ISPRS, Vol.34, Part 2W2, “Dynamic and Multi-Dimensional GIS", Bangkok, May 23-25, 2001 
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NON-LINEAR RECTIFICATION OF MAP WITH COLLINEAR CONSTRAIN 
Wei LU, Takeshi DOIHARA 
Research Institute, Asia Air Survey Co., Ltd., 3F Asahi-Seimei Bldg. 
8-6 Tamura-cho, Atsugi-shi, Kanagawa-ken, 243-0016, JAPAN 
Tel:+81-462-95-1886, Fax:+81-462-95-1934 
E-mail:luwei@aiiko.co.jp 
Key Words: Digital mapping, Map rectification, GIS 
Abstract 
Map rectification has been playing a very important role in digital mapping processes. Especially in Japan, the ancient cadastral maps- 
even though being only roughly correct in topology, area, and shape- are still being used as formal legal documents for clarification of 
land rights. To digitize such kind of maps, rectification methods of non-linear transformation are required. In many cases, cadastral line 
segments that are collinear to each other must also be kept collinear after transform. This constrain makes non-linear transformation 
more difficult. In this paper, we propose a method that performs non-linear rectification while keeping the collinear relationship. 
1. Introduction 
Nowadays, with the rapid development of information technology 
from algorithms to infrastructures, more and more GIS data are 
being generated digitally. Even though digital data is the most 
favorable form for GIS system, their tremendous cost does not 
allow production from scratch when budget is not feasible. On the 
other hand, there has been a huge collection of paper-based map 
in all kinds of organizations. By digitizing these paper-based 
maps and making proper edition/modification, we can generate 
up-to-date map more economically. Since paper-based maps 
usually have distortions due to the precision limitation of 
production or data source, map rectification has been playing a 
very important role in digital mapping processes. Especially in 
Japan, the ancient cadastral maps- whereas being roughly 
correct in topology, area, and shape- are still being used as 
formal legal documents for clarification of land rights. To digitize 
such kind of maps, rectification methods of non-linear 
transformation are required. In many cases, cadastral line 
segments that are collinear to each other must also be 
maintained the same after transform. This constrain makes 
non-linear transformation more difficult. In this paper, we propose 
a method that performs non-linear rectification while keeping the 
collinear relationship. 
2. System Overview 
Fig. 1 shows the overview of our system. The paper-based map is 
first automatically converted to polyline and text. Due to 
deterioration of paper or ink, there will be missing, corrupted, or 
extra noisy data, which will be modified in the “Initial Manual 
Modification” module. The next module generates the collinear 
constrains in a semiautomatic way. The “Non-linear 
transformation” module will then transform the digitized map 
without breaking the collinear condition. Finally, the map will be 
modified against the topographical map and database of 
cadastral attributes. The details of each processing module will 
be described in the following section. 
3. The Proposed Algorithms 
Our proposed method for digitizing consists of the following 
phases: 
a. Vectorization of paper-based map 
b. Semi-automatic collinear grouping 
c. Specification of corresponding point 
d. Non-linear rectification 
e. Manual modification 
3.1 Vectorization of paper based map 
This phase consists of two steps: automatic vectorization and 
initial manual modification. 
Paper based maps are scanned and vectorized with a system 
developed by the author’s group [1]. This system makes use of 
mathematical morphology for extraction of line segments and text. 
Fig. 1 Overview of cadastral map digitization system 
It also has user-friendly interface for manually modify 
unsuccessfully processed elements. When existing database of 
land information exists, this system can also automatically check 
the possible processing or original errors. 
The output result is cadastral line segments, the intersection 
information, the index line that indicates the position of text string 
of cadastral number and arcs that shows the relationship of 
separated lands. 
3.2 Semi-automatic collinear grouping 
The line segments that are likely to be collinear are recognized 
automatically by algorithm that is similar to generalization of 
chained point list. Each group of collinear segments is given a 
unique group number. 
Exceptional cases are modified manually through GIS system. 
3.3 Specification of corresponding point 
Corresponding points with existing topographical map are 
manually specified. The top priority for locations of corresponding 
points is the boundaries of each area and internal major roads. 
3.4 Non-linear rectification 
This is the central part of the proposed method and consists of 
the following procedures: 
a. Generation of TIN with the corresponding points 
b. Classification of intersection nodes