Electrical Engineering
      and Computer Sciences

Electrical Engineering and Computer Sciences

COLLEGE OF ENGINEERING

UC Berkeley

Detecting and localizing edges composed of steps, peaks and roofs

Pietro Perona and Jitendra Malik

EECS Department
University of California, Berkeley
Technical Report No. UCB/CSD-90-590
November 1990

http://www.eecs.berkeley.edu/Pubs/TechRpts/1990/CSD-90-590.pdf

It is well known that the projection of depth or orientation discontinuities in a physical scene results in image intensity edges which are not ideal step edges but are more typically a combination of steps, peak and roof profiles. However most edge detection schemes ignore the composite nature of these edges, resulting in systematic errors in detection and localization. We address the problem of detecting and localizing these edges, while at the same time also solving the problem of false responses in smoothly shaded regions with constant gradient of the image brightness. We show that a class of nonlinear filters, known as quadratic filters, are appropriate for this task, while linear filters are not. A series of performance criteria are derived for characterizing the SNR, localization and multiple responses of these filters in a manner analogous to Canny's criteria for linear filters. A two-dimensional version of the approach is developed which has the property of being able to represent multiple edges at the same location and determine the orientation of each to any desired precision. This permits to recover edge junctions, and to calculate the orientation and curvature of the edges at each point. Experimental results are presented.


BibTeX citation:

@techreport{Perona:CSD-90-590,
    Author = {Perona, Pietro and Malik, Jitendra},
    Title = {Detecting and localizing edges composed of steps, peaks and roofs},
    Institution = {EECS Department, University of California, Berkeley},
    Year = {1990},
    Month = {Nov},
    URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/1990/5684.html},
    Number = {UCB/CSD-90-590},
    Abstract = {It is well known that the projection of depth or orientation discontinuities in a physical scene results in image intensity edges which are not ideal step edges but are more typically a combination of steps, peak and roof profiles. However most edge detection schemes ignore the composite nature of these edges, resulting in systematic errors in detection and localization. We address the problem of detecting and localizing these edges, while at the same time also solving the problem of false responses in smoothly shaded regions with constant gradient of the image brightness. We show that a class of nonlinear filters, known as quadratic filters, are appropriate for this task, while linear filters are not. A series of performance criteria are derived for characterizing the SNR, localization and multiple responses of these filters in a manner analogous to Canny's criteria for linear filters. A two-dimensional version of the approach is developed which has the property of being able to represent multiple edges at the same location and determine the orientation of each to any desired precision. This permits to recover edge junctions, and to calculate the orientation and curvature of the edges at each point. Experimental results are presented.}
}

EndNote citation:

%0 Report
%A Perona, Pietro
%A Malik, Jitendra
%T Detecting and localizing edges composed of steps, peaks and roofs
%I EECS Department, University of California, Berkeley
%D 1990
%@ UCB/CSD-90-590
%U http://www.eecs.berkeley.edu/Pubs/TechRpts/1990/5684.html
%F Perona:CSD-90-590