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2. AN EDGE AND TIN BASED APPROACH (ETBA) FOR BUILDING EXTRACTION AND RECONSTRUCTION
ETBA consists of two components: an edge-based building classification process and a TIN-based building
reconstruction process.
2.] Edge-Based Building Classification
Buildings are extracted by edge analysis and classification. Since contours have the same properties regarding shape
and geometry as edges have, ETBA can work with contours as well. For simplification, edges are used to represent both
of them in the rest portion of the paper. Edges are detected from an elevation image generated by a terrain surface data.
Detected edges usually represent buildings and other objects that stand out of the ground surface. The purpose of edge
analysis and classification is to separate buildings from other objects, mainly trees, by using shape and geometric
information contained in edges. The edge analysis is responsible for quantitatively deriving shape and geometric
measurements from edges. And, the classification takes care of extracting building edges based on their shape and
geometric measurements.
Geometric properties, such as orthogonality and parallelism, have been widely used as constraints for building
extraction in many previous researches. In this approach, besides orthogonality and parallelism, symmetry and
circularity are two additional properties to be used. Here, the circularity is defined as the ratio of an edge's length (L)
over its area (A): C=L?/A. For a circle, C=4B, and for a square, C=16. Instead of line segments, this approach uses closed
edges, which allows analyzing the symmetry and circularity of an object. Symmetry and circularity describe an object's
shape as a whole, and only a closed edge can represent it. Since almost all building edges are closed, this constraint
actually only filter out non-building edges. Circularity is chosen because it is a measure of object boundary's complexity
for covering an area. Most buildings have simpler boundaries than tree edges have, which means that the circularity of a
building edge is smaller. Usually for an equal length, a building edge covers a larger area than a tree edge does.
Symmetry is selected for object classification because most buildings have symmetric or semi-symmetric (i.e., symmetric
referring only to one axis) shapes, but most non-building objects do not have symmetry. ETBA uses 3"-order
normalized moments to represent symmetry. There is one problem, however, with the traditional normalized moments:
they are only invariant to translation and scale changes, but variant to rotation. Since the symmetry of an object is
measured against the axes of the coordinate system where the object is located, a rotation will change the measure of the
symmetry of the object. Therefore, a rotation, which can rotate an object to its symmetric orientation, has to be applied
to the object before symmetry can be calculated. Such a rotation makes an orientation normalization. In mechanics, there
is an inertia-tensor-based rotation that can rotate an object to its principal axis so that around the axis the object will
rotate with minimum inertia (Jáhne, 1995). This approach borrows the inertia-tensor concept and applies it to obtain the
orientation normalization. A flowchart of the edge-based building classification is given in figure 1.
Edges
Generic Geometric Condition Checks
(Size, Height, and Closure)
|
| Orientation Normalization
|
Moments (Symmetry) and
Circularity Computations
Classification on Symmetry & Circularity |
| |
| Straight Segments Extraction | | Right Corners Detection |
| Orthogonality & Parallel Checks
|
Building Edges
Figure 1. A flowchart of the edge-based building classification
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 989
