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. 2014;2014:801587.
doi: 10.1155/2014/801587. Epub 2014 Apr 14.

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

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Free PMC article

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

Antonio Jimeno-Morenilla et al. ScientificWorldJournal. .
Free PMC article

Abstract

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.

Figures

Figure 1
Figure 1
Examples of several possible representations of structuring elements. The leftmost figures show the analytical expressions of SEs; on the right, the corresponding classical SEs are shown.
Figure 2
Figure 2
Geometric description of an instant basic operation. (a) Initial position. (b) Transformation of object X. (c) Distance computing.
Figure 3
Figure 3
Classical morphological operations on 2D images. On the left, a morphological dilation. On the right, a morphological erosion. The structuring element (SE)—a circle of 20 pixels in radius—is shown at the top left corner.
Figure 4
Figure 4
Partial morphological erosion as a subset of the complete erosion (over the subrange defined by the dotted line).
Figure 5
Figure 5
Analysis of segments S 1 and S 2 of a five-segment shape C. Dark-grey SE positions are discarded due to shape collision. Note that discontinuity at p d is solved by a vector swept generation.
Figure 6
Figure 6
Morphological dilation tests. On the left, influence of the size of the structuring element. On the right, influence on the size of objects.
Figure 7
Figure 7
Morphologic dilation. Comparative study between MM2 and MTM models for SE sizes of 20, 40, and 80 pixels.
Figure 8
Figure 8
Morphological dilation and erosion. Results of different morphological operations used for the experiments. In the upper part, two erosions and in the lower part, two dilations. The boundary of the original object is represented in green and the result of MM1 operation in black, with the MTM result in red.
Figure 9
Figure 9
Erosion of figures using our morphological approach. (a) Using a circle as a structuring element. (b) Using a rectangle as a structuring element.
Algorithm 1
Algorithm 1
Basic pseudo-code algorithm for the morphological trajectory erosion.
Algorithm 2
Algorithm 2
Pseudo-code used for the 2D experiments.

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References

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