramembrane particles.

The roughness spectrum $g(\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}})$ (or spectral density function) for surfaces of silver, copper, gold, and magnesium deposits is deduced from surface profiles determined by using microdensitometer analysis of micrographs of shadowed-surface carbon replicas. A process based on computation of autocovariance function via the fast-Fourier-transform algorithm is used. It is shown that the $g(\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}})$ function is not a perfect Gaussian function as is usually assumed. An analytical model is given that provides a rather suitable fit to the computed $g(\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}})$ functions. Results are compared with those obtained from optical experiments (mainly the attenuated-total-reflection method). Discrepancies between the values of $\ensuremath{\delta}$ (rms roughness) and $\ensuremath{\sigma}$ (autocorrelation length) determined by the use of our procedure and corresponding values deduced from optical experiments are elucidated.

From the micrograph density of a shadowed carbon replica of a surface it is possible by using a microdensitometer analysis to rebuild line by line the profile of that surface. The different stages necessary for such a reconstruction are summarized. Various reconstructions connected with metallic, optical, dielectric and biological surfaces are presented. Those restored profiles are used to estimate the moments (particularly the second one named the autocovariance function) that summarize statistical information on the various characteristic lengths describing the surface.

A new approach to study order and disorder in biological membranes and more generally in biological structures is developed. It is based on a graph constructed on the set points representing the position of particles. From this graph, which is called the minimal spanning tree, it is possible to deduce two parameters, namely the average length m and the standard deviation sigma which are characteristic of the repartition to be studied. The use of a diagram involving both m and sigma makes it possible to determine the degree of order by taking a simple reading in the (m, sigma) plane.

Autocovariance functions (ACF's) for rough surfaces of copper, silver, and gold deposits are deduced from surface profiles determined by the use of microdensitometer analysis of surface-shadowed carbon replicas. It is shown that the initial portions of the ACF's have a Gaussian form. The root-mean-square (rms) surface roughness $\ensuremath{\delta}$ and the autocorrelation length $\ensuremath{\sigma}$ are deduced for each surface. Values of $\ensuremath{\sigma}$ agree with corresponding values deduced from the ACF's of the surface slopes. Results of this study are compared with those previously obtained for rough magnesium deposits. We conclude that the Gaussian model is suitable to represent in general the ACF's of rough metallic surfaces. Lastly, it is shown that $\ensuremath{\sigma}$ increases with $\ensuremath{\delta}$, and within the accuracy range of their measurements there is a linear relation between $\ensuremath{\delta}$ and $\ensuremath{\sigma}$.

The action of air on thin layers of lithium prepared under a static ultrahigh vacuum is investigated. It is shown, during the degradation, that small grains develop at the metal surface. The growth of these small grains, whose contours are regular, takes place in an orderly manner. The presence of LiOH and LiNO3 in degraded films are shown, using electron diffraction patterns.

The dependence of the surface roughness of CaF 2 thin films on the film thickness d is determined by a technique using microdensitometer analysis of electron micrographs of surface replicas. The rms surface roughness δ and the autocovariance length σ have been found to depend linearly on d in the range 250 d

It is shown that a graph called the minimal spanning tree (MST) is capable of detecting several kinds of cluster structure in arbitrary points set. From a MST it is possible to deduce the average edge lengthm and the standard deviationσ, which are characteristics for the corresponding distribution. The use of a diagram involving bothm andσ makes it possible to determine the degree of order by taking a simple reading in the (m,σ) plane. It is also possible, through angular diagrams retrieved from the MST, to bring out directional properties. The method is applied to the study of the growth of granular thin films.

The minimal spanning tree (MST) method to analyse order and disorder in distributions of objects is used to investigate the percolation transition on a triangular lattice. It is shown numerically that the value of the threshold probability is retrieved, simultaneously with a new geometrical parameter: the mean edge length. This is expected to be useful in the conductivity studies of percolation networks such as dielectric breakdown, conductivity and other propagation phenomena. The potentialities of the method in dealing with an extensive study of percolation on continuous as well as lattice systems are also exhibited.

In this paper we present some results about the dependence of the surface roughness for thin silver films deposited upon calcium and lithium fluorides. It is found out that the underlayer’s effect is not the commonly expected one.

Experimental results dealing with the interband optical conductivity of granular deposits of lithium at room temperature are in good agreement with most recent theories. In this paper, results obtained at 6 K are different from the theoretical predictions and may be explained on the basis of a phase change in lithium at low temperature

Surface topography restitution from electronmicrographs of extended surface replicas in situA. LlebariaLaboratoire d'Astronomie Spatiale du Centre National de la Recherche ScientifiqueTraverse du Siphon, les Trois Lucs, 13012. Marseille, FranceM. Rasigni, G. Rasigni, J.P. Palmari, F. VarnierCentre d'Etudes des Couches Minces, Laboratoire Associe au Centre National de laRecherche Scientifique, Departement de Physique des Interactions Photons- Matiere,Universite Aix -Marseille III, Rue Henri Poincarre, 13397. Marseille Cedex 13, FranceAbstractAn original image processing procedure that reconstructs the surface topography of a hea-vy metal- shadowed replica from a digitized micrograph is presented. The theory of thismethod is established and its limits are discussed. The usefulness and validity of themedian filtering algorithm used in the data reduction are shown. The entire procedure hasbeen implemented in a small 16 bit minicomputer.The method has been used to study the rough surfaces of copper, silver, magnesium and golddeposits by autocovariance functions of surface profiles. The results show that good recons-tructions of extended surface replicas are obtained. Several new methods of improving thereconstruction process have been tested and are briefly presented.Under goodexperimental conditions the lateral resolution was 50 A for an overall field sizeof 40.000 A. This shows that our method may have important applications besides the study ofalterable metallic surfaces.11111111

From the micrograph density of a shadowed carbon replica of a surface it is possible, by using a microdensitometer analysis, to rebuild line by line the profile of that surface. After summarizing the different stages necessary for such a reconstruction, we study the influence on the restored profiles of the various parameters that are encountered during the various steps of experiment and computation. It is shown that the most important parameters are the shadow-casting angle, microdensitometer scanning aperture, and filtering characteristics. Other parameters such as magnification micrograph, microdensitometer scanning speed, and microdensitometer noise play a minor role. The best way to choose and fit the appropriate value of the various parameters is discussed.

