Building outlines have many applications. However, owing to the diversity of buildings and the complexity of the surrounding environment, automatic extraction of building outlines from remote sensing data remains challenging. This paper presents a novel approach for extracting building outlines from digital surface models (DSM) and orthophotographs. The DSM provides initial contour lines, while the orthophotograph indicates where vegetation is obstructing the building outline. The approach introduces two key algorithms: Distance-Constrained Clustering (DCC), to cluster contour lines, and Gradient-based Optimal Contour Selection (G-OCS), to select building outlines. Vegetation information is used to recover obstructed building outlines and improve outline accuracy and completeness. Experimental results, using the International Society for Photogrammetry and Remote Sensing (ISPRS) Vaihingen benchmark dataset, demonstrate the method’s performance (quality metric: 85.0% for individual regions, 73.6% for individual objects, and 99.1% for objects >50 m). Validation using a dataset from Shandong Province (China) confirmed the method’s robustness and applicability for complex urban environments. The approach effectively handles challenges such as interference from vegetation and irregular building structures, outperforming techniques such as WHUZ, CNN/8F+, and HD-Net. This novel method automates building outline extraction and provides useful building information, with applications in urban planning, disaster management, and smart city development.

Neural network capability in symbolic computation has emerged in much recent work. However, symbolic computation is always treated as an end-to-end blackbox prediction task, where human