Introduction State of the art (Active contours and Shape priors)
Description of the proposed method
Experimental results Conclusion & perspectives
M. A. MEZGHICH, S. M’HIRI and F. GHORBEL
Cristal Lab., GRIFT ENSI, Campus Univ. of Manouba, Tunisia
[email protected], {slim.mhiri,faouzi.ghorbel}@ensi.rnu.tn
March 27 , 2012
1/18
M. A. MEZGHICH, S. M’HIRI and F. GHORBEL Fourier-based Multi-references shape prior for active contours
Introduction State of the art (Active contours and Shape priors)
Description of the proposed method
Experimental results Conclusion & perspectives
1 Introduction
2 State of the art (Active contours and Shape priors)
3 Description of the proposed method
4 Experimental results
5 Conclusion & perspectives
2/18
M. A. MEZGHICH, S. M’HIRI and F. GHORBEL Fourier-based Multi-references shape prior for active contours
Introduction State of the art (Active contours and Shape priors)
Description of the proposed method
Experimental results Conclusion & perspectives
3/18
M. A. MEZGHICH, S. M’HIRI and F. GHORBEL Fourier-based Multi-references shape prior for active contours
Introduction State of the art (Active contours and Shape priors)
Description of the proposed method
Experimental results Conclusion & perspectives
Active contours are methods of edge detection by energy minimization.
3/18
M. A. MEZGHICH, S. M’HIRI and F. GHORBEL Fourier-based Multi-references shape prior for active contours
Introduction State of the art (Active contours and Shape priors)
Description of the proposed method
Experimental results Conclusion & perspectives
Active contours are methods of edge detection by energy minimization.
The energy of the active contours is based on gray-levels of the image.
3/18
M. A. MEZGHICH, S. M’HIRI and F. GHORBEL Fourier-based Multi-references shape prior for active contours
Introduction State of the art (Active contours and Shape priors)
Description of the proposed method
Experimental results Conclusion & perspectives
Publicité
Active contours are methods of edge detection by energy minimization.
The energy of the active contours is based on gray-levels of the image.
Real images are complex (low contrast, clutter, noisy).
3/18
M. A. MEZGHICH, S. M’HIRI and F. GHORBEL Fourier-based Multi-references shape prior for active contours
Introduction State of the art (Active contours and Shape priors)
Description of the proposed method
Experimental results Conclusion & perspectives
Active contours are methods of edge detection by energy minimization.
The energy of the active contours is based on gray-levels of the image.
Real images are complex (low contrast, clutter, noisy).
Segmentation results are sometimes not satisfactory.
3/18
M. A. MEZGHICH, S. M’HIRI and F. GHORBEL Fourier-based Multi-references shape prior for active contours
Introduction State of the art (Active contours and Shape priors)
Description of the proposed method
Experimental results Conclusion & perspectives
Active contours are methods of edge detection by energy minimization.
The energy of the active contours is based on gray-levels of the image.
Real images are complex (low contrast, clutter, noisy).
Segmentation results are sometimes not satisfactory.
Need to add prior information such as shape.
3/18
M. A. MEZGHICH, S. M’HIRI and F. GHORBEL Fourier-based Multi-references shape prior for active contours
Introduction State of the art (Active contours and Shape priors)
Description of the proposed method
Experimental results Conclusion & perspectives
Ωand I are respectively the image domain and intensity.
φ is the level set function embedding the active contour.
c 1 and c 2 are respectively the averages of gray-level intensities inside and outside the evolving curve. µ, ν ≥ 0 and λ 1, λ 2 > 0 are fixed parameters.
4/18
M. A. MEZGHICH, S. M’HIRI and F. GHORBEL Fourier-based Multi-references shape prior for active contours
Introduction State of the art (Active contours and Shape priors)
Description of the proposed method
Experimental results Conclusion & perspectives
Many works have been proposed which can be classified into statistical or geometrical shape priors.
