Title: Two Approaches for Orientation field segmentation based on Directional Morphology
1Two Approaches for Orientation field segmentation
based on Directional Morphology
UNIVERSIDAD AUTÓNOMA DE QUERÉTARO
- Luis A. Morales Hernández, Federico Manríquez
Guerrero, Iván Terol-Villalobos
2Morphological segmentation of directional
structure
Fingerprint
Pearlite phase
Field orientation
Field orientation
3Directional Morphological Transformations
If then, for
If then, for
Dilation ?80 a?5
Dilation ?80 a?10
4Directional Morphological Transformations
The directional morphological opening and closing
are given by
where the morphological erosion and dilation
filters are given by
(a)
(b)
(c)
(d)
5Directional Segmentation Based on a Quadtree
Structure
Directional distribution function
6Directional Segmentation Based on a Quadtree
Structure
7Directional Segmentation Based on a Quadtree
Structure
Original Image
Final quadtree color representation
First hierarchy of the quadtree
8 Directional Segmentation Based on a Quadtree
Structure
9Line Segment Function and Sup of Directional
Erosions
Definition The line-segment function DmX(x) is a
transformation that associates with each pixel x
of a set X the length of the longest symmetrical
line segment, centered at the origin, placed at
point x and completely included in X.
The line segment function is computed by
Binary Image (BI)
10Line Segment and Orientation Functions
Definition The orientation function OmX(x) is a
transformation that associates with each pixel x
of a set X the angle of the longest symmetrical
line segment, centered at the origin, placed at
point x and completely included in X.
Binary image Line-segments function
Orientation function
11Orientation Functions
Original image
Original image
Orientation image
Orientation image
12Orientation Function
Binary image
Angles function color
representation
13Image Segmentation Based on a RAG Structure
Catchment basins of the partition weighted by
the orientation
Watershed image
Orientation image after fusion using an angle
criterion of 20
Orientation image
14Image Segmentation Based on a RAG Structure
Mask image
Binary image
Weighted partition Weighted
partition filtered by size criterion
15Image Segmentation Based on a RAG Structure
Segmented image partition with angle criterion 15
and infinite value of the variance criterion and
its color representation
connected components of the segmented image
16Conclusion
This paper has shown the possibilities for
application of morphological directional
transformations to segment images with
orientation fields. Initially, one investigates
the directional granulometries and the notion of
quadtree structure. The quadtree is used to
describe a class of hierarchical data structures
thus it permits one to classify the orientation
fields at different scales. This approach
involves a local analysis using the notions of
the line-segment and orientation functions
proposed in this paper.
17Conclusion cont.
The maxima of the line-segment function were used
for computing the loci of maximal structuring
elements, and the orientation function was used
to obtain the angles of the line segments. These
pairs of local parameters enable us to produce a
good description of the image by means of line
segments. Then, a partition of the image may be
computed by means of the catchment basins
associated with the watershed transform. This
enables us to realize a neighborhood analysis,
using a RAG structure, in order to merge adjacent
regions of the partition according to appropriate
criteria, thus segmenting the images into
orientation fields. The results based on the
algorithms presented in this paper show the good
performance of the approach.
18 Reconstruction of fingerprint