Vector Field Convolution (VFC)

vfc pic.jpg

Project Info

Title Vector Field Convolution
Paper B. Li and S.T. Acton, "Active contour external force using vector field convolution for image segmentation," IEEE Transactions on Image Processing, vol. 16, 2096-2106, 2007. [.pdf]
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Develop a novel method to calculate the external force for deformable models, including snakes, (a.k.a., active contours), and deformable surfaces.


Snakes, or active contours, have been widely used in image processing applications. Typical roadblocks to consistent performance include capture range, noise sensitivity, and poor convergence to concavities. The major drawback of standard external forces is that the force field has an initially zero magnitude in the homogeneous regions of the image. An external force for active contours, called gradient vector flow (GVF) was introduced to overcome two key difficulties of active contours. The active contour using the GVF field provides a large capture range and the ability to capture concavities by diffusing the gradient vectors of an edge map generated from the image. Although the GVF field has been widely used and improved in various active models. , there are some disadvantages, such as noise sensitivity, parameter sensitivity, high computational cost and the ambiguous relationship between the capture range and parameters.

The calculation of the external force can be broken down to two independent steps: the formation of edge map from the image, and the computation of the external force from the edge map. Although the quality of the edge map is a critical factor in snake performance, this project focuses on how to obtain a desirable external force field given an edge map, which is likely to be corrupted by noise.

We present a novel external force for active models called vector field convolution (VFC) to address the above problems. This external force is calculated by convolving a vector field with the edge map derived from the image. Active contours that use VFC external force are termed VFC snakes. Like GVF snakes, instead of being formulated using the standard energy minimization framework, VFC snakes are constructed by way of a force balance condition. The novel static external force has not only a large capture range and ability to capture concavities, but also reduced computational cost, superior robustness to noise and initialization, flexibility of changing the force field. We demonstrate these desirable properties by comparing the VFC forces with the GVF forces as following. For more examples and details, please refer to the related publications.

We also find that the GVF field in homogeneous regions of the image is a special case of VFC. The standard external force, i.e., the gradient of edge map, is also a special case of VFC.

Fig 1. Both GVF and VFC snakes have a large capture range and converge to boundary concavities.

Fig 2. Impulse noise corrupted U-shape images. GVF snake still fails to capture the U-shape using Gaussian filtering with standard deviation of 5. VFC snake capture the edges accurately and promptly without filtering.

Fig 3. An ellipse represents a synthetic cell. An anisotropic term can be included in the magnitude function to obtain a VFC field similar to the motion GVF (MGVF).

Fig 4. MR image of a human ankle. GVF snake becomes stuck in the interior and does not converge to boundary, whereas VFC snake converges to the boundary concavities on the lower right precisely from the same initialization at the center.

Isosurface Rendering

*VFC active surface*
Fig 5. Isosurface rendering of a 3D star-like object in (left) a noise-free image and (right) a impulse noise corrupted image with -6 dB SNR. VFC active surface is able to capture the object in both cases without filtering the image.

Fig 6. VFC active surfaces segmentation result of the pericardium border (red) and endocardial border (green). Two slices of the MR image of human heart is shown for reference.
Topic revision: r2 - 01 Jun 2014, AndreaVaccari
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