Zhu Xu 
  
LEAST MEDIAN OF SQUARES MATCHING FOR AUTOMATED DETECTION OF SURFA CE 
DEFORMATIONS 
"Zhu XU and "Zhilin LI 
Dept. of Land Surveying and Geo-Informatics 
The Hong Kong Polytechnic University, Hong Kong 
"E-mail: 98900969r@ polyu.edu.hk 
"E-mail: Iszlli @ polyu.edu.hk 
  
KEY WORDS: surface matching, robust estimator, least median of squares estimator, local deformation 
ABSTRACT 
Detecting the difference between two surfaces without the aid of control points is desirable for many industrial 
applications. We tackle this problem by means of robust surface matching. In presence of local deformation, 
conventional surface matching algorithm with least square condition would fail. Efforts have been made by some 
researches to robustify the surface matching algorithm using M-estimators. We use least median of squares estimator 
and data snooping technique to robustify the surface matching algorithm and use a M-estimator to improve the 
efficiency of least median of squares estimator. Evaluation and comparison of these methods are carried out using 
simulative data. The result shows robust matching using least median of squares estimator can detect a local 
deformation that covers up to 50 percents of the surface and very small deformation can detected and it is not sensitive 
to position of deformation, which is much superior to other methods of robustifying surface matching. 
1. INTRODUCTION 
There are many industrial applications where the detection of the difference between two 3-D (digital) surfaces is of 
great concern, such as monitoring surface deformation and soil erosion, product quality control and object recognition. 
The surfaces of concern could belong to one of the following three categories: (a). The same surface acquired at two 
different epochs, i.e. in the case of monitoring surface deformation, soil erosion etc.; (b). One surface representing a 
design model and the other measured from a product, i.e. in the case of quality control; and (c). The two surfaces 
representing two different models but for similar objects, i.e. in the case of object recognition and security analysis. 
Traditional techniques for surface deformation detection involve an extensive use of control points. For example, in 
order to monitoring stream channel erosion, ground control points including stable stokes were established and 
periodically maintained by investigators to provide common reference system for DEMs acquired at different epochs 
[Wetch and Jordan 1983]. In applications of tool and component inspection in aircraft manufacturing by means of 
photogramonetry, absolute or relative monitoring networks were required to provide common datum between each 
measurement epoch [Fraser 1988]. However, in many circumstances, the establishment of control points is a difficult, 
unreliable and even impossible process. This is especially the case for surface deformation monitoring in engineering, 
industrial inspection and medical sciences. Techniques without the use of control points are therefore very desirable in 
these cases. : 
Digital elevation model is used in our study for surface representation. To detect the difference between two surfaces, 
the essential task is to transform the two DEMs representing the two surfaces respectively into a common datum. With 
absolute control networks, this could be done by coordinate transformation. With relative control networks, this is a 
procedure of deformation analysis. When no control points exist, the two DEMs have to be mutually registered by 
means of surface matching. However, the two surfaces cannot be precisely matched until the difference between them 
has been identified and removed from the data sets used for matching and the difference cannot be detected until the 
two surfaces have been precisely matched. Therefore, the procedure of surface matching must be performed 
simultaneously with the procedure of difference detection. 
There have been some studies on surface deformation detection by means of surface matching. Karras and Potsa (1993) 
addressed medical applications of deformation detection through DEM matching. In their study, the DEM matching 
technique developed by Resenholm and Torlegard (1988) was applied and extended with data snooping technique to 
detect deformation of human body. Experiments showed such a process performs well when deformation is of large 
magnitude but small proportion while it gives inferior results for deformation of relatively small magnitude but large 
proportion. Instead of data snooping, M-estimator is used to robustify the matching procedure by Pilgrim (1991,1996) 
for the purpose of detecting surface difference. It is reported that the robust matching procedure is capable of detecting 
difference covering up to 25% of surfaces being matched. 
Surface deformation can be of different forms. One form is that only parts of one surface differ from their 
corresponding parts of the other surface and the rest parts are identical to their corresponding parts expect for random 
errors. We call it local deformation this case of the difference between two surfaces. Nevertheless, surface difference 
could also be throughout the whole surface, i.e. global deformation. In this paper we discuss only the detection of local 
deformation. 
  
1000 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000.