Title:
Morphological Simplification

dc.contributor.author Williams, Jason Daniel
dc.contributor.author Rossignac, Jarek
dc.date.accessioned 2004-07-27T19:43:56Z
dc.date.available 2004-07-27T19:43:56Z
dc.date.issued 2004
dc.description.abstract Morphological filters, such as closuer, opening, and their combinations, may be used for cleaning and analyzing images and shapes. We focus on the most popular special cases of these operators: the rounding R(S) and filleting F(S) of an arbitrary set S and the combinations R(F(S)) and F(R(S)). These operators may be obtained by combining growing and shrinking operators, which are Minkowski sums and differences with a ball of a given radius r. We define the mortar M(S) as F(S)-R(S). Note that the mortar occupies the thin cracks, protrusions, constrictions, and areas near the high-curvature portions of the boundary of S. Thus, we argue that confining the effect of shape simplification to the mortar has advantages over previously proposed tolerance zones and error metrics, which fail to differentiate between the irregular regions contained in the mortar and the regular (low-curvature) regions of S. We point out that R(F(S)) and F(R(S)) are suitable filters in this context, because their effects are confined to M(S) and leave the core R(S) and the anticore, which is the complement of F(S), unchanged. Furthermore, they tend to replace the high-curvature portions of the boundary of S with with regular portions where the radius of curvature exceeds r. Unfortunately, these operators have a bias, which may result in a large total volume of the symmetric difference between S and its simplified version S'. In order to minimize this volume, we propose to select the filter locally, for each connected component of the mortar. Thus, some portions of the mortar will be simplified using F(R(S)) and some using R(F(S)). This approach, which we call the Mason filter, can be used for the simplification of shapes regardless of their representation or dimensionality. We demonstrate its application to discrete two-dimensional binary sets (i.e. black and white images) and discuss implementation details. en
dc.format.extent 5161527 bytes
dc.format.mimetype application/pdf
dc.identifier.uri http://hdl.handle.net/1853/54
dc.language.iso en
dc.publisher Georgia Institute of Technology en
dc.relation.ispartofseries GVU Technical Report;GIT-GVU-04-05
dc.subject Mathematical morphology en
dc.subject binary image processing en
dc.subject shape simplification en
dc.title Morphological Simplification en
dc.type Text
dc.type.genre Technical Report
dspace.entity.type Publication
local.contributor.author Rossignac, Jarek
local.contributor.corporatename GVU Center
local.relation.ispartofseries GVU Technical Report Series
relation.isAuthorOfPublication d854d72c-9694-4442-bd2f-fb8859bade72
relation.isOrgUnitOfPublication d5666874-cf8d-45f6-8017-3781c955500f
relation.isSeriesOfPublication a13d1649-8f8b-4a59-9dec-d602fa26bc32
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