2 State of the Art
The automatic detection of elementary geometric features (line segments, elliptical
arcs) in images, is quite an old issue in computer vision [8, 9]. The current proce-
dures for geometric features recognition can be roguhly classified into two categories:
Hough-based and edge chaining methods.
The Hough-based algorithms implement variants of the Hough transform. These
methods ensure that pixels belonging to the same geometric stucture are mapped to the
same point into an appropriately defined parameter space. We can define an accumulator
array in which every cell, corresponding to specific parameter values, is augmented ev-
ery time that a pixel is mapped on that cell. Computing the peaks of this array allows to
identify the potential candidates. Standard Hough-based implementation requires high
computational burden handling, especially for elliptical shape recognition: indeed, in
that case the parameter space has five dimensions, corresponding to the five parame-
ters of the ellipse, resulting in a O(n
5
) complexity. Basc¸a et al. [10] have proposed
a method for speeding up the candidate identification process by implementing a ran-
dom search method. This allows to lower the computational complexity more than two
orders of magnitude.
A second class of detection methods relies on edge chaining techniques, which use
extensively the geometric properties of the sought features, such as straightness criteria
for line segments or curvature properties for ellipses. Usually these algorithms begin
with a seed pixel (or a group of pixels), and subsequently, other pixels are added, pro-
vided they obey some geometric properties of the sought feature.
Nguyen and Kerautret proposed a method for ellipse detection based on a prelimi-
nary decomposition of an edge image into curve primitives followed by a fitting tech-
niques. First the image is processed by an edge detection filter in order to extract a set
of digital curves representing the image contours. The analysis is then limited to every
single group of pixels representing a contour curve in the image. The curve undergoes
a particular transformation that maps the contour lines into the so called tangent space.
As it is explained in [11] the tangent space representation allows a much easier assess-
ment of the curvature properties of the grouped contour. More in detail it is possible
to decide whether a set of line segments belongs to a straight line or if these segments
are part of more elliptical structures. The final assessment is carried out by a fitting
procedure in order to decide whether the curve can be classified as a circle or an ellipse.
This paper is inspired by a successful parameterless approach that was introduced
by Desolneux et al. [12], known as the a contrario approach. The detection algorithm is
based on a three-stage process: first, a candidate selection stage is carried out by gather-
ing groups of pixels sharing appropriate orientation properties (for example line recog-
nition requires the alignment between pixels where as for circles and ellipses detection
some curvature constraints must be fulfilled); in a second stage (validation stage), the
candidates are further analysed in order to decide whether they are meaningful struc-
tured groups of pixels or if they represent an unstructured cluster. This is an important
step since it allows the rejection of false positives by automatic computation of detec-
tion threshold. The estimation process is based on the so called Helmoltz’s perception
principle: it essentially states that there is no perception in white noise. In the final
stage (model selection) the candidates are classified as belonging to a specific model
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