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.

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.