Edge Based SegmentationXinyu Chang

Outline•Introduction

•Canny Edge detector

•Edge Relaxation

•Border Tracing

Introduction• Edge detecting an image significantly reduces the

amount of data and filters out useless information, while preserving the important structural properties in an image.

• Edge-based segmentations rely on edges found in an image by edge detecting operators.

• but the image resulting from edge detection cannot be used as a segmentation result.

• The final aim is to reach at least a partial segmentation

Canny Edge detectorThe Canny edge detection algorithm is known to many as the optimal edge detector.

Canny Edge detectorIt aims to achieve 3 criterions• The detection criterion expresses the fact that

important edges should not be missed and that there should be no spurious responses.

• The localization criterion says that the distance between the actual and located position of the edge should be minimal.

• The one response criterion minimizes multiple responses to a single edge.

Canny Edge detectorCanny Edge Detection has 6 steps:Step 1, Smooth the image (The larger the width of the Gaussian mask, the lower is the detector's sensitivity to noise.)

Canny Edge detectorStep 2, find the edge strength by taking the gradient of the image.

The magnitude, or EDGE STRENGTH, of the gradient is then approximated using the formula:

|G| = |Gx| + |Gy|

Canny Edge detectorStep 3, Finding the edge direction.

theta = invtan (Gy / Gx)

Step 4, Assign theta into a certain range.

Canny Edge detectorStep 5, Apply maximum suppression1) For each pixel with non-zero edge magnitude, inspect the two adjacent pixels indicated by the direction of its edge

Canny Edge detector2) If the edge magnitude of either of these two exceeds that of the pixel under inspection, mark it for deletion.

3) When all pixels have been inspected, re-scan the image and erase to zero all edge data marked for deletion.

Canny Edge detectorStep 6 Finally, hysteresis is used as a means of eliminating streaking. Streaking is the breaking up of an edge contour caused by the operator output fluctuating above and below the threshold

To avoid this, hysteresis uses 2 thresholds, a high and a low. Any pixel in the image that has a value greater than T1 is presumed to be an edge pixel, and is marked as such immediately. Then, any pixels that are connected to this edge pixel and that have a value greater than T2 are also selected as edge pixels.

If you think of following an edge, you need a gradient of T2 to start but you don't stop till you hit a gradient below T1.

Canny Edge detector

Canny Edge detector•Result on axon image

Canny Edge detector•Another result on axon image

Edge RelaxationBorders resulting from the previous method are strongly affected by image noise, often with important parts missing. Considering edge properties in the context of their mutual neighbors can increase the quality of the resulting image.

For example, A weak edge positioned between two strong edges provides an example of context; it is highly probablethat this inter-positioned weak edge should be a part of a resulting boundary. If, on the other hand, an edge (even a strong one) is positioned by itself with no supporting context, it is probably not a part of any border.

Edge Relaxation

Edge Relaxation

Edge Relaxation

Edge Relaxation