Profiles for the exoplasmic face (EF) of the freeze-fractured plasma membrane from the root storage tissue of red beets are reconstructed by microdensitometry of micrographs of surface-shadowed-platinum carbon replicas. Autocovariance functions (ACFs) are computed from those profiles. The initial portions of the ACFs have a Gaussian form whose parameters (root mean square surface roughness and autocovariance length) are estimated. The parameter estimates are used to show that the pits on the EF faces are in good complementarity with the intramembrane particles seen on the complementary protoplasmic fracture faces.

We develop a new approach for studying order and disorder in sets of particles. This approach is based on a graph constructed from the set of points locating the positions of the particles. This graph, which is called the minimal spanning tree, allows us to deduce two parameters, namely, the average edge length $m$ and the standard deviation $\ensuremath{\sigma}$, which are characteristic of the repartition to be studied. The method is applied to particles of an aggregated lithium thin film deposited on a dielectric substrate. These particles are found to be partially ordered. The use of a diagram involving both $m$ and $\ensuremath{\sigma}$ turns out to be a powerful tool for the determination of the degree of order in very various systems.

A new methodology was developed to study dynamic processes topographically in biological systems by means of a graph-theoretical method. It is based upon order parameters obtained from a minimal spanning tree analysis coupled with computer simulations. The method was used to analyse the heterogeneous behavior of two neoplastic cell lines after treatment with laminin. The laminin-induced cell detachment was quantitated and shown to be inversely related to cell population density and thus to cellular interactions. Our statistical analysis is a very powerful tool to obtain information from seemingly disorderly heterogeneous biological models.

The spectral density functions g(k) of the surface roughness for polished optical surfaces of CaF2, MgF2, and LiF are computed from autocovariance functions, which in turn have been determined from surface profiles obtained by using a microdensitometer analysis of electron micrographs of shadowed surface replicas. The fast-Fourier-transform algorithm and a smoothing procedure have been used to determine the g(k) estimates. It is shown that g(k) is not a Gaussian function throughout, as is usually assumed. Spectral density functions gS′(k) of the surface slopes are also computed, and it is shown that results obtained are consistent with those deduced from g(k). Limitations of our method at low spatial frequency are discussed. An analytical model for g(k) is investigated that should be useful in performing theoretical calculations on scattering problems.

The different steps leading to the determination of a surface profile deduced from microdensitometer analysis of electron micrographs of shadowed surface replicas are reviewed. It is shown that monodimensional median filtering is sometimes inadequate to remove the low-frequency noise generated by the Levy–Wiener process. A new treatment is proposed that corrects this disadvantage.

We reconstruct the micrograph images from surface profiles previously obtained1 by using microdensitometer analysis of electron micrographs of surface replicas. These micrograph images compare favorably with the original images.

Autocovariance functions (ACF’s) G(x) for polished optical surfaces of CaF2, MgF2, and LiF are deduced from surface profiles determined by using microdensitometer analysis of micrographs of surface-shadowed carbon replicas. The different estimators allowing the ACF computation from its standard definition are reviewed, and their values are compared. ACF’s are also computed by using the fast-Fourier-transform algorithm. Results of both computations are in good agreement. It is shown that initial portions of ACF’s have a reasonable Gaussian form. The rms roughness height δ and the autocovariance length σ are deduced for each surface. The ACF’s of the surface slopes Gs′(x) are also computed, and it is shown that results obtained are consistent with results deduced from ACF’s for surface profiles. In particular, the standard relation between the second derivative of G(x) and Gs′(x) is reasonably verified. Finally, the exponential ACF model is discussed, and it is shown that this model would not be suitable to describe the initial portions of the ACF’s for the polished optical surfaces that we have studied.

A new method for studying surface roughness is presented that uses a microdensitometer to analyze electron micrographs of shadowed surface replicas. First we give a preliminary description of the replication technique and the microdensitometer analysis. Then we proceed to show that the micrograph density (or transmittance) is approximately proportional to the slope of the surface elements, which enables us to determine the surface profile by integration of the microdensitometer data. Bidimensional and monodimensional median-filtering algorithms are used in the data reduction, and their validity is analyzed. With the help of a computer program that plots a perspective view of rough surfaces, we find that a close approach to the real profiles is obtained. This shows that our method may have other important applications in addition to the study of alterable metallic surfaces.

Autocovariance functions (ACF’s) for rough surfaces of nickel electrodeposits are deduced from surface profiles determined by using microdensitometer analysis of micrographs of surface-shadowed carbon replicas. It is shown that the initial portions of the ACF’s have a Gaussian form. The root-mean-square surface roughness δ and the autocovariance length σ are deduced for each surface. Values of δ agree with corresponding values deduced from total integrated scattering measurements. Actually, surfaces of nickel electrodeposits are apparently random surfaces, so that more than one autocovariance length has to be defined. Finally, we discuss the relationship between the statistical parameters.