2. Related Works
2.1. Building Simplification Constraints
- Granularity (C2): Building edges needs to be large enough to avoid visual confusion, e.g., 0.3 mm .
- Data correctness (C3): No data error is allowed, e.g., self-intersection .
- Shape (C4): The building shape needs to be maintained, e.g., orthogonal features .
- Size (C5): The building area needs to be maintained .
- Orientation (C6): The main orientation of the building needs to be maintained .
- Position (C7): The simplified building needs to be close to its original position .
2.2. Building Simplification Approaches
- Step 1.
- Perform preprocessing to remove potential abnormal nodes of buildings before applying any simplification operation (Section 3.2.)
- Step 2.
- Violation detection at the next possible scale. Violations are defined based on whether the legibility constraints are violated at the next possible scale (Section 3.3).
- Step 3.
- If RBji violates granularity constraints at the next possible scale, perform a local-structure-based simplification (LS) algorithm (Section 3.4). This algorithm classifies local structures and defines their based operations (Section 3.4.1). Rules considering preservation constraints supporting the application of local-structure-based operation at the current step are provided (Section 3.4.2). A backtracking searching strategy is also provided in case an invalid local-structure-based operation is applied. If a satisfactory result can be obtained with LS algorithm, return to Step 1; otherwise, proceed to Step 4. Whether the result is a satisfactory one is defined based on preservation constraints (Section 3.4.3).
- Step 4.
- If the LS algorithm cannot obtain a satisfactory result, use a template-based simplification (TS) algorithm; then return to Step 1 (Section 3.5).
- Step 5.
- If the minimum size constraint will be violated at the next possible scale, use a building enlargement (BE) algorithm (Section 3.5).
3.2. Step 1: Building Preprocessing
3.3. Step 2: Definitions of Legibility Constraint Violations
3.4. Step 3: Local-Structure-Based Simplification Algorithm
3.4.1. Local Structure Classification and Their Based Operations
3.4.2. Selection of Applied Local-Structure-Based Operation
3.4.3. Evaluation and Backtracking Strategy
- Rule 1: If , then the result obtained by applying qn is evaluated as unsatisfactory.
- Rule 2: If , then the result obtained by applying qn is evaluated as unsatisfactory.
- Rule 3: If , then the result obtained by applying qn is evaluated as unsatisfactory.
- Rule 4: If the building obtained by applying the selected operation pn has fewer than four nodes, then it is evaluated as unsatisfactory.
|Input: Obtained representations of Bi as , available operations for RBji in RBS as ; maximum searching step as MaxS |
Set searching step as p, and
Get Qj: Obtain available operation set Qj based on RBji and start with
When AND AND , Then
Selection: Select an operation qmj in Qj based on the binary decision tree defined in Section 3.4.2 to obtain needs to be determined.
If , remove qmj in Qj, Continue
Else if , Then
Evaluation: Determine whether RBki satisfies rules defined for simplified building:
If evaluation accepted, Then return to RBki, End.
Else if evaluation denied, remove qmj in Qj.
When AND AND , Then
, return to Get Qj
Else Return null, End.
3.5. Steps 4 and 5: Template-Based and Building Enlargement Simplification
- Rule 1: If Bi violates STa at the next possible scale, it is enlarged by replacing it with a rectangle as STL × STW.
- Rule 2: If Bi violates STW at the next possible scale, it is enlarged by replacing it with a rectangle as LBi × STW.
- Rule 3: If Bi violates STL at the next possible scale, it is enlarged by replacing it with a rectangle as WBi × STL.
- Rule 4: If no violation of minimum size constraint is found at the next possible scale, no building enlargement will be performed.
5.2. Possible Use for Continuous Scale Transformation of Buildings
Data Availability Statement
Conflicts of Interest
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|Minimum size (violates STa)|
|Minimum size (violates STL)|
|Minimum size (violates STW)|
|Granularity (violates GTL)|
|ID||Int||Unique building identification code.|
|SType||Int||Denotes type of local structure: 1 = bend, 2 = convex or concave, 3 = offset, 4 = corner.|
|IsInt||Bool||Denotes whether self-intersection is generated after applying qn: true or false.|
|SDame||Bool||Denotes whether orthogonal features are damaged after applying qn: true or false.|
|AreaC||Double||Denotes area change rate by comparing to original after applying qn, as , in which AreaA is the area of original one, AreaS is the area of the obtained building after applying qn.|
|OriC||Double||Denotes main orientation change compared to original after applying qn, as , in which OriC is the MBR orientation of the original one, OriS is the MBR orientation of the obtained building after applying qn.|
|PosC||Double||Denotes displaced distance by comparing to original after applying qn.|
|Scale||Number of Simplified Buildings|
|LS without Backtracking||LS without Backtracking||TS||BE|
|Start scale (1:M)||10,000||11,000||15,333||19,000||14,666||42,000||11,000||56,400|
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