A machine learning approach for digital image restoration

This paper illustrates the process of image restoration in the sense of detecting images within a scanned document such as a photo album or scrapbook. The primary use case of this research is to accelerate the cropping process for the employees of Cinetis, a company based in Martigny, Switzerland that specializes in the digitalization of old media formats. In this paper, we will first summarize the state of the art in this field of research. This will include explanations of various techniques and algorithms involved with feature and document detection used by various digital companies

On the Complexity of the Class of Regions Computable by a Two-Layered Perceptron

This work is concerned with the computational complexity of the recognition of \mbox{LP}_2, the class of regions of the Euclidian space that can be classified exactly by a two-layered perceptron. Several subclasses of \mbox{LP}_2 of particular interest are also considered. We show that the recognition problems of \mbox{LP}_2 and of other classes considered here are intractable, even in some favorable circumstances. We then identify special cases having polynomial time algorithms

On the Complexity of Recognizing Regions Computable by Two-Layered Perceptrons

This work is concerned with the computational complexity of the recognition of $ÞPtwo$, the class of regions of the Euclidian space that can be classified exactly by a two-layered perceptron. Some subclasses of $ÞPtwo$ of particular interest are also studied, such as the class of iterated differences of polyhedra, or the class of regions $V$ that can be classified by a two-layered perceptron with as only hidden units the ones associated to $(d-1)$-dimensional facets of $V$. In this paper, we show that the recognition problem for $ÞPtwo$ as well as most other subclasses considered here is \NPH\ in the most general case. We then identify special cases that admit polynomial time algorithms

Modélisation et visualisation infographiques tridimensionnelles de structures et propriétés géologiques

This project, the computer-aided three-dimensional modeling and visualization of geological structures and properties, was conceived in the framework of the INFOGEOL project, "Modeling of Underground Civil Engineering Works Intersecting Geologic Structures". This project is carried out by the Laboratory of Geology of the Swiss Federal lnstitute of Technology in Lausanne (GEOLEP-EPFL). The work presented here is oriented to solving problems connected with modeling geologic structures rather than civil works, which already benefit from sophisticated 3-D modeling CAD (Computer Aided Design) packages. The research had three primary goals: to determine the 3-D graphic computer situation available in the modeling and visualizing of geological structures and properties; to present a method and software that solve the major geological modeling problems; and to illustrate the benefits of 3-D modeling in solving problems in the Earth Sciences. Statement of the 3-D representation of geological objects The main characteristics of the application of the 3-D computer modeling in geology are discussed in this section. The visualization principle is based on the representation of block diagrams similar to those created by geologists since the first geological studies. The evolution of computer technology has made the construction of such models easier. In addition, computer technology has optimized the use of such models by creating tools for viewing these blocks from any angle, for separating the blocks into the objects that compose them, for slicing through the blocks in any direction, and so on. To obtain this goal of visualizing and manipulating these block diagrams, some additional constraints must be discussed : they concern the available hardware and software techniques. Because of their design, workstations are the only computers that allow efficient work in the 3-D computing domain. As such, these workstations were used in the development of our methods. From the standpoint of the methodology, the techniques used in this study are different from those of a CAD system: the aim is not to create objects as an architect does (an ab initio process), but to build objects from existing data (an interpolation process). The main problems encountered in developing the new method are : the modeling of overturned structures, such as recumbent folds; the computation of intersections between surfaces; and the volume representation of each object. In addition, the modeling process must be done with the maximum amount of data precision, which ultimately determines the quality and the validity of the model. Presentation of the method and software In the framework of this research project, a partnership has been established with Dynamic Graphics, Inc., a Californian software Company specializing in mapping and modeling of geologic data. From that arrangement, developments have allowed the production of a system that solves all the problems discussed above. In addition, the software allows the computation and visualization of the spatial distribution of geological properties, represented within their structural framework of geologic layers. A general modeling methodology is suggested in the four steps described below: Acquisition, introduction, and organization of data. Modeling of surfaces using interpolation processes. Organization of surfaces by dividing the model into fault blocks, defining a chronological sequence in each fault block, and computing the intersections between the surfaces and the fault blocks. Volume creation by filling the space between surfaces. The software can model and represent any kind of geological or civil work structure as a surface or volume, as long as suitable and usable information is available. Benefits of the three-dimensional approach Several practical examples illustrate the use of the proposed software and show that any geological domain can benefit from this modeling approach. The 3-D approach allows the greater control of geological data and how they are incorporated into a model. It encourages an in-depth look into the structural geometry and enhances the comprehension of the geologic relationships. It makes possible the testing of different interpretations and to show off eventual geometric inconsistencies. From an engineering viewpoint, such visualization makes the implementation of civil works much easier, and aids in making decisions and following the construction progress. Use of such software requires some precautions: users must have computer knowledge, must know how to understand and avoid extrapolation in areas lacking data, and must never forget that the models are only as good as the data input to the computer. Results must be considered as possible solutions and not as the exact representation of reality. The validity of an interpretation done from the model depends on such prudence. The quality of the collaboration existing between the person who develops the model and the responsible project geologist is also important in determining an accurate and reliable model. The evolution of computer software and hardware technology promises a beautiful future for 3-D graphic computing as applied to the Earth Sciences. As the method and software become incorporated throughout the geologic community, every level of geologist will be able to benefit from the advantages of 3-D modeling in order to better understand and solve problems in any geologic study

On the Power of Democratic Networks

Linear Threshold Boolean units (LTU) are the basic processing components of artificial neural networks of Boolean activations. Quantization of their parameters is a central question in hardware implementation, when numerical technologies are used to store the configuration of the circuit. In the previous studies on the circuit complexity of feedforward neural networks, no differences had been made between a network with ``small'' integer weights and one composed of majority units (LTU with weights in {-1,0, 1}), since any connection of weight w (w integer) can be simulated by |w| connections of value Sgn(w). This paper will focus on the circuit complexity of democratic networks, i.e. circuits of majority units with at most one connection between each pair of units. The main results presented are the following: any Boolean function can be computed by a depth-3 non-degenerate democratic network and can be expressed as a linear threshold function of majorities; AT-LEAST-k and AT-MOST-k are computable by a depth-2, polynomial size democratic network; the smallest sizes of depth-2 circuits computing PARITY are identical for a democratic network and for a usual network; the VC of the class of the majority functions is n 1, i.e. equal to that of the class of any linear threshold functions