Modeling Complex Architectures: Bridging Granular Computing and Ontologies

TL;DR

Reconstituting ancient architectural wonders digitally is often hampered by "noisy" expert rules. This paper presents a sophisticated framework that uses Granular Computing (GrC) and Rough Set Theory to automatically filter redundant and incorrect construction rules. By treating architectural styles as ontology domains, the researchers achieved a near-perfect (99.7%) success rate in generating stylistically accurate models.

Problem & Motivation: The Conflict of Expert Rules

In the realm of procedural modeling, we use L-systems—recursive grammars that define how components like windows, gates, and roofs combine. However, when architects translate their subjective expertise into these rules, they introduce four types of Redundancy:

1. Other-style: Rules belonging to different cultures.
2. Share-redundancy: Overlapping rules between styles.
3. Wrong-rule: Errors that put roofs below columns.
4. Repeating-redundancy: Multiple rules describing the same relationship.

The authors observed that using a raw, experts-provided library for ancient Chinese architecture resulted in over 50% incorrect instances. The core challenge: how do you mathematically distinguish "correct" style rules when the boundaries of style are inherently vague?

Methodology: Indirect Knowledge Manipulation

The authors propose a "manipulating knowledge indirectly" approach. Instead of analyzing the rules in isolation, they analyze the instances those rules produce.

1. The Ontology Structure

Architecture is formalized as $D=⟨W,R,V⟩$:

• $V$ (Vocabulary): Basic components (e.g., bracket sets, beams).
• $W$ (Workplace): The set of all valid architectural instances.
• $R$ (Relations): The SBNS (Sequence Binary Neighborhood System) defining correct combinations.

2. Roughness Function and Monotonicity

To find the optimal rule set $P^{\ast }$, the authors utilize the Upper and Lower Approximations from Rough Set Theory. They define a Roughness Function: $E_{P_D}={\chi }_{N{P}_D}-{\chi }_{P_D}$ Where $\chi$ represents the "vagueness" of the boundary.

The paper proves a Monotonicity Theorem: adding a "correct" rule always increases the value of $E_{P_D}$. This allows them to implement the DKHS (Domain-Knowledge-based Heuristic-Selection) algorithm, which prunes the massive search space of potential rule combinations by following the gradient of this roughness function.

Experiments & Results: Precision in Heritage

The team tested their method against several baselines, including random selection and standard greedy algorithms like QUICKREDUCT (QR).

Above: (a)-(c) show flawed houses from the unselected library; (lower) shows the purified, architecturally sound results from the proposed method.

The results are striking. Not only did the system filter out the "wrong" rules, but it also reduced the rule-count by over 50%, significantly enhancing the performance of the auto-modeling engine.

Critical Insight & Future Outlook

The brilliance of this work lies in its realization that architectural style is a "vague concept" best handled by Granular Computing. By calculating the "roughness" of a rule set relative to a target domain, the system acts as an automated "editor" for expert knowledge.

Limitations: While the system handles "wrong-rule" and "other-style" redundancy effectively, "share-redundancy" (rules common to multiple styles) remains difficult to isolate without larger cross-domain datasets.

As we move toward AI-driven 3D generation, the logic of "indirect knowledge manipulation" via ontologies remains a foundational principle for ensuring that generative models respect structural and historical truth.

Conclusion

This paper transforms subjective architectural "feeling" into a rigorous mathematical search problem. The DKHS algorithm provides a blueprint for any field where expert knowledge is plentiful but messy, offering a way to distill precision from the sea of redundancy.