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.

A Performance Evaluation of Surface Normals-Based Descriptors for Recognition of Objects using CAD-Models

This paper describes a study and analysis of surface normal-base descriptors for 3D object recognition. Specifically, we evaluate the behaviour of descriptors in the recognition process using virtual models of objects created from CAD software. Later, we test them in real scenes using synthetic objects created with a 3D printer from the virtual models. In both cases, the same virtual models are used on the matching process to find similarity. The difference between both experiments is in the type of views used in the tests. Our analysis evaluates three subjects: the effectiveness of 3D descriptors depending on the viewpoint of camera, the geometry complexity of the model and the runtime used to do the recognition process and the success rate to recognize a view of object among the models saved in the database.

Deterministic mathematical morphology for CAD/CAM

Purpose – The purpose of this paper is to present a new geometric model based on the mathematical morphology paradigm, specialized to provide determinism to the classic morphological operations. The determinism is needed to model dynamic processes that require an order of application, as is the case for designing and manufacturing objects in CAD/CAM environments. Design/methodology/approach – The basic trajectory-based operation is the basis of the proposed morphological specialization. This operation allows the definition of morphological operators that obtain sequentially ordered sets of points from the boundary of the target objects, inexistent determinism in the classical morphological paradigm. From this basic operation, the complete set of morphological operators is redefined, incorporating the concept of boundary and determinism: trajectory-based erosion and dilation, and other morphological filtering operations. Findings – This new morphological framework allows the definition of complex three-dimensional objects, providing arithmetical support to generating machining trajectories, one of the most complex problems currently occurring in CAD/CAM. Originality/value – The model proposes the integration of the processes of design and manufacture, so that it avoids the problems of accuracy and integrity that present other classic geometric models that divide these processes in two phases. Furthermore, the morphological operative is based on points sets, so the geometric data structures and the operations are intrinsically simple and efficient. Another important value that no excessive computational resources are needed, because only the points in the boundary are processed.

A new boundary-based morphological model

Mathematical morphology addresses the problem of describing shapes in an n-dimensional space using the concepts of set theory. A series of standardized morphological operations are defined, and they are applied to the shapes to transform them using another shape called the structuring element. In an industrial environment, the process of manufacturing a piece is based on the manipulation of a primitive object via contact with a tool that transforms the object progressively to obtain the desired design. The analogy with the morphological operation of erosion is obvious. Nevertheless, few references about the relation between the morphological operations and the process of design and manufacturing can be found. The non-deterministic nature of classic mathematical morphology makes it very difficult to adapt their basic operations to the dynamics of concepts such as the ordered trajectory. A new geometric model is presented, inspired by the classic morphological paradigm, which can define objects and apply morphological operations that transform these objects. The model specializes in classic morphological operations, providing them with the determinism inherent in dynamic processes that require an order of application, as is the case for designing and manufacturing objects in professional computer-aided design and manufacturing (CAD/CAM) environments. The operators are boundary-based so that only the points in the frontier are handled. As a consequence, the process is more efficient and more suitable for use in CAD/CAM systems.

3D model reconstruction using neural gas accelerated on GPU

In this work, we propose the use of the neural gas (NG), a neural network that uses an unsupervised Competitive Hebbian Learning (CHL) rule, to develop a reverse engineering process. This is a simple and accurate method to reconstruct objects from point clouds obtained from multiple overlapping views using low-cost sensors. In contrast to other methods that may need several stages that include downsampling, noise filtering and many other tasks, the NG automatically obtains the 3D model of the scanned objects. To demonstrate the validity of our proposal we tested our method with several models and performed a study of the neural network parameterization computing the quality of representation and also comparing results with other neural methods like growing neural gas and Kohonen maps or classical methods like Voxel Grid. We also reconstructed models acquired by low cost sensors that can be used in virtual and augmented reality environments for redesign or manipulation purposes. Since the NG algorithm has a strong computational cost we propose its acceleration. We have redesigned and implemented the NG learning algorithm to fit it onto Graphics Processing Units using CUDA. A speed-up of 180× faster is obtained compared to the sequential CPU version.