Deformable Model for Image Segmentation 
Yaonan Zhang 
Faculty of Geodesy, Delft University of Technology 
Thijsseweg 11, 2629 JA Delft, The Netherlands 
Commission IV 
ABSTRACT: 
This paper presents an approach for image segmentation using Minimum Description Length (MDL) principle and 
integrating region growing, region boundary fitting, model selection in an integrated manner, on which the final result 
is a kind of compromise of various sources of knowledge such as the original grey level image and deformable object 
models. The deformable model is a closed polygon depicted by a number of straight line segments. The formulae for 
encoding the image intensity and shape of region are presented. The whole process is carried out by a split-and-merge 
mechanism which is based on a new data structure. We also introduce the method for optimal curve fitting. We believe 
that such approach can be used in the segmentation and feature detection for remote sensing image, urban scene image 
as well as in the automated integration of GIS, remote sensing and image processing. 
KEYWORDS: Image Segmentation, Image Analysis, Feature Extraction. 
1. INTRODUCTION 
Image segmentation is one of the fundamental 
requirements in image analysis. The techniques for 
image segmentation roughly fall into two general 
processes: 
1). Edge detection and line following. This category 
of techniques studies various of operators applied 
to raw images, which yield primitive edge 
elements, followed by a concatenating procedure 
to make a coherent one dimensional feature from 
many local edge elements. 
2). | Region-based methods. Region-based methods 
depend on pixel statistics over localized areas of 
the image. Regions of an image segmentation 
should be uniform and homogeneous with respect 
to some characteristics such as grey tone or 
texture. Region interiors should be. simple and 
without many small holes. Adjacent regions of a 
segmentation should have significantly different 
values with respect to the characteristics on 
which they are uniform. Boundary of each 
segment should be simple, not ragged, and must 
be spatially accurate [Haralick and Shapiro,84]. 
Image segmentation is hard because there is generally no 
theory on it. Segmentation techniques are basically ad 
hoc and differ precisely in the way they emphasize one 
or more of the desired properties and in the way balance 
and compromise one desired property against another. 
The whole content of this paper is concentrated on the 
region-based methods. Region-based image segmentation 
techniques can be classified as: measurement space 
guided spatial clustering, single linkage region schemes, 
720 
hybrid linkage region growing schemes, centroid linkage 
region growing schemes, spatial clustering schemes, and 
split and merging schemes [Haralick and Shapiro] 
[Benie] [Besl,88a,88b] [Bharu] [Blanz] [Haddon] [Hu] 
[Liou] [Pappas] [Rodriquez] [Snyder] [Sumanaweera] 
[Tsikos]. 
Recently, There is increasing interest in applying the 
information theory to automatically interpret and 
analysis the image data [Foerstner and Pan] [Kim] 
[Hua,89a,89b,90] [Leclerc,89,90] [Leonardis] [Meer] 
[Pavlidis]. The fundamental concept in information 
theory is the idea that the amount of information derived 
from some event, or experiment, is related to the 
number of degrees of freedom available beforehand or 
the reduction in uncertainty about some other event 
gleaned from an observation of the outcome. Among the 
tremendous tools provided by information theory, 
Minimum Description Length (MDL) principle has been 
quite successfully applied in computer vision field. 
MDL principle studies estimation based upon the 
principle of minimizing the total number of binary digits 
required to rewrite the observed data, when each 
observation is given with some precision. Instead of 
attempting at an absolutely shortest description, which 
would be futile, it looks for the optimum relative to a 
class of parametrically given distributions. This MDL 
principle turns out to degenerate to the more familiar 
Maximum Likehood (ML) principle in case the number 
of parameters in the models is fixed, so that the 
description length of the parameters themselves can be 
ignored. In another extreme case, where the parameters 
determine the data, it similarly degenerates to Jaynes's 
principle of maximum entropy. The main power of the 
MDL principle is that it permits estimates of the entire 
model, its parameters, their number, and even the way