Introduction
Finding the boundaries of objects and surfaces in a scene is a fundamental
problem for computer vision, which has immediate appliations in higherlevel
tasks such as object recognition. Traditionally people do edge detection
locally: the "boundariness" of each pixel is decided based on a small local
neighborhood around it, independently of other locations in the image. This is
limited by the amount of information avaiable in such small patches. There is
evidence
from psychophysical experiments that the performance of local edge detectors
has been approaching this limit.



 (a) the outlook of a local boundary detector, 21x21 pixel patches.





 (b) context emerges in 71x71 patches.


Figure 1: purely local boundary detection can easily be fooled. Utilizing more
context could greatly improve boundary detection.

One way to incorporate more contextual information is to use shapemes which try to capture shape/appearance context
in a generic way.
Or, more specifically, one well known source of contextual information is that provided by curvilinear
continuity, i.e. the fact that contours in natural images are extended and smooth.
In this work we develop probabilistic models of continuity (as well as junction
type) and show that curvilinear continuity is quantitatively useful for
a large variety of natural images.
Using the CDT Graph
We bulid our approach on top of the CDT graph, a
discrete scaleinvariant image representation. For every edge e in the
CDT graph, we can associate a random variable X_{e}, where
X_{e}=1 if e corresponds to a true boundary contour and
X_{e}=0 otherwise. The variables {X_{e}}
interact with each other through vertices or junctions in the graph. Our goal
is to build a probabilistic model of continuity and junction frequency on the
CDT graph and make inferences about {X_{e}}.
A Baseline Model of Local Continuity
In our baseline model, each X_{e} is estimated independently in
its local context, including: neighboring edges, their lowlevel contrast
(measured by Pb), and the continuity of their connections.

 (a)  (b)

Figure 2: (a) A simple 2edge model of local curvilinear continuity. (b) Evidence of continuity come from both
ends.

The simplest model of local context consists of two edges ( see Figure 2(a) ).
Each edge has associated features: Pb (average lowlevel contrast), G (whether it is a Gedge or Cedge), and
continuity (measured by the angle θ). A logistic classifier is trained to predict P(X_{0}=1 and X_{1}=1) and P(X_{0}=0 and X_{1}=0).
To compute a new continuityenhanced "probability of boundary" Pb_{local}, recall that contours are extended, and evidence of continuity come from both
ends of edge e_{0}.
Therefore we compute Pb_{local} as the product of the 2edge model on both pairs (e_{0},e_{1}) and (e_{0},e_{2}).
