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Introduction
Boundary detection is a fundamental problem in vision and, just like any other
vision task, is multi-scale in nature. The 1980s saw a large number of studies
on edge detection and many explicitly addressed the scale issue. In fact, the
fabled Canny edge detector [2] was multi-scale -- i.e.
feature synthesis. Scale-space theories were developed, in the context
of edge detection leading to Lindeberg's scale-space edge detector [3].
However, these studies on multi-scale edge detection did not materialize. The
matlab implementation of Canny is single-scale. The recent
Probability-of-Boundary detector (Pb) [4], outperforming previous detectors on
natural images in the Berkeley Segmentation Dataset, is also single-scale. In
fact, the authors of [4] specifically claimed that they did not find any
benefit going multi-scale.
I find that hard to believe -- surely natural images are multi-scale! The goal
of this work is to empirically "prove" that multi-scale significantly improves
boundary detection in natural images.
Multi-Scale Boundary Cues
We base our approach on Pb, which combines brightness, color and texture
contrasts of two half-disks with a fixed size. The simplest multi-scale
extension of Pb is to compute the Pb contrast value under multiple disk
sizes. Combining these contrast values can be cast in the same classification
formulation, and in our case a linear logistic classifier is used.
There are many other cues that provide boundary information at multiple scales.
One cue is contrast normalization; a salient boundary has a contrast much
higher than its surroundings. Another cue is localization -- the peak location
of contrast for a smooth boundary does not change when we measure contrast
under varying scales; while the peak of a false boundary, say in texture
regions, shifts around.
Once we have a dense contrast map combining multi-scale signals, one important
detail is how to do non-maximum suppression. Empirically we find out that it is
best to do non-maximum suppression using only fine-scale contrast. This is
consistent with intuition that fine-scale edges are better at localization.
Empirical Results on Five Datasets
This is empirical work and we have tested our algorithms on five datasets with
groundtruth boundaries. Results are shown in the form of precision-recall
curves (as in [4]). In all cases multi-scale improves boundary detection by a
significant margin. We also compare to Canny and Scale-Space Edges.
Thus we have empirically proved that multi-scale improves boundary detection
performance. It is our hope that soon every boundary detector will be
multi-scale in nature and can work with high-resolution images from modern
cameras.
References
- Multi-Scale Improves Boundary Detection in Natural Images.
[abstract]
[pdf]
Xiaofeng Ren, in ECCV '08, Marseille 2008.
- A Computational Approach to Edge Detection.
J. Canny, in PAMI 8(6), 1986.
- Edge detection and ridge detection with automatic scale selection.
T. Lindeberg, in IJCV 30, 1998.
- Learning to Detect Natural Image Boundaries Using Local Brightness, Color and Texture Cues.
D. Martin, C. Fowlkes and J. Malik, PAMI 2004.
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