Bilateral edge filter: Photometrically weighted, discontinuity based edge detection Source: Journal of Structural Biology 160 (2007) 92-102 Authors: Radosav S.Pantelic, Geoffery Ericksson, Nicholas Hamilton, Ben Hankamer Presenter : 張瑞修 Date: 12/12

Outline Introduction Proposed Method Results Conclusions

Introduction Edges are significant discontinuities. Target is significant discontinuous on edge. Source from : http://www2.cch.org.tw/lungcancer/Dx%20Chest_CT.htm Scanning electron microscope (SEM) photograph of normal blood cells. Shown in these paragraphs are erythrocytes (E), a lymphocyte (L), a platelet (P) and a reticulocyte (R). The cell to the left of the reticulocyte is probably a more mature reticulocyte. Source from: http://images.google.com.tw/imgres?imgurl=http://history.nasa.gov/SP-368/p212.jpg&imgrefurl=http://history.nasa.gov/SP-368/s3ch3.htm&h=486&w=280&sz=27&hl=zh-TW&start=236&um=1&tbnid=7L9EQepqPk192M:&tbnh=129&tbnw=74&prev= scanning electron microscope (SEM) photograph of normal blood cells computed tomography photograph of lung cancer

Proposed Method Pre-filtering Pre-filtering is widely used in conjunction with edge detection to suppress noise, and impose a progressive continuity.

Proposed Method Adaptation of the Bilateral filter Calculate the difference between a given focal pixel and each of its neighboring pixels. 100 78 98 84 σ2 increase, the edge will emerge and noise will be suppressed. is called photometric parameter. ( m, n) is the relative coordinate of ( x, y). Image data

Proposed Method is spatial weight. This imposes a property that pixels further from the focal pixel have a weaker contribution to the final photometric score.

Proposed Method The average photometric scores for a given focal pixel is calculated by

Proposed Method To remove any excessively weak photometric scores ( i.e., scores close to 1).

Proposed Method Calculate the differences. n 2 1 -1 -2 -2 -1 0 1 2 m 100 84 98 78 Calculate the differences. 2 1 -1 -2 -2 -1 0 1 2 m n examples:

Proposed Method Calculate the average photometric scores.

Proposed Method Calculate the thresholded photometric score

Proposed Method original image data photometric scores 100 78 98 84 1 100 78 98 84 1 0.480825 0.828792 0.537471 0.824126 0.574827 0.674166 0.56946 0.567979 0.841253 0.843957 0.639504 0.828314 0.503219 0.462432 photometric scores

Proposed Method Non-minimal edge suppression If the focal pixel is part of a continuous edge or at the end of a edge, its average photometric score will be within the four smallest scores of a 3×3 pixel neighborhood. 1 0.480825 0.828792 0.537471 0.824126 0.574827 0.674166 0.56946 0.567979 0.841253 0.843957 0.639504 0.828314 0.503219 0.462432 photometric scores

Results image of keyhole limpet hemocyanin Bilateral edge filter Canny edge filter

Results Cryo-EM tomogram of insulin-secreting pancreatic β-cell Bilateral edge filter Canny edge filter

Conclusions The Bilateral edge filter and Canny edge-detector are on a par on a level of accuracy. The Bilateral edge filter uses one parameter.