Publication

Locally Adaptable Mathematical Morphology

Olivier Cuisenaire
2005
Conference Papers

Abstract

We investigate how common binary mathematical morphology operators can be adapted so that the size of the structuring element (SE) can vary across the image. We show that when the SE are balls of a metric, locally adaptable erosion and dilation can be efficiently implemented as a variant of distance transformation algorithms. Opening and closing are obtained by a local threshold of a distance transformation, followed by the adaptable dilation.

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Olivier Cuisenaire
2005
Conference Papers

Abstract

Official source

Related concepts (16)

Transformation matrix

In linear algebra, linear transformations can be represented by matrices. If is a linear transformation mapping to and is a column vector with entries, then for some matrix , called the transformation matrix of . Note that has rows and columns, whereas the transformation is from to . There are alternative expressions of transformation matrices involving row vectors that are preferred by some authors. Matrices allow arbitrary linear transformations to be displayed in a consistent format, suitable for computation.

Geometric transformation

In mathematics, a geometric transformation is any bijection of a set to itself (or to another such set) with some salient geometrical underpinning. More specifically, it is a function whose domain and range are sets of points — most often both or both — such that the function is bijective so that its inverse exists. The study of geometry may be approached by the study of these transformations. Geometric transformations can be classified by the dimension of their operand sets (thus distinguishing between, say, planar transformations and spatial transformations).

Rigid transformation

In mathematics, a rigid transformation (also called Euclidean transformation or Euclidean isometry) is a geometric transformation of a Euclidean space that preserves the Euclidean distance between every pair of points. The rigid transformations include rotations, translations, reflections, or any sequence of these. Reflections are sometimes excluded from the definition of a rigid transformation by requiring that the transformation also preserve the handedness of objects in the Euclidean space.

Related publications (1)

Locally Adaptable Mathematical Morphology

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