Fernando Muge

A system for reconstructing and visualising three-dimensional objects

Abstract This paper presents a software program for three-dimensional separation, geometrical reconstruction and visualisation of subsurface objects. It uses as input a file containing 3-D co-ordinates of object points and respective attributes converted into a grey scale level. The software consists of two main components: recognition software; 3-D reconstruction and visualisation software. Based on the input file, the first component generates a set of planes, containing two-dimensional sections. If the information needed (i.e. the number of points) is insufficient, an approximation or interpolation method is applied to build smooth 2-D section borders. The first software component divides the set of all 2-D sections into subsets of similar 2-D sections. The second one uses each subset to build geometrically different 3-D subsurface objects. An experiment is performed to validate the program capabilities. Data obtained by prospective drills from the Aljustrel mine located in the South of Portugal is used for generation of the input file. The surfaces of three ore bodes are reconstructed and visualised from three different viewpoints. The main differences between the presented software program and some packages for 3-D modelling and visualisation are discussed.

Map Segmentation by Colour Cube Genetic K-Mean Clustering

In this work, a method is described for evolving adaptive procedures for colour image segmentation. We formulate the segmentation problem as an optimisation problem and adopt evolutionary strategy of Genetic Algorithms (GA) for the clustering of small regions in colour feature space. The present approach uses k-Means unsupervised clustering methods into GA, namely for guiding this last Evolutionary Algorithm in his search for finding the optimal or sub-optimal data partition, task that as we know, requires a non-trivial search because of its intrinsic NP-complete nature. To solve this task, the appropriate genetic coding is also discussed, since this is a key aspect in the implementation. Our purpose is to demonstrate the efficiency of GA to automatic and unsupervised texture segmentation. Some examples in Colour Maps are presented and overall results discussed.

Interpolation approach for 3D smooth reconstruction of subsurface objects

The present paper assumes that 2D sections are cut from multiple 3D subsurface objects by means of a sparse set of finite planes. The problem considered is to develop an approach capable of creating a geodesic set by means of spatial 2D sections, which do not intersect after orthogonal projection on a plane. The geodesic set is to be used for generating intermediate 2D sections. Next, with the help of the generated 2D sections, together with the initial sections, 3D object reconstruction and visualization may be achieved. To fulfil this task, specific terms are introduced, such as extreme left (right) visible border points interpolated by means of a spatial polynomial curve. Then, each spatial couple of adjacent 2D sections are projected on a plane. If the projections cross each other, their union is considered to be a geodesic set. If the projections do not cross each other, they are linked at the extreme points by polynomial projections and again form a geodesic set. Each geodesic set is used for a morphological interpolation, and intermediate 2D sections are generated. Together with the initial sections, are used to build a 3D object surface. To validate the theory, a set of 2D sections is generated, using six cross sections (images) of an impermeable unit. Then, 3D unit visualizations are realized, using at first the initial section only, then the initial sections together with the generated set of 2D sections afterwards. The contributions of this approach to the problem of object visualization are discussed and compared with some other interpolation methods.

Automatic Feature Extraction and Recognition for Digital Access of Books of the Renaissance

Antique printed books constitute a heritage that should be preserved and used. With novel digitising techniques is now possible to have these books stored in digital format and accessible to a wider public. However it remains the problem of how to use them. DEBORA (Digital accEss to BOoks of the RenAissance) is a European project that aims to develop a system to interact with these books through world-wide networks. The main issue is to build a database accessible through client computers. That will require to built accompanying metadata that should characterise different components of the books as illuminated letters, banners, figures and key words in order to simplify and speed up the remote access. To solve these problems, digital image analysis algorithms regarding filtering, segmentation, separation of text from non-text, lines and word segmentation and word recognition were developed. Some novel ideas are presented and illustrated through examples.

Application of Morphological Operators to Supervised Multidimensional Data Classification

In this paper the use of mathematical morphology (MM) operators in the several steps of supervised multidimensional data classification methods is discussed. In a first step, that can be called low-level feature extraction, morphological operators are usually applied with filtering purposes but can also be applied to extract topological features that can be used to generate extra information enhancing the phenomena representation. In a second step, MM operators can also be used to to improve pixel based classification algorithms in the following phases: i) modelling of clusters hulls training samples, ii) defmition of criteria for processing overlapping clusters hulls and iii) 2D pattern space partition and distance function definition. Finally, in a third and last step of the classification procedure, low-level generalization algorithms can be used to perform the spatial arrangement of primitive image objects, giving a smoother, more simplified view of the classified image. Two examples of the application of this methodology to supervised classification are presented. The first one concerns the interpretation of geochemical data in a region in the south of Portugal, while the second one concerns the identification and mapping of the areas occupied by different forest cover types.

A Morphological Interpolation Approach — Geodesic Set Definition in Case of Empty Intersection

This article presents a morphological approach for the generation of intermediate 2D objects, using others 2D objects, as initial ones. The approach is useful for a smooth realistic 3D object’s visualisation, in case of shortage input information. The study is based on mathematical morphology concepts, such as geodesic distance and geodesic set definition, dealing with the case of empty intersection between the objects, in a orthogonal projection over a plane. A classical approach is used to define spatial polynomial curves, interpolating the extreme left and right sets of visible essential border points of the initial objects. Further, the arc of each curve bordered between a couple of initial 2D objects is orthogonal projected over the lower plane together with the upper 2D object. The projections and the object, all over the same plane, are used to create the geodesic set. Then, a set of intermediate sections, between each couple of initial objects, is defined by the application of a morphological linear interpolation. Experiments were performed in order to validate the theory. Real data obtained by well logs performed in Vale de Milhacos (Setubal - Portugal) was used for this propose, and the results are given in the article.

A mathematical morphology contribution to study some aspects of hydrogeological systems

In order to study groundwater flow and contaminant transport it is important to model the aquifer heterogeneities in terms of the spatial distribution of its hydrostratigraphic units. These units can vary strongly in thickness and can also be geometrically anisotropic and present different features concerning their neighbourhood relationships. In this paper a contribution of mathematical morphology is presented to study several aspects of hydrogeological systems, namely to create regular bodies, to identify flow paths in media and to establish a graph of vicinity relationships between hydrostratigraphic units. The developed methodologies are tested on a real case study in the aquifer system of Tejo river.

A Morphological Methodology for Features Identification in Satellite Images for Semi-automatic Cartographic Updating

This work investigates a way to exploit the information of satellite images in order to identify cartographic features, aiming at developing a software tool able to update digital maps automatically. A cartographic feature, like any object present in a multi-channel image, is a set of pixels with similar spectral response and a certain spatial relation between them. The current algorithm works iteratively and mixes the spatial information with the spectral one in an appropriate way to finally detect the whole shape of a cartographic feature starting from a pixel marked previously by the user in a remotely sensed image. It is also shown that Mathematical Morphology (MM) operators can handle the spatial and spectral information decreasing the computational cost. First, the structure of the main algorithm is presented, showing each step of its operational sequence. Then, some application examples are reported and, finally, some remarks illustrate the future possibilities of implementation and development of the algorithm.

A Case Study on the Application of Geostatistics and Image Analysis to Mine Planning

Geostatistical and image analysis techniques have been used in the mine planning of an underground wolframite mine (Panasqueira Mine, Portugal). The orebody is composed of a complex series of a near-horizontal quartz veins, associated with Hercynian granitic intrusion into the schist-greywake complex country rocks. Within the vein the ore minerals occur very erratically as individual large crystals which has made conventional chemical assay impractical. A technique based on the measurements of the areas of wolframite crystals exposed in the sidewalls of the mining faces has been used at the mine to estimate the ore reserves. It is based on the assumption that the area of wolframite per unit length can be considered an unbiased estimator of the product (accumulation) of the wolframite tenor and vein width. The purpose of this work is to study the cross-correlation between the spatial distribution of thickness and wolframite grade as a function of the measurement support. To characterize the spatial distribution of the wolframite crystals in the mining faces, textural parameters were obtained through mathematical morphology based image analysis. Results of this study could be applied to the estimation of the wolframite average grades of large panels for long term planning.