ISPRS, Vol.34, Part 2W2, “Dynamic and Multi-Dimensional GIS", Bangkok, May 23-25, 2001 
The motion vector aims to support continuous change modeling, 
to facilitate future queries, and simultaneously to reduce data 
storage volume. MOST model makes possible real-time update 
of spatial locations of object, but it doesn’t emphasize keeping 
the whole history of spatial data. In contrast, Erwig, M., R.H. 
Gueting et al. (1997) designed the abstract data type of moving 
object into their geo-relational algebra. Extended geo-relational 
algebra has formally defined two abstract data types of moving 
object (moving point mpoint and moving region mregion) and 
relevant operators. The types mpoint and mregion are defined 
as mappings from time to space mathematically, that is, 
Mpoint time ->point 
Mregion: time ->region 
The type mpoint indicates that the location of object is varying 
over time. The type mregion indicates that extent of object is 
varying over time, e.g., shrinking or expanding. The authors 
insist that moving line is the trajectory of moving point, so it is 
somewhat unnecessary to define moving line type. 
In contrast to MOST model, extended geo-relational algebra put 
special emphasis on history maintenance of time-varying spatial 
data. Another difference is that MOST model pays more 
attention to implementation with motion vector data structure, but 
extended geo-relational algebra mainly focuses on conceptual 
abstraction of time-varying property of geographical objects. It is 
obvious that both MOST model and extended geo-relational 
algebra classify spatial changes by the joint criterion of 
geometrical dimensionality and location movement. 
2.4 The Criterion of Spatial Variables 
Pierre Gagnon, Yvan Bedard and Geoffrey Edwards (1992) 
categorized spatial changes into three groups: one-entity 
change, two-entity change and multi-entity change. One-entity 
changes consist of existence, extinction, location (position) 
change, direction (orientation) change, shape change and size 
change of an entity. Two-entity changes consist of spatial 
relationship (topological relationship) changes between two 
entities. Multi-entity changes are population changes formed 
with 3 entities or more, including location (position) change, 
direction (orientation) change, shape change and size change 
(cumulative size change or population size change) and change 
of spatial distribution type of a population. The cumulative size is 
the summation of all individual sizes of entities of a population. 
When combined with the number of entities, it provides 
“presence rate”. The spatial population size corresponds to the 
size of distribution area, when combined with the number of 
entities, it provides “occupation rate”, and when combined with 
cumulative size, it provides “spatial density”. There are three 
types of spatial distribution, regular, random and grouped 
distributions. This change classification is referred to be based 
on the criterion of spatial variables, spatial variables of a single 
entity (location, direction, shape and size) and spatial variables 
of multi-entity (cumulative size, population size and spatial 
distribution type). 
2.5 The Joint Criterion of Spatial Variables and 
Geographical Functions 
Christophe Claramunt and Marius Theriaut (1995, 1996) posed 
three types of spatio-temporal process: (1) the evolution of a 
single entity; (2) the processes involving functional relationships 
between several entities; (3) the evolution of spatial structures 
involving several entities. 
For the evolution of a single entity, there exist three types of 
process: 
• Basic processes including appearance, disappearance and 
spatial stability to allow representation of attribute variation 
without spatial effects; 
• Transformation processes involving changes in shape or 
size, including expansion, contraction and deformation (shape 
modification without size change); 
• Movement processes involving only position changes, 
including displacement and rotation. 
For the processes involving functional relationships, it can be 
grouped into two categories: 
• Replacement processes involving a sequence of entities of 
comparable types that accomplish the same function or occupy 
the same position in space (without necessarily having identical 
locations), e.g., succession and permutation. 
• Diffusion processes involving a transfer of characteristics 
between two or more spatial entities. It seems useful to 
distinguish between production (creation of new entities by 
actions of one or more entities of different natures), reproduction 
(creation of new entities by actions of essentially identical 
entities called parents) and transmission (modification of 
characteristics of a receiver due to influence of a transmitter). 
Each process carries a precedence constraint. Contagion is a 
specific form of diffusion. 
For the evolution of spatial structures involving several entities, 
three restructuring processes are introduced. They are splitting, 
union and reallocation. 
It is easy to know that the change classification of single entity is 
mainly based on spatial variables (shape, size, location, 
direction), and functional relationship evolutions on geographical 
functions. Also, some basic processes of single entity and 
spatial structure evolutions are associated with changes of 
object identity 
2.6 The Joint Criterion of Entity Identity and Geographical 
Functions 
Kathleen Hornsby and Max J.Egenhofer (1997, 1998) proposed 
a change classification based on object identity and a set of 
operations that preserve or change object identity. In conjunction 
with geographical functions, they defined four kinds of change 
(or operation): (1) transitions (concretely, transition between 
object existence and object extinction, issue transition, and 
separate transition); (2) identity operations on a single object 
(creation, destruction, continuing existence, continuing non 
existence, and equivalent reincarnation, same reincarnation); 
issuing operations (spawning and metamorphosis); operations of 
combining single objects (merge, generate and mix); splitting 
operations (splinter and division); (3) Operations on a single 
object and a composite object, i.e., operations of forming 
composite object (aggregation, compound, union, amalgamation 
and combination), operations of splitting composite objects 
(secession and dissolution); (4) Operations of selecting an object 
or a portion of an object. 
3 PRIMARY SPATIAL CHANGES 
From the above investigations, we can see that spatial changes 
are usually described in four respects, i.e., spatial property 
change, object identity change, spatial distribution change and 
functional change. Among them, functional change is application 
dependent, and is of various number, which can be explained at 
different levels of abstraction. Thus, in a general form, we define 
various changes at three levels, property change, object change 
and scene change. Scene change is similar to spatial distribution 
change, which is an overall change composed of property and 
object changes. Meanwhile, we recognize time semantics with 
three simple time-varying patterns, i.e., discrete change, 
stepwise change and continuous change. 
3.1 Three Levels of Spatial Change 
In the bottom-up order, three levels of spatial change are spatial 
property change, spatial object change and spatial scene 
change (Figure 1). Spatial property change refers to geometrical 
property change and geometrical dimensionality change. Spatial 
object change is related to change of object identity. Spatial