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Edge detection in microscopy images using curvelets.

Gebäck T, Koumoutsakos P - BMC Bioinformatics (2009)

Bottom Line: Optionally, the edges may then be extended along the directions given by the curvelets to provide a more connected edge map.We compare our scheme to the Canny edge detector and an edge detector based on Gabor filters, and show that our scheme performs better in detecting larger, elongated structures possibly composed of several step or ridge edges.The proposed curvelet based edge detection is a novel and competitive approach for imaging problems.

View Article: PubMed Central - HTML - PubMed

Affiliation: Computational Science, ETH Zürich, Universitätstrasse 6, CAB H69,2, ETH Zürich, CH-8092 Zürich, Switzerland. tobias.gebaeck@inf.ethz.ch

ABSTRACT

Background: Despite significant progress in imaging technologies, the efficient detection of edges and elongated features in images of intracellular and multicellular structures acquired using light or electron microscopy is a challenging and time consuming task in many laboratories.

Results: We present a novel method, based on the discrete curvelet transform, to extract a directional field from the image that indicates the location and direction of the edges. This directional field is then processed using the non-maximal suppression and thresholding steps of the Canny algorithm to trace along the edges and mark them. Optionally, the edges may then be extended along the directions given by the curvelets to provide a more connected edge map. We compare our scheme to the Canny edge detector and an edge detector based on Gabor filters, and show that our scheme performs better in detecting larger, elongated structures possibly composed of several step or ridge edges.

Conclusion: The proposed curvelet based edge detection is a novel and competitive approach for imaging problems. We expect that the methodology and the accompanying software will facilitate and improve edge detection in images available using light or electron microscopy.

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Related in: MedlinePlus

Cross section of an edge in the image. Investigation of the cross section of an edge from the image in figure 2. Top: image data from the horizontal line indicated by arrows in figure 2, in the region of the rightmost membrane (solid line), and the curvelet magnitudes on level 4 as extracted by the algorithm (dotted line, arbitrary scale). Bottom: cross section of a curvelet on level 4, approximately aligned with the edge.
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Figure 4: Cross section of an edge in the image. Investigation of the cross section of an edge from the image in figure 2. Top: image data from the horizontal line indicated by arrows in figure 2, in the region of the rightmost membrane (solid line), and the curvelet magnitudes on level 4 as extracted by the algorithm (dotted line, arbitrary scale). Bottom: cross section of a curvelet on level 4, approximately aligned with the edge.

Mentions: In order to better understand which structures are detected by our edge detection scheme, we extract the pixel values along a horizontal line of the image in figure 2, as indicated by the small arrows in that figure. The pixel values in a region near the rightmost membrane of the vesicle are shown as the solid line in the topmost graph in figure 4. The dotted line is the magnitude of the curvelet coefficients at level 4 along the same line as extracted by our scheme. In the bottom graph, the profile of a curvelet on level 4 almost aligned with the edge is shown for comparison. It is clear that the magnitude of the curvelet coefficients is large where the signal matches the shape of the curvelet, which in this case is exactly the area of the double membranes.


Edge detection in microscopy images using curvelets.

Gebäck T, Koumoutsakos P - BMC Bioinformatics (2009)

Cross section of an edge in the image. Investigation of the cross section of an edge from the image in figure 2. Top: image data from the horizontal line indicated by arrows in figure 2, in the region of the rightmost membrane (solid line), and the curvelet magnitudes on level 4 as extracted by the algorithm (dotted line, arbitrary scale). Bottom: cross section of a curvelet on level 4, approximately aligned with the edge.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2663783&req=5

Figure 4: Cross section of an edge in the image. Investigation of the cross section of an edge from the image in figure 2. Top: image data from the horizontal line indicated by arrows in figure 2, in the region of the rightmost membrane (solid line), and the curvelet magnitudes on level 4 as extracted by the algorithm (dotted line, arbitrary scale). Bottom: cross section of a curvelet on level 4, approximately aligned with the edge.
Mentions: In order to better understand which structures are detected by our edge detection scheme, we extract the pixel values along a horizontal line of the image in figure 2, as indicated by the small arrows in that figure. The pixel values in a region near the rightmost membrane of the vesicle are shown as the solid line in the topmost graph in figure 4. The dotted line is the magnitude of the curvelet coefficients at level 4 along the same line as extracted by our scheme. In the bottom graph, the profile of a curvelet on level 4 almost aligned with the edge is shown for comparison. It is clear that the magnitude of the curvelet coefficients is large where the signal matches the shape of the curvelet, which in this case is exactly the area of the double membranes.

Bottom Line: Optionally, the edges may then be extended along the directions given by the curvelets to provide a more connected edge map.We compare our scheme to the Canny edge detector and an edge detector based on Gabor filters, and show that our scheme performs better in detecting larger, elongated structures possibly composed of several step or ridge edges.The proposed curvelet based edge detection is a novel and competitive approach for imaging problems.

View Article: PubMed Central - HTML - PubMed

Affiliation: Computational Science, ETH Zürich, Universitätstrasse 6, CAB H69,2, ETH Zürich, CH-8092 Zürich, Switzerland. tobias.gebaeck@inf.ethz.ch

ABSTRACT

Background: Despite significant progress in imaging technologies, the efficient detection of edges and elongated features in images of intracellular and multicellular structures acquired using light or electron microscopy is a challenging and time consuming task in many laboratories.

Results: We present a novel method, based on the discrete curvelet transform, to extract a directional field from the image that indicates the location and direction of the edges. This directional field is then processed using the non-maximal suppression and thresholding steps of the Canny algorithm to trace along the edges and mark them. Optionally, the edges may then be extended along the directions given by the curvelets to provide a more connected edge map. We compare our scheme to the Canny edge detector and an edge detector based on Gabor filters, and show that our scheme performs better in detecting larger, elongated structures possibly composed of several step or ridge edges.

Conclusion: The proposed curvelet based edge detection is a novel and competitive approach for imaging problems. We expect that the methodology and the accompanying software will facilitate and improve edge detection in images available using light or electron microscopy.

Show MeSH
Related in: MedlinePlus