17-03-2014, 05:26 PM
Abstract—Image analysis deals with discrete picture, obtained
by a process of digitization. Through this process, losing some
information is inevitable. Length of a curve belongs to this
category. Since the existence of digital image there are many
algorithms proposed for estimating the length of the curve.
Length estimation in digital image is tied to the method of
digitization. We chose four-neighborhood digitization in two
dimensions. This digitization makes it possible for length
estimator to apply the Vertex Chain Code. A trace contour
algorithm is applied to extract the Vertex Chain Code. The
output is used for global length estimation, namely maximumlength
digital straight segments. In this paper we compare this
global length estimator for both Freeman Chain Code and
Vertex Chain Code.
Keywords-Vertex Chain Code; global length estimator;
maximum-length digital straight segments
I. INTRODUCTION
For real images true feature size is not known and the
most feasible means of comparing possible estimators is via
a simulation study, which allows assessment of the error of
estimation since true feature length is known [1]. The true
length of the underlying smooth line is calculated using
Euclidean distance between the (real) end points, True curve
length is computed using numerical approximation of arc
length[1]. The length estimator can divided in two important
categories, namely local length estimators and global length
estimators. Local length estimators can be based on local
metrics such as weighted or chamfer distance [2]. A local
estimator makes use of a polygonization of the digital arc or
curve obtains by the connecting successive grid points or
grid vertices in the neighborhood of constant size. Global
estimators, on the other hand, do not use fixed neighborhood.
They may be based on maximum-length digital straight
segments (DSSs), on minimum-length polygons (MLPs), or
on approximation of normals or tangents[2].
Length estimators are strongly depended on the method
of discretization. The output of this process can be chain
code. In this study we focus on the length estimators having
digitized curve as input which means chain code. The review
of two different kinds of chain codes was given, it is proofed
that the VCC has advantages over Freeman chain code.
A useful property that a discrete geometric estimator may
have is to converge toward the geometric quantity of the
continuous shape boundary when the digitization grid gets
finer[3]. In [4]is proofed that except local metrics the other
kinds of length estimators satisfied the multigird
convergence theorem. There exists extension for 3D length
estimators for the DSS and MLP approaches.
by a process of digitization. Through this process, losing some
information is inevitable. Length of a curve belongs to this
category. Since the existence of digital image there are many
algorithms proposed for estimating the length of the curve.
Length estimation in digital image is tied to the method of
digitization. We chose four-neighborhood digitization in two
dimensions. This digitization makes it possible for length
estimator to apply the Vertex Chain Code. A trace contour
algorithm is applied to extract the Vertex Chain Code. The
output is used for global length estimation, namely maximumlength
digital straight segments. In this paper we compare this
global length estimator for both Freeman Chain Code and
Vertex Chain Code.
Keywords-Vertex Chain Code; global length estimator;
maximum-length digital straight segments
I. INTRODUCTION
For real images true feature size is not known and the
most feasible means of comparing possible estimators is via
a simulation study, which allows assessment of the error of
estimation since true feature length is known [1]. The true
length of the underlying smooth line is calculated using
Euclidean distance between the (real) end points, True curve
length is computed using numerical approximation of arc
length[1]. The length estimator can divided in two important
categories, namely local length estimators and global length
estimators. Local length estimators can be based on local
metrics such as weighted or chamfer distance [2]. A local
estimator makes use of a polygonization of the digital arc or
curve obtains by the connecting successive grid points or
grid vertices in the neighborhood of constant size. Global
estimators, on the other hand, do not use fixed neighborhood.
They may be based on maximum-length digital straight
segments (DSSs), on minimum-length polygons (MLPs), or
on approximation of normals or tangents[2].
Length estimators are strongly depended on the method
of discretization. The output of this process can be chain
code. In this study we focus on the length estimators having
digitized curve as input which means chain code. The review
of two different kinds of chain codes was given, it is proofed
that the VCC has advantages over Freeman chain code.
A useful property that a discrete geometric estimator may
have is to converge toward the geometric quantity of the
continuous shape boundary when the digitization grid gets
finer[3]. In [4]is proofed that except local metrics the other
kinds of length estimators satisfied the multigird
convergence theorem. There exists extension for 3D length
estimators for the DSS and MLP approaches.