DE-9IM

Understanding the DE-9IM Model

The Dimensionally Extended 9-Intersection Model (DE-9IM) is a powerful tool in spatial analysis and GIS. But what exactly does it do, and why should you care?

What Does DE-9IM Do?

The DE-9IM model provides a way to describe the spatial relationships between two regions using a 3×3 matrix. This matrix can classify up to 512 different topological relations, making it incredibly versatile for various applications.

Key Concepts

Interior and boundary terms are used in a specific sense, with the dimension of empty sets denoted as −1 or F (false).

The model is based on a 3×3 intersection matrix that helps us understand how two regions interact. Each cell in this matrix represents whether one region intersects another’s interior, boundary, or exterior.

DE-9IM and Spatial Predicates

How do we use DE-9IM to describe spatial relationships?

Simplified DE-9IM Matrix

A simplified version of the DE-9IM matrix can be expressed using a boolean domain {T,F}. This makes it easier to understand and apply in practical scenarios.

Common Spatial Predicates

• Intersects: Do two regions share any part of their space?
• Touches: Are the boundaries of two regions adjacent without overlapping interiors?
• Equals: Is one region completely contained within another, and vice versa?

Properties of Spatial Predicates

The spatial predicates have specific properties such as reflexive, anti-reflexive, symmetric, and transitive relationships. These properties help us understand how these relations behave under different conditions.

Applications and Standards

The DE-9IM model is widely used in GIS and spatial databases to classify geometry relations and compute spatial predicates.

OGC Standards for Spatial Predicates

The Open Geospatial Consortium (OGC) has developed standards based on the DE-9IM model. These include:

• DE-9IM model: A function that returns a string code with domain {0,1,2,F}
• SQL/MM Spatial standard: Recommends supported routines and function labels
• Simple Feature Access (ISO 19125) standard: Recommends support for certain functions

Implementation in Databases

Most spatial databases implement the DE-9IM model using standard functions like ST_Relate, ST_Equals, and ST_Intersects.

For example, you can use ST_Relate() to quickly check if two geometries intersect or overlap. This function is faster than direct computation of corresponding predicates.

Synonyms and Variations

The DE-9IM model has several synonyms and variations that make it more flexible and applicable in different contexts.

Common Synonyms

• Egenhofer-Matrix for the 9IM matrix
• Clementini-Matrix for the DE-9IM model
• Egenhofer operators and Clementini operators for matrix elements used in boolean operations
• Meets as a synonym for Touches, Inside as a synonym for Within

Oracle Synonyms

• ANYINTERACT and OVERLAPBDYINTERSECT as synonyms for Intersects and Overlaps, respectively
• OVERLAPBDYDISJOINT does not have a corresponding named predicate.

Region Connection Calculus Operators

In Region connection calculus, operators like disjoint (DC), touches (EC), and equals (EQ) offer additional synonyms for predicates. Overlaps (PO) needs context analysis or composition to be fully understood.

Conclusion

The DE-9IM model is a cornerstone in spatial analysis, providing a comprehensive framework for understanding the relationships between geometric objects. By mastering its concepts and applications, you can unlock deeper insights into complex spatial data. Whether you’re working with GIS systems or developing spatial databases, the DE-9IM offers a robust solution to manage and analyze spatial information effectively.