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update manual: Euclidean distance transform
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‎doc/MorphoLibJ-manual/MorphoLibJ-manual.lyx‎

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@@ -14186,6 +14186,53 @@ Binary image,
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\end_inset
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\end_layout
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\begin_layout Standard
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Different algorithms exist for computing distance transforms,
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mostly depending on the choice of the metric for the distance.
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MorpholLibJ provides implementations for both Euclidean and chamfer masks distance transforms.
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\end_layout
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\begin_layout Subsection
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Euclidean distance transform
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\end_layout
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\begin_layout Standard
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The most natural choice for computing distance map is to consider the
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\series bold
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Euclidean distance
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\series default
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to the background.
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Several algorithms have been proposed,
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with various performance
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\begin_inset CommandInset citation
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LatexCommand citep
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key "Borgefors1984,Cuisenaire1999,Maurer_2003_PAMI,Fabbri_2008_ACMCS,Wang_2013_PattRec"
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literal "false"
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\end_inset
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.
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The MorphoLibJ library implements Euclidean distance transforms based on the algorithm from
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\begin_inset CommandInset citation
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LatexCommand citet
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key "Saito_Toriwaki_1994_PattRec"
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literal "false"
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\end_inset
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.
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This algorithm has the advantage of being rather simple to implement,
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and to generalize easily to arbitrary dimension.
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\end_layout
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\begin_layout Standard
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\begin_inset Newpage newpage
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\end_inset
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\end_layout
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\begin_layout Subsection
@@ -14203,13 +14250,7 @@ name "subsec:Chamfer-Distances"
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\end_layout
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\begin_layout Standard
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Several methods exist for computing distance maps.
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The MorphoLibJ library implements distance transforms based on
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\series bold
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chamfer masks
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\series default
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,
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that are simpler to compute than exact Euclidean distance
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Chamfer distance transform is an alternative to Euclidean distance transform that is often simpler to compute
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\begin_inset CommandInset citation
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LatexCommand citep
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key "Rosenfeld_1968_PattRec,Borgefors1984,Borgefors1986"
@@ -14288,8 +14329,9 @@ Computation of distance maps using chamfer masks.
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\begin_layout Standard
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In practice,
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using integer weights may result in faster computations.
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This also allows to store the resulting distance map within 16-bits grayscale images,
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resulting in more efficient memory usage than floating point computation.
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This allows to store the resulting distance map within 16-bits grayscale images,
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resulting in more efficient memory usage than 32-bits floating point computation,
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and may be computationnally more efficient.
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\end_layout
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\begin_layout Standard
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of the distance map.
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\end_layout
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\begin_layout Standard
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\begin_inset Newpage clearpage
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\end_inset
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\end_layout
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\begin_layout Subsubsection
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Chamfer distance computation
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\end_layout
@@ -15192,7 +15227,7 @@ Enhancement of 3D distance maps when using larger chamfer masks.
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Masks are based on (a) four,
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(b) five,
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or (c) six weights.
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Using All images represent the threshold of the distance 100 from image center.
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All images represent the threshold for the distance 100 from image center.
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\end_layout
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\end_inset
@@ -15249,18 +15284,18 @@ Starting from version 1.5,
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\begin_layout Standard
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As for the 2D case,
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the choice of the chamfer distance is compromise between the accuracy (larger neighborhood and weights are usually more accurate) and the largest distance that can be represented.
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the choice of the chamfer distance is a compromise between the accuracy (larger neighborhood and weights are usually more accurate) and the largest distance that can be represented.
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\end_layout
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\begin_layout Subsubsection
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\begin_layout Subsection
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Case of label images
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\end_layout
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\begin_layout Standard
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The distance transform algorithm may also be applied to label images.
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The distance transform algorithms may also be applied to label images.
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However,
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as regions corresponding to each label may be continuous,
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the algorithm need to be adapted.
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the algorithms need to be adapted.
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\end_layout
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For label image,
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distances are computed between each foreground (greater than zero) pixel and the nearest pixel with a different value :
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either 0 (the background) or another label.
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Distances are propagated as for binary images,
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using a pair of forward and backward passes.
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Distances are propagated as for binary images.
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An example of result is provided on Figure
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\begin_inset space ~
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\end_inset
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.
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\end_layout
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\begin_layout Subsubsection
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\begin_layout Standard
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\begin_inset Newpage newpage
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\end_inset
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\end_layout
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\begin_layout Subsection
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Plugin usage
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\end_layout
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\begin_layout Standard
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The MorphoLibJ library provides two plugins for computing chamfer distance maps for 2D or 3D binary images:
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\end_layout
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\begin_layout Minisec
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Euclidean Distance Map
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\begin_inset Index plu
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range none
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pageformat default
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status collapsed
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\begin_layout Plain Layout
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\family roman
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\series medium
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\shape up
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\size normal
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\emph off
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\nospellcheck off
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\bar no
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\strikeout off
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\xout off
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\uuline off
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\uwave off
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\noun off
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\color none
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Euclidean Distance Map
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\end_layout
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\end_inset
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\end_layout
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\begin_layout Standard
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\begin_inset CommandInset label
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LatexCommand label
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name "op:Euclidean-Distance-Map"
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\end_inset
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Computes the Euclidean distance map from a binary or label image,
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between each foreground pixel to the nearest pixel with a different value (either background or another label).
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\end_layout
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\begin_layout Minisec
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Euclidean Distance Map 3D
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\begin_inset Index plu
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range none
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pageformat default
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status collapsed
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\begin_layout Plain Layout
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\family roman
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\series medium
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\shape up
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\size normal
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\emph off
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\nospellcheck off
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\bar no
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\strikeout off
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\xout off
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\uuline off
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\uwave off
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\noun off
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\color none
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Euclidean Distance Map 3D
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\end_layout
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\end_inset
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\end_layout
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\begin_layout Standard
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\begin_inset CommandInset label
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LatexCommand label
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name "op:Euclidean-Distance-Map-3D"
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\end_inset
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Computes the Euclidean distance map from a 3D binary or label image,
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between each foreground pixel to the nearest pixel with a different value (either background or another label).
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\end_layout
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\begin_layout Minisec
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Chamfer Distance Map
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\begin_inset Index plu
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\end_inset
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computes a chamfer distance map from a binary or label image,
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Computes a chamfer distance map from a binary or label image,
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between each foreground pixel to the nearest pixel with a different value (either background or another label).
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\end_layout
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\begin_layout Standard
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\begin_inset CommandInset label
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LatexCommand label
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name "op:Chamfer-Distance-Map-3d"
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name "op:Chamfer-Distance-Map-3D"
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\end_inset
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computes a chamfer distance map from a 3D binary image between each foreground voxel to the nearest voxel with a different value (either background or another label).
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Computes a chamfer distance map from a 3D binary image between each foreground voxel to the nearest voxel with a different value (either background or another label).
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Input image is assumed to have cubic voxels.
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\end_layout
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\begin_layout Standard
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For each plugin,
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a dialog opens and allows to select the following parameters:
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The following options may be adjusted:
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\end_layout
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\begin_layout Labeling
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\end_layout
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\begin_layout Subsection
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\begin_layout Section
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Geodesic distance transform
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\end_layout
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\end_layout
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\begin_layout Subsubsection
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\begin_layout Subsection
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Plugins
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\end_layout
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Binary image is assumed to have cubic voxels.
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\end_layout
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\begin_layout Subsubsection
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\begin_layout Subsection
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Results interpretation
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\end_layout
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\end_layout
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\begin_layout Subsubsection
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\begin_layout Subsection
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Algorithms
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\end_layout
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\begin_layout Plain Layout
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\begin_inset CommandInset ref
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LatexCommand pageref
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reference "op:Chamfer-Distance-Map-3d"
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reference "op:Chamfer-Distance-Map-3D"
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nolink "false"
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\end_inset

‎doc/MorphoLibJ-manual/bibliography.bib‎

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@@ -808,4 +808,72 @@ @Misc{Kovesi_2015
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url = {https://arxiv.org/abs/1509.03700},
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}
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@Article{Saito_Toriwaki_1994_PattRec,
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author = {Toyofumi Saito and Jun-Ichiro Toriwaki},
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journal = {Pattern Recognition},
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title = {New algorithms for euclidean distance transformation of an n-dimensional digitized picture with applications},
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year = {1994},
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issn = {0031-3203},
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number = {11},
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pages = {1551-1565},
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volume = {27},
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abstract = {In this paper, we propose a new method to obtain the Euclidean distance transformation and the Voronoi diagram based on the exact Euclidean metric for an n-dimensional picture. We present four algorithms to perform the transformation which are constructed by the serial composition of n-dimensional filters. When performed by a general purpose computer, they are faster than the method by H. Yamada for a two-dimensional picture. Those algorithms require only one n-dimensional array for storing input/output pictures and a single one-dimensional array for a work area, if an input picture needs not be preserved.},
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creationdate = {2025-11-20T17:18:58},
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doi = {https://doi.org/10.1016/0031-3203(94)90133-3},
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file = {:Saito_Toriwaki_1994_PattRec.pdf:PDF},
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groups = {distance transform, Distance transform},
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keywords = {Image processing,Distance transformation,Euclidean distance,Voronoi diagram},
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timestamp = {2021.10.15},
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url = {https://www.sciencedirect.com/science/article/pii/0031320394901333},
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}
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@Article{Fabbri_2008_ACMCS,
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author = {Fabbri, Ricardo and Bruno, Odemir M. and Costa, Luciano da F. and Torelli, Julio C.},
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journal = {ACM Computing Surveys},
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title = {{2D} euclidean distance transform algorithms: a comparative survey},
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year = {2008},
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pages = {1--44},
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volume = {40},
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creationdate = {2025-11-20T17:19:18},
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doi = {10.1145/1322432.1322434},
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file = {:Fabbri_2008_ACMCS.pdf:PDF},
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groups = {Distance transform},
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owner = {legland},
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timestamp = {2008.09.24},
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}
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@Article{Wang_2013_PattRec,
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author = {Jun Wang and Ying Tan},
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journal = {Pattern Recognition},
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title = {Efficient {Euclidean} distance transform algorithm of binary images in arbitrary dimensions},
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year = {2013},
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issn = {0031-3203},
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number = {1},
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pages = {230 - 242},
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volume = {46},
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creationdate = {2025-11-20T17:22:11},
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doi = {10.1016/j.patcog.2012.07.030},
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file = {:Wang_2013_PattRec.pdf:PDF},
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groups = {distance transform, Distance transform},
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keywords = {Euclidean distance transform},
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owner = {David Legland},
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timestamp = {2012.09.12},
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url = {http://www.sciencedirect.com/science/article/pii/S0031320312003482},
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}
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@Article{Maurer_2003_PAMI,
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author = {Maurer, C. R. and Rensheng, Qi and Raghavan, V.},
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journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence},
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title = {A linear time algorithm for computing exact {Euclidean} distance transforms of binary images in arbitrary dimensions},
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year = {2003},
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number = {2},
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pages = {265--270},
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volume = {25},
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creationdate = {2025-11-20T17:25:07},
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doi = {10.1109/TPAMI.2003.1177156},
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file = {:Maurer_2003_PAMI.pdf:PDF},
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groups = {Distance transform},
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keywords = {Euclidean distance;Skeleton;Image processing;Computer vision;Interpolation;Pattern matching;Surface morphology;Image registration;Anisotropic magnetoresistance;Nearest neighbor searches},
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}
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@Comment{jabref-meta: databaseType:bibtex;}

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