Characterization of changes in blood vessel width and tortuosity in retinopathy of prematurity using image analysis.

By concentrating on the analysis of the spatial relationships between groups of pixels, mathematical morphology provides us with an image processing strategy complementary to those based on the analysis of the spectral signature of single pixels. A wide variety of morphological transformations are available for extracting structural information in spatial data. Accordingly, a stream of successful applications in geoscience and remote sensing have been reported since the mid-1980s as highlighted in a brief survey. However, recent advances in the theory of mathematical morphology still remain largely unexplored. We show in this paper that they can enhance methodologies for the processing and analysis of Earth observation data for tasks as diverse as filtering, simplification, directional segmentation and crest line extraction. We also address important issues overlooked in the past and concerning the applicability of a given morphological filter to Earth observation data. In particular, we point out that self-dual or even self-complementary filters are required in many applications to produce results independent of the local contrast of the searched image structures.

Advances in mathematical morphology applied to geoscience and remote sensing

In this paper, we describe a multiscale and multishape morphological method for pattern-based analysis and classification of gray-scale images using connected operators. Compared with existing methods, which use structuring elements, our method has three advantages. First, in our method, the time needed for computing pattern spectra does not depend on the number of scales or shapes used, i.e., the computation time is independent of the dimensions of the pattern spectrum. Second, size and strict shape attributes can be computed, which we use for the construction of joint 2D shape-size pattern spectra. Third, our method is significantly less sensitive to noise and is rotation-invariant. Although rotation invariance can also be approximated by methods using structuring elements at different angles, this tends to be computationally intensive. The classification performance of these methods is discussed using four image sets: Brodatz, COIL-20, COIL-100, and diatoms. The new method obtains better or equal classification performance to the best competitor with a 5 to 9-fold speed gain

/pdf/connected-shape-size-pattern-spectra-for-rotation-and-scale-mocktw0o1m.pdf

Connected Shape-Size Pattern Spectra for Rotation and Scale-Invariant Classification of Gray-Scale Images

We propose an efficient and deterministic algorithm for computing the one-dimensional dilation and erosion (max and min) sliding window filters. For a p-element sliding window, our algorithm computes the 1D filter using 1.5 + o(1) comparisons per sample point. Our algorithm constitutes a deterministic improvement over the best previously known such algorithm, independently developed by van Herk (1992) and by Gil and Werman (1993) (the HGW algorithm). Also, the results presented in this paper constitute an improvement over the Gevorkian et al. (1997) (GAA) variant of the HGW algorithm. The improvement over the GAA variant is also in the computation model. The GAA algorithm makes the assumption that the input is independently and identically distributed (the i.i.d. assumption), whereas our main result is deterministic. We also deal with the problem of computing the dilation and erosion filters simultaneously, as required, e.g., for computing the unbiased morphological edge. In the case of i.i.d. inputs, we show that this simultaneous computation can be done more efficiently then separately computing each. We then turn to the opening filter, defined as the application of the min filter to the max filter and give an efficient algorithm for its computation. Specifically, this algorithm is only slightly slower than the computation of just the max filter. The improved algorithms are readily generalized to two dimensions (for a rectangular window), as well as to any higher finite dimension (for a hyperbox window), with the number of comparisons per window remaining constant. For the sake of concreteness, we also make a few comments on implementation considerations in a contemporary programming language.

/pdf/efficient-dilation-erosion-opening-and-closing-algorithms-56mt4jgmmj.pdf

Efficient dilation, erosion, opening, and closing algorithms

Connected filters are edge-preserving morphological operators, which rely on a notion of connectivity. This is usually the standard 4 and 8-connectivity, which is often too rigid since it cannot model generalized groupings such as object clusters or partitions. In the set-theoretical framework of connectivity, these groupings are modeled by the more general second-generation connectivity. In this paper, we present both an extension of this theory, and provide an efficient algorithm based on the max-tree to compute attribute filters based on these connectivities. We first look into the drawbacks of the existing framework that separates clustering and partitioning and is directly dependent on the properties of a preselected operator. We then propose a new type of second-generation connectivity termed mask-based connectivity which eliminates all previous dependencies and extends the ways the image domain can be connected. A previously developed dual-input max-tree algorithm for area openings is adapted for the wider class of attribute filters on images characterized by second-generation connectivity. CPU-times for the new algorithm are comparable to the original algorithm, typically deviating less than 10 percent either way

/pdf/mask-based-second-generation-connectivity-and-attribute-2v1pj299wl.pdf

Mask-Based Second-Generation Connectivity and Attribute Filters

Van Herk (1992) has shown that the erosion/dilation operator with a linear structuring element of an arbitrary length can be implemented in only three min/max operations per pixel. In this paper, the algorithm is generalized to erosions and dilations along discrete lines at arbitrary angles. We also address the padding problem; so that the operation can be performed in place without copying the pixels to and from an intermediate buffer. Applications to image filtering and to radial decompositions of discs are presented.

Recursive implementation of erosions and dilations along discrete lines at arbitrary angles

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Recursive implementation of erosions and dilations along discrete lines at arbitrary angles