Flat zones filtering, connected operators, and filters by reconstruction

This correspondence deals with the notion of connected operators. Starting from the definition for operator acting on sets, it is shown how to extend it to operators acting on function. Typically, a connected operator acting on a function is a transformation that enlarges the partition of the space created by the flat zones of the functions. It is shown that from any connected operator acting on sets, one can construct a connected operator for functions (however, it is not the unique way of generating connected operators for functions). Moreover, the concept of pyramid is introduced in a formal way. It is shown that, if a pyramid is based on connected operators, the flat zones of the functions increase with the level of the pyramid. In other words, the flat zones are nested. Filters by reconstruction are defined and their main properties are presented. Finally, some examples of application of connected operators and use of flat zones are described.Peer ReviewedPostprint (published version

Combining constructive and equational geometric constraint solving techniques

In the past few years, there has been a strong trend towards developing parametric, computer aided design systems based on geometric constraint solving. An efective way to capture the design intent in these systems is to define relationships between geometric and technological variables. In general, geometric constraint solving including functional relationships requires a general approach and appropiate techniques toachieve the expected functional capabilities. This work reports on a hybrid method which combines two geometric constraint solving techniques: Constructive and equational. The hybrid solver has the capability of managing functional relationships between dimension variables and variables representing conditions external to the geometric problem. The hybrid solver is described as a rewriting system and is shown to be correct.Postprint (published version

Fast recursive grayscale morphology operators: from the algorithm to the pipeline architecture

International audienceThis paper presents a new algorithm for an efficient computation of morphological operations for gray images and its specific hardware. The method is based on a new recursive morphological decomposition method of 8-convex structuring elements by only causal two-pixel structuring elements (2PSE). Whatever the element size, erosion or/and dilation can then be performed during a unique raster-like image scan involving a fixed reduced analysis neighborhood. The resulting process offers low computation complexity combined with easy description of the element form. The dedicated hardware is generic and fully regular, built from elementary interconnected stages. It has been synthesized into an FPGA and achieves high frequency performances for any shape and size of structuring element

Isogeometric Analysis and Harmonic Stator-Rotor Coupling for Simulating Electric Machines

This work proposes Isogeometric Analysis as an alternative to classical finite elements for simulating electric machines. Through the spline-based Isogeometric discretization it is possible to parametrize the circular arcs exactly, thereby avoiding any geometrical error in the representation of the air gap where a high accuracy is mandatory. To increase the generality of the method, and to allow rotation, the rotor and the stator computational domains are constructed independently as multipatch entities. The two subdomains are then coupled using harmonic basis functions at the interface which gives rise to a saddle-point problem. The properties of Isogeometric Analysis combined with harmonic stator-rotor coupling are presented. The results and performance of the new approach are compared to the ones for a classical finite element method using a permanent magnet synchronous machine as an example

Image morphological processing

Mathematical Morphology with applications in image processing and analysis has been becoming increasingly important in today\u27s technology. Mathematical Morphological operations, which are based on set theory, can extract object features by suitably shaped structuring elements. Mathematical Morphological filters are combinations of morphological operations that transform an image into a quantitative description of its geometrical structure based on structuring elements. Important applications of morphological operations are shape description, shape recognition, nonlinear filtering, industrial parts inspection, and medical image processing. In this dissertation, basic morphological operations, properties and fuzzy morphology are reviewed. Existing techniques for solving corner and edge detection are presented. A new approach to solve corner detection using regulated mathematical morphology is presented and is shown that it is more efficient in binary images than the existing mathematical morphology based asymmetric closing for corner detection. A new class of morphological operations called sweep mathematical morphological operations is developed. The theoretical framework for representation, computation and analysis of sweep morphology is presented. The basic sweep morphological operations, sweep dilation and sweep erosion, are defined and their properties are studied. It is shown that considering only the boundaries and performing operations on the boundaries can substantially reduce the computation. Various applications of this new class of morphological operations are discussed, including the blending of swept surfaces with deformations, image enhancement, edge linking and shortest path planning for rotating objects. Sweep mathematical morphology is an efficient tool for geometric modeling and representation. The sweep dilation/erosion provides a natural representation of sweep motion in the manufacturing processes. A set of grammatical rules that govern the generation of objects belonging to the same group are defined. Earley\u27s parser serves in the screening process to determine whether a pattern is a part of the language. Finally, summary and future research of this dissertation are provided

Colour image processing and texture analysis on images of porterhouse steak meat

This paper outlines two colour image processing and texture analysis techniques applied to meat images and assessment of error due to the use of JPEG compression at image capture. JPEG error analysis was performed by capturing TIFF and JPEG images, then calculating the RMS difference and applying a calibration between block boundary features and subjective visual JPEG scores. Both scores indicated high JPEG quality. Correction of JPEG blocking error was trialled and found to produce minimal improvement in the RMS difference. The texture analysis methods used were singular value decomposition over pixel blocks and complex cell analysis. The block singular values were classified as meat or non- meat by Fisher linear discriminant analysis with the colour image processing result used as ‘truth.’ Using receiver operator characteristic (ROC) analysis, an area under the ROC curve of 0.996 was obtained, demonstrating good correspondence between the colour image processing and the singular values. The complex cell analysis indicated a ‘texture angle’ expected from human inspection

Trajectory-Based Morphological Operators: A Model for Efficient Image Processing

Mathematical morphology has been an area of intensive research over the last few years. Although many remarkable advances have been achieved throughout these years, there is still a great interest in accelerating morphological operations in order for them to be implemented in real-time systems. In this work, we present a new model for computing mathematical morphology operations, the so-called morphological trajectory model (MTM), in which a morphological filter will be divided into a sequence of basic operations. Then, a trajectory-based morphological operation (such as dilation, and erosion) is defined as the set of points resulting from the ordered application of the instant basic operations. The MTM approach allows working with different structuring elements, such as disks, and from the experiments, it can be extracted that our method is independent of the structuring element size and can be easily applied to industrial systems and high-resolution images