Leventon et al. 2001, associated a statistical shape model to the geodesic active contours. A set of training shapes is used to define a Gaussian distribution over shapes.
Fang et al. 2007, introduced a statistical shape prior into geodesic active contour to detect partially occluded object.
5/18
M. A. MEZGHICH, S. M’HIRI and F. GHORBEL Fourier-based Multi-references shape prior for active contours
Publicité
Introduction State of the art (Active contours and Shape priors)
Description of the proposed method
Experimental results Conclusion & perspectives
Many works have been proposed which can be classified into statistical or geometrical shape priors.
Leventon et al. 2001, associated a statistical shape model to the geodesic active contours. A set of training shapes is used to define a Gaussian distribution over shapes.
Fang et al. 2007, introduced a statistical shape prior into geodesic active contour to detect partially occluded object.
Foulonneau et al. 2003, use Legendre moments to add geometric prior knowledge to region-based active contours.
Charmi et al. 2008, use a set of similarity invariant descriptors to add geometric shape prior to snake.
5/18
M. A. MEZGHICH, S. M’HIRI and F. GHORBEL Fourier-based Multi-references shape prior for active contours
Introduction State of the art (Active contours and Shape priors)
Description of the proposed method
Experimental results Conclusion & perspectives
If one takes a template shape which is not defined in the image reference, it is necessary to apply a transformation to align it with the shape to segment. We used the method of shapes alignment proposed by Persoon and Fu, 1977. Ghorbel et al. 1996, presented the first implementation of this method and its application in rigid motion estimation.
6/18
M. A. MEZGHICH, S. M’HIRI and F. GHORBEL Fourier-based Multi-references shape prior for active contours
Introduction State of the art (Active contours and Shape priors)
Description of the proposed method
Experimental results Conclusion & perspectives
Consider the Figure below :
Figure: (a) φref : level set function of the template image, (b) φ : level set function of the test image, (c) φprod : the product function of φ by φref .
Our goal is the minimize the region of variability between the reference and target shapes. This region corresponds to
7/18
M. A. MEZGHICH, S. M’HIRI and F. GHORBEL Fourier-based Multi-references shape prior for active contours
Introduction State of the art (Active contours and Shape priors)
Description of the proposed method
Experimental results Conclusion & perspectives
where g ( x, y )=- φ ( x, y ) · sign ( φref ( x, y )).
As we can see, this energy corresponds to the area of occlusion. This energy is minimum only if the curve γ corresponds to the true contour of the object to be detected.
where λ is a weighting factor.
8/18
M. A. MEZGHICH, S. M’HIRI and F. GHORBEL Fourier-based Multi-references shape prior for active contours
Introduction State of the art (Active contours and Shape priors)
Description of the proposed method
Experimental results Conclusion & perspectives
Minimization is done using the gradient descent method: ∂E ∂φ [=] [−] [∂φ] ∂t [.]
Since we are interested in updating the level set function in the regions of variability between shapes, we take δϵ ( gij [) = 0] points which are outside these regions.
9/18
M. A. MEZGHICH, S. M’HIRI and F. GHORBEL Fourier-based Multi-references shape prior for active contours
Introduction State of the art (Active contours and Shape priors)
Publicité
Description of the proposed method
Experimental results Conclusion & perspectives
Figure: First row: The Template, Test Image, Initial Curve, Second row: Curve evolution under Chan-Vese model without shape prior, Last row: Curve evolution under the proposed shape prior
10/18
M. A. MEZGHICH, S. M’HIRI and F. GHORBEL Fourier-based Multi-references shape prior for active contours
Introduction State of the art (Active contours and Shape priors)
Description of the proposed method
Experimental results Conclusion & perspectives
The proposed algorithm proceeds as follows :
First, the initial curve evolves under Chan and Vese energy only.
Second, for a given iteration (when the contours is being stable), we align the reference shape with the evolving contour.
Then, we compute the proposed shape prior term.
Finally, we evolve the curve under both forces (data and prior forces). Big weight is given to the prior term.
11/18
M. A. MEZGHICH, S. M’HIRI and F. GHORBEL Fourier-based Multi-references shape prior for active contours
Introduction State of the art (Active contours and Shape priors)
Description of the proposed method
Experimental results Conclusion & perspectives
We compare the results of our method with existing methods.
Figure: (a) : Chan et al. 2001, (b) : Foulonneau et al. 2004, (c) and (d): Our model
It is visually clear that results obtained by our model are better. The image at the right shows the robustness with respect to rotation and noise.
12/18
M. A. MEZGHICH, S. M’HIRI and F. GHORBEL Fourier-based Multi-references shape prior for active contours
Introduction State of the art (Active contours and Shape priors)
Description of the proposed method
Experimental results Conclusion & perspectives
Heart’s left ventricule segmentation.
Figure: First row: The Template, Test Image, Initial Curve, Second row: Chan & Vese model without shape prior, iteration 50, 450, 800, Last row: Chan & Vese model with shape prior, iteration 450, 460 and 500
13/18
M. A. MEZGHICH, S. M’HIRI and F. GHORBEL Fourier-based Multi-references shape prior for active contours
Introduction State of the art (Active contours and Shape priors)
Description of the proposed method
Experimental results Conclusion & perspectives
In presence of many templates, we have to choose the most suitable one according to the evolving curve.
We used a complete and stable set of invariant Fourier descriptors introduced by Ghorbel, 1998.
M. A. MEZGHICH, S. M’HIRI and F. GHORBEL Fourier-based Multi-references shape prior for active contours
Introduction State of the art (Active contours and Shape priors)
Description of the proposed method
Experimental results Conclusion & perspectives
To compare the evolving curve and the available templates, we used the following distance:
Publicité
The shape having the minimum distance to the evolving active contour is used as template.
Not need to prior shapes alignment like Fang et al. 2006.
More fast versus Foulonneau et al. 2009 (A FFT is performed for descriptors computation and motion estimation).
15/18
M. A. MEZGHICH, S. M’HIRI and F. GHORBEL Fourier-based Multi-references shape prior for active contours
Introduction State of the art (Active contours and Shape priors)
Description of the proposed method
Experimental results Conclusion & perspectives
Case of synthetic data (Robusteness to noise and rotation)
Figure: The used Templates : T1, T2, T3, T4
| Col1 | T1 | T2 | T3 | T4 |
|---|---|---|---|---|
| Evolving curve | 0.9772 | 0.9963 | 0.9981 | 0.9993 |
Table: Distances between the evolving curve and the used templates.
16/18
M. A. MEZGHICH, S. M’HIRI and F. GHORBEL Fourier-based Multi-references shape prior for active contours
Introduction State of the art (Active contours and Shape priors)
Description of the proposed method
Experimental results Conclusion & perspectives
Case of real data (Robusteness to scale factor and rotation)
Figure: The used Templates : T1, T2, T3, T4
| Col1 | T1 | T2 | T3 | T4 |
|---|---|---|---|---|
| Evolving curve | 0.9856 | 0.9904 | 0.9955 | 0.9973 |
Table: Distances between the evolving curve and the used templates.
17/18
M. A. MEZGHICH, S. M’HIRI and F. GHORBEL Fourier-based Multi-references shape prior for active contours
Introduction State of the art (Active contours and Shape priors)
Description of the proposed method
Experimental results Conclusion & perspectives
In this work :
A new method of active contours with geometric shape prior has been presented.
The proposed method presents invariance with repect to Euclidean transformations.
A set of experimental results has been presented.
As perspectives, we intend to :
Apply the method to stereo images and motion tracking.
Extend the method to more general transform such as affine transformation.
Extend the method in case of images with many objects (Mezghich et al., Taima’11).
18/18
M. A. MEZGHICH, S. M’HIRI and F. GHORBEL Fourier-based Multi-references shape prior for active contours