Scale-invariant contour completion using conditional random fields
Xiaofeng Ren,Charless C. Fowlkes,Jitendra Malik +2 more
- 17 Oct 2005
- Vol. 2, pp 1214-1221
TL;DR: This is the first time that curvilinear continuity has been shown quantitatively useful for a large variety of natural images and better boundary detection has immediate application in the problem of object detection and recognition.
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Abstract: We present a model of curvilinear grouping using piece-wise linear representations of contours and a conditional random field to capture continuity and the frequency of different junction types. Potential completions are generated by building a constrained Delaunay triangulation (CDT) over the set of contours found by a local edge detector. Maximum likelihood parameters for the model are learned from human labeled ground truth. Using held out test data, we measure how the model, by incorporating continuity structure, improves boundary detection over the local edge detector. We also compare performance with a baseline local classifier that operates on pairs of edgels. Both algorithms consistently dominate the low-level boundary detector at all thresholds. To our knowledge, this is the first time that curvilinear continuity has been shown quantitatively useful for a large variety of natural images. Better boundary detection has immediate application in the problem of object detection and recognition
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Figures
Figure 1: Finding potential completions: (a) an object may appear at any scale in the visual field (b) a piecewise linear curve approximates the boundaries regardless of scale. (c) Constrained Delaunay Triangulationconnects the gaps and completes a scale-invariant representation. 
Figure 2: Building a discrete graph.(a) we recursively split a line until the angleθ is below a threshold.(b) an illustration of the process: the input edge map, the linearization, and the Constrained Delaunay Triangulation. 
Figure 8: Pixel-based precision-recall evaluations comparing the local classifier (PbL), global CRF (PbG) and rawPb. Both techniques improve boundary detection on all three datasets and the overall ordering of the curves is generally preserved. 
Figure 4: This Precision-Recall curve verifies that moving from pixels to the CDT completion doesn’t give up any boundaries found by the local measurement. For comparison, we show the upper-bound performance given by the training data on the CDT edges. The upper bound curve has a precision near1 even at high recall and achieves a greater asymptotic recall than the local boundary detector, indicating it is completing some gradientless gaps. 
Figure 3: Examples of the CDT triangulation.G-edges (gradient edges detected byPb) are in black andC-edges (completed by CDT) in green. Note how the CDT manages to complete gaps on the front legs of the elephant (highlighted on the inset at right). These gaps are commonly formed when an object contour passes in front of a background whose appearance (brightness/texture) is similar to that of the object. 
Figure 9: Example results on the three data sets. The two columns of edge maps show the local boundary detectorPb output and the CRF model respectively. The algorithms outputs have been thresholded at a level which yields 2000 boundary pixels for the baseball/BSDS images and 1000 pixels for the smaller horse images.
Citations
Contour Detection and Hierarchical Image Segmentation
TL;DR: This paper investigates two fundamental problems in computer vision: contour detection and image segmentation and presents state-of-the-art algorithms for both of these tasks.
Semantic contours from inverse detectors
Bharath Hariharan,Pablo Arbeláez,Lubomir Bourdev,Subhransu Maji,Jitendra Malik +4 more
- 06 Nov 2011
TL;DR: A simple yet effective method for combining generic object detectors with bottom-up contours to identify object contours is presented and a principled way of combining information from different part detectors and across categories is provided.
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TL;DR: An overview of invariant interest point detectors can be found in this paper, where an overview of the literature over the past four decades organized in different categories of feature extraction methods is presented.
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Beyond pixels: exploring new representations and applications for motion analysis
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