Image filtering using
morphological amoebas
Romain Lerallut, Étienne Decencière, Fernand Meyer
[email protected]
Centre de Morphologie Mathématique
École des Mines de Paris
ISMM 2005 - Image filtering using morphological amoebas – p. 1/21
Outline
The problem
Construction and use of a dynamic SE
Examples
Extensions
Limitations
Future work
Amoeba proteus
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The problem
Morphological filtering can reduce noise in objects
while preserving strong contours (see Levelings)
However, the noise is sometimes reconstructed:
Original
ASF
ASF + leveling
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The problem
In 3D imaging, pure contours are essential:
Original image
Noisy image
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Classic filtering
“Classic” median filter:
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A new class of filters
Classic filters don’t preserve well the contours:
weakening of the contours
excessive fusion of distinct regions
artefacts appearing due to the kernels’ shape
Hence the interest for anisotropic approaches . . .
Our approach consists in combining a non fixed-shaped
structuring element with a measure, hereby creating a
class of shape-adaptive neighborhood transforms.
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Shape-adaptive structuring
elements
In some cases, we would like to use local image
information to drive the shape of our structuring
elements.
Closing by a square SE
Closing by an amoeba
The amoeba can be used to selectively preserve small
features such as small but strong canals, while still
sampling over a significative number of pixels.
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Construction of a dynamic
SE
For each point x, the neighborhood defined by the
structuring element is given by:
Namoeba (x) = {y /damoeba (x, y) ≤ T hresh}
Where damoeba is a weighted grey-level distance.
On a flat image (left), the amoeba stretches as if it were
a normal kernel. However its growth is slowed (center) or
even stopped (right) by a gradient line.
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The pilot image
The weighted grey-level distance is usually computed on
a smoothed image, rather than the original:
Original image
Filtered image
A gaussian is a good candidate
for the smoothing, as is any filter that reduces speckle noise.
An amoeba at
various positions on
top of its pilot image.
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Using a dynamic SE
A dynamic SE and a “pilot” image define a neighborhood
for each point of the original image.
A measure is performed on each neighborhood and the
result is set on the central point:
∀p ∈ Imageorig. , Imagef ilt. (p) = M (NSE,Imagepilot (p))
The measure defines the type of filter: minimum
(erosion), maximum (dilation), median, mean, rank filter,
etc.
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Examples: median and
mean
Original
Classic median
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Examples: median and
mean
Classic median
Amoeba median
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Examples: median and
mean
Original
Amoeba mean
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Examples: ASF
Alternate sequential filters, size 1:
Original
Normal ASF
Amoeba ASF
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Examples: ASF
Alternate sequential filters, size 1 “+” size 2:
Original
Normal ASF
Amoeba ASF
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Examples: ASF
Alternate sequential filters, size 1 “+” size 2 “+” size 3:
Original
Normal ASF
Amoeba ASF
Openings and closings can be replaced by less active
rank filters for a little increase in result quality.
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Extensions and
improvements
Extensions
The amoeba framework can seamlessly be extended to
two important types of images:
3D images
Color images
Improvements
An interesting improvement is to use amoeba filterings to
generate a better pilot image.
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Extension: 3D images
Original image
Noisy image
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Extension: 3D images
Original image
Amoeba median
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Extension: color images
Original image
Color amoeba RGB
“median”
Color amoeba RGB mean
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Improvement: iterations
A method to improve greatly the quality of the amoeba
filtering process is to use a better pilot image.
Original
Gaussian-smoothed
Amoeba RGB mean
The fingers are blurred and the eyebrows are merging
with the eyes.
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Improvement: iterations
What better pilot image that the result of a strong
amoeba-based filtering ?
Original
Amoeba RGB mean (pilot)
Amoeba RGB mean (final)
The amoeba RGB mean filter is applied to the original
image, but with the result of the previous filtering as a
pilot image.
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Improvement: iterations
Side-by-side comparison of the improvement:
Original
Amoeba RGB mean
(gaussian-based)
Amoeba RGB mean
(iterated)
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Current limitations
Number of parameters
Some parameters are of a numeric nature (thresholds)
but others are not: the pilot image, the type of distance,
choice of colorspace, etc.
Computation cost
The theoretical complexity, slightly more than O(n ∗ k) is
reasonable, but the naive implementation remains quite
slow, in particular for the processing of 3D images.
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Future work
Geodesic operations
In order to be meaningful, geodesic operations require
slight modifications of the current process, but can be
wholly integrated in the present framework.
More complex amoebas
It is possible to add constraints on the shape of
amoebas, for instance preventing them from squeezing
in a narrow space. A possible use would be to create
watershed-like flooding algorithms, with a viscous
behavior in front of irregular gradient lines.
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Image filtering using
morphological amoebas
Romain Lerallut, Étienne Decencière, Fernand Meyer
[email protected]
Centre de Morphologie Mathématique
École des Mines de Paris
ISMM 2005 - Image filtering using morphological amoebas – p. 21/21