This paper addresses the noise estimation in the digital domain and proposes a noise estimator based on the step signal model. It is efficient for any distribution of noise because it does not rely only on the smallest amplitudes in the signal or image. The proposed approach uses polarized/directional derivatives and a nonlinear combination of these derivatives to estimate the noise distribution (e.g., Gaussian, Poisson, speckle, etc.). The moments of this measured distribution can be computed and are also calculated theoretically on the basis of noise distribution models. The 1D performances are detailed, and as this paper is mostly dedicated to image processing, a 2D extension is proposed. The 2D performances for several noise distributions and noise models are presented and are compared with selected other methods.

This paper presents a nonlinear derivative approach to addressing the problem of discrete edge detection. This edge detection scheme is based on the nonlinear combination of two polarized derivatives. Its main property is a favorable signal-to-noise ratio (SNR) at a very low computation cost and without any regularization. A 2D extension of the method is presented and the benefits of the 2D localization are discussed. The performance of the localization and SNR are compared to that obtained using classical edge detection schemes. Tests of the regularized versions and a theoretical estimation of the SNR improvement complete this work.

Supershape model is a recent primitive that represents numerous 3D shapes with several symmetry axes. The main interest of this model is its capability to reconstruct more complex shape than superquadric model with only one implicit equation. In this paper we propose a genetic algorithms to reconstruct a point cloud using those primitives. We used the pseudo-Euclidean distance to introduce a threshold to handle real data imperfection and speed up the process. Simulations using our proposed fitness functions and a fitness function based on inside-outside function show that our fitness function based on the pseudo-Euclidean distance performs better.

In this paper, we apply genetic algorithms to reconstruct Gielis surfaces from 3D data sets. The Levenberg-Marquardt method has been used as a standard for superquadrics recovery and has recently been extended to Gielis surfaces. Unfortunately, the non homogeneity of the Gielis surface parameters requires additional heuristic to determine discrete parameters such as the number of symmetries. Genetic algorithms overcome this issue and provide a more general framework for Gielis surface reconstruction.

In this letter, we address the problem of the influence of neighbor edges and their effect on the edge delocalization while extracting a neighbor contour by a derivative approach. The properties to be fulfilled by the regularization operators to minimize or suppress this side effect are deduced, and the best detectors are pointed out. The study is carried out in 1-D for discrete signal. We show that among the derivative filters, one of them can correctly detect our model edges without being influenced by a neighboring transition, whatever their separation distance is and their respective amplitude is. A model of contour and close transitions is presented and used throughout this letter. The noise effect on the edge delocalization is recalled through one of the Canny criteria. Different derivative filters are applied onto synthetic images, and their performances are compared

In this paper, we apply supershapes and R-functions to surface recovery from 3D data sets. Individual supershapes are separately recovered from a segmented mesh. R-functions are used to perform Boolean operations between the reconstructed parts to obtain a single implicit equation of the reconstructed object that is used to define a global error reconstruction function. We present surface recovery results ranging from single synthetic data to real complex objects involving the composition of several supershapes and holes.

We present a new multiresolution analysis framework for irregular meshes with attributes based on the lifting scheme. We introduce a surface prediction operator to compute the detail coefficients for the geometry and the attributes of the model. Attribute analysis gives appearance information to complete the geometrical analysis of the model. A set of experimental results are given to show the efficiency of our framework. We present two applications to adaptive visualization and denoising.

We present a new and efficient algorithm to accurately polygonize an implicit surface generated by multiple Boolean operations with globally deformed primitives. Our algorithm is special in the sense that it can be applied to objects with both an implicit and a parametric representation, such as superquadrics, supershapes, and Dupin cyclides. The input is a Constructive Solid Geometry tree (CSG tree) that contains the Boolean operations, the parameters of the primitives, and the global deformations. At each node of the CSG tree, the implicit formulations of the subtrees are used to quickly determine the parts to be transmitted to the parent node, while the primitives' parametric definition are used to refine an intermediary mesh around the intersection curves. The output is both an implicit equation and a mesh representing its solution. For the resulting object, an implicit equation with guaranteed differential properties is obtained by simple combinations of the primitives' implicit equations using R-functions. Depending on the chosen R-function, this equation is continuous and can be differentiable everywhere. The primitives' parametric representations are used to directly polygonize the resulting surface by generating vertices that belong exactly to the zero-set of the resulting implicit equation. The proposed approach has many potential applications, ranging from mechanical engineering to shape recognition and data compression. Examples of complex objects are presented and commented on to show the potential of our approach for shape modeling.

The accessibility of inexpensive and powerful computers has allowed true digital holography to be used for industrial inspection using microscopy. This technique allows the capture of a complex image (i.e., one containing magnitude and phase), and the reconstruction of the phase and magnitude information. Digital holograms give a new dimension to texture analysis, since the topology information can be used as an additional way to extract features. This new technique can be used to extend previous work on the image segmentation of patterned wafers for defect detection. The paper presents a comparison between the features obtained using Gabor filtering on complex images under illumination and focus variations.

This paper describes an efficient method to compare two triangular meshes. Meshes considered here contain geometric features as well as other surface attributes such as material colors, texture, temperature, radiation, etc. Two deviation measurements are presented to assess the differences between two meshes. The first measurement, called geometric deviation, returns geometric differences. The second measurement, called attribute deviation, returns attribute differences regardless of the attribute type. We present an application of this method to the mesh simplification algorithm (MSA) quality assessment according to the appearance attributes. This assessment allows the appreciation of local quality and the computation of global quality statistics of a simplified mesh.

Wavelet transforms computed by the decimated Mallat's ( see A Wavelet Tour on Signal Processing. Academic Press, 2nd ed., 1999) algorithm present a pyramidal aspect. This pyramidal analysis combined with a prediction of high-frequency coefficients is used to produce a magnified signal. The prediction is based on a zero-crossings representation and on the construction of a multiscale edge-signature database. Performances are evaluated for synthetic-noisy and natural images. A improvement regarding some classical methods is observed.

The Karhunen-Loeve transform (KLT) is used to perform region-based segmentation of aerial colour images from colour and texture features. A region-based segmentation method is developed in the KL colour image representation space and KLT is extended to texture analysis by local linear transform (LLT). An algorithm to merge colour and texture segmentation is presented in order to improve results.

The Karhunen-Loeve transform (KLT) is used to perform region-based segmentation of aerial color images from color and texture features. A region-based segmentation method is developed in the KL color image representation space and KLT is extended to texture analysis by the local linear transform (LLT). An algorithm to merge color and texture segmentations is presented in order to improve results.

Wavelet transforms are superior tools for signal analysis. They are used in this paper in order to perform a texture study of the evolution state of ovocyte cells. The analysis is based on a multiscale parameter. High order orthogonal B-spline wavelet basis are used to obtain significant parameters. Separable and quincunx schemes are studied and compared.