Topology-Preserving Data Augmentation for Ring-Type Polygon Annotations

1. Problem Statement

In computer vision segmentation tasks, particularly in structured domains like architectural floorplan analysis, object regions often contain interior voids (e.g., courtyards, rooms within walls). These "ring-type" regions are frequently encoded as a single cyclic polygon chain where the outer boundary and inner boundary are connected by implicit "bridge" edges to form a continuous traversal order.

The Core Issue:
Standard geometric data augmentation pipelines (rotation, scaling, cropping, flipping) typically assume polygons represent simply connected regions. When these operations are applied:

• Vertex Removal: Clipping or cropping often removes intermediate vertices, including the critical "bridge" vertices that connect the outer and inner boundaries.
• Topological Collapse: The removal of these vertices breaks the cyclic connectivity. A single ring annotation can fragment into two disconnected polygons (one for the outer boundary, one for the inner), destroying the semantic meaning of the region.
• Detection Difficulty: This failure is often invisible at the pixel level (the mask may still look correct) but catastrophic at the annotation level, leading to inconsistent training data and flawed downstream geometric reasoning.

2. Methodology

The authors propose a lightweight, order-preserving connectivity repair strategy that operates in three main stages:

A. Mask-Based Geometric Augmentation

Instead of directly transforming polygon vertices (which risks breaking connectivity if vertices fall outside the image), the method:

1. Rasterizes the original polygon $P$ into a binary mask $M$.
2. Applies geometric transformations (rotation, crop, scale, etc.) to the mask to generate $M' = T(M)$.
3. Extracts the new boundary from $M'$.

B. Vertex Projection and Index Preservation

1. The original polygon vertices are associated with their original traversal indices ($1$ to $n$).
2. Surviving vertices from the transformed mask are projected back into index space.
3. If a vertex is clipped out, it is discarded, but its index is noted as missing. The remaining vertices retain their original indices to preserve the original traversal order.

C. Order-Preserving Connectivity Repair

This is the core innovation. The algorithm enforces successor consistency among the surviving vertices:

• Let $J = (k_1, k_2, \dots, k_m)$ be the sorted indices of surviving vertices.
• The algorithm checks if the successor relation holds: $k_{t+1} = (k_t \mod n) + 1$.
• Gap Repair: If a gap is detected (i.e., intermediate vertices were removed), the algorithm reconnects the surviving vertices by creating a directed edge between the current vertex and its next surviving neighbor in the sequence.
• This effectively "jumps" over the missing vertices, restoring the cyclic chain without needing to re-detect contours or introduce new, dense vertices.

Algorithm Complexity: The repair process runs in $O(m)$ time (where $m$ is the number of surviving vertices), introducing negligible computational overhead compared to standard augmentation.

3. Key Contributions

1. Identification of a Specific Failure Mode: The paper highlights a critical, often overlooked issue where standard augmentation breaks the topological integrity of ring-type polygon annotations (single-chain encodings with holes).
2. Index-Space Repair Mechanism: A novel method to restore cyclic adjacency by projecting surviving vertices back into their original index space and reconnecting them based on traversal order, rather than relying on pixel-level contour re-extraction.
3. Cyclic Adjacency Preservation (CAP) Metric: A new evaluation metric designed specifically to measure the structural integrity of polygon connectivity. Unlike mIoU (which measures spatial overlap), CAP measures whether the topological relationships between vertices are preserved after augmentation.
4. Integration Compatibility: The method is lightweight and designed to integrate seamlessly into existing pipelines (e.g., Albumentations, YOLO training loops) without requiring complex re-training or heavy computation.

4. Experimental Results

The authors evaluated their method against standard baselines (YOLOv11 pipeline, Roboflow) on architectural floorplan datasets.

• Cyclic Adjacency Preservation (CAP):
  • Baselines: YOLOv11 achieved a CAP of 0.3278, and Roboflow achieved 0.5497. This indicates that standard pipelines frequently break ring topology (often <50% of annotations remain topologically correct).
  • Proposed Method: Achieved a CAP of 0.9758 (near-perfect preservation) across various transformations, including rotation, cropping, scaling, and compound transformations.
• Qualitative Analysis:
  • Baselines often resulted in fragmented masks (outer and inner boundaries separated) or inflated polygons with excessive, redundant vertices due to raster-to-vector re-extraction.
  • The proposed method successfully maintained the single closed cyclic chain, preserving the bridge connections between boundaries.
• Impact on Segmentation Performance:
  • Training segmentation models (YOLOv11-Seg and Mask R-CNN) with topology-preserving data resulted in higher mean Intersection over Union (mIoU).
  • YOLOv11-Seg: Improved from 88.4 (Standard) to 90.8 (Proposed).
  • Mask R-CNN: Improved from 85.2 (Standard) to 87.0 (Proposed).
  • This demonstrates that eliminating structural inconsistencies in annotations allows models to learn geometric boundaries more reliably.

5. Significance

This work addresses a subtle but critical gap in the data augmentation pipeline for polygon-based segmentation. By ensuring that topological consistency is maintained during data augmentation, the method:

• Prevents the generation of "hallucinated" or fragmented training samples that confuse models.
• Is particularly vital for domains like architectural floorplan analysis, map processing, and technical drawing interpretation, where ring structures are common.
• Provides a generalizable principle (index-aware repair) that can be applied to any polygon annotation where vertex ordering encodes structural relationships, not just ring types.
• Offers a practical, low-cost solution that significantly boosts model performance without requiring architectural changes to the segmentation models themselves.

The implementation is open-source as a Python package (polyaug), facilitating immediate adoption in the computer vision community.