Composing morphological filters

Heijmans, H.J.A.M.

doi:10.1109/83.568928

Cited by 56 publications

(50 citation statements)

References 8 publications

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“…In particular, each LU LU -operator is a composition of dilations and erosions, that is, an erosion-dilation cascade (EDC). More generally, each alternating sequential filter (ASF), which by definition [4] is a composition of morphological openings and closings with structural elements of increasing size, is a EDC with the extra property of featuring the same number of erosions and dilations.…”

Section: Lemma 7 For Any Random Variablesmentioning

confidence: 99%

Calculating the output distribution of stack filters that are erosion-dilation cascades, in particularLU LU-filters

Anguelov

Butler

Rohwer

et al. 2015

Quaestiones Mathematicae

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Abstract. Two procedures to compute the output distribution ϕS of certain stack filters S (so called erosion-dilation cascades) are given. One rests on the disjunctive normal form of S and also yields the rank selection probabilities. The other is based on inclusion-exclusion and e.g. yields ϕS for some important LU LU -operators S. Properties of ϕS can be used to characterize smoothing properties of S. Also, in the same way as our polynomials phiS are computed one could compute the reliability polynomial of a connected graph, or more generally the reliability polynomial w.r.t. any positive Boolean function.Mathematics Subject Classification (2010): 94A12, 05A15, 68M15.

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Section: Lemma 7 For Any Random Variablesmentioning

confidence: 99%

Calculating the output distribution of stack filters that are erosion-dilation cascades, in particularLU LU-filters

Anguelov

Butler

Rohwer

et al. 2015

Quaestiones Mathematicae

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show abstract

“…Typical examples are the alternating-sequential filters or AS-filters [1], [22], [23] which are excluded since they are neither extensive nor antiextensive operators. AS-filters modify the original image by introducing regions that appear as the result of local clustering or partitioning.…”

Section: Drawbacks Of Conventional Second-generation Connectivitymentioning

confidence: 99%

Mask-Based Second-Generation Connectivity and Attribute Filters

Ouzounis

Wilkinson

2007

IEEE Trans. Pattern Anal. Mach. Intell.

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Abstract-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.

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“…Filters based on connected operators [12], [13], [14], [15], [16], [17], [18] can either remove a connected component or retain it unmodified, but cannot introduce new ones. This edge preserving property is highly desirable in many applications.…”

Section: Introductionmentioning

confidence: 99%

Hyperconnected Attribute Filters Based on k-Flat Zones

Ouzounis

Wilkinson

2011

IEEE Trans. Pattern Anal. Mach. Intell.

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Abstract-In this paper, we present a new method for attribute filtering, combining contrast and structural information. Using hyperconnectivity based on k-flat zones, we improve the ability of attribute filters to retain internal details in detected objects. Simultaneously, we improve the suppression of small, unwanted detail in the background. We extend the theory of attribute filters to hyperconnectivity and provide a fast algorithm to implement the new method. The new version is only marginally slower than the standard Max-Tree algorithm for connected attribute filters, and linear in the number of pixels or voxels. It is two orders of magnitude faster than anisotropic diffusion. The method is implemented in the form of a filtering rule suitable for handling both increasing (size) and nonincreasing (shape) attributes. We test this new framework on nonincreasing shape filters on both 2D images from astronomy, document processing, and microscopy, and 3D CT scans, and show increased robustness to noise while maintaining the advantages of previous methods.

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Composing morphological filters

Cited by 56 publications

References 8 publications

Calculating the output distribution of stack filters that are erosion-dilation cascades, in particularLU LU-filters

Calculating the output distribution of stack filters that are erosion-dilation cascades, in particularLU LU-filters

Mask-Based Second-Generation Connectivity and Attribute Filters

Hyperconnected Attribute Filters Based on k-Flat Zones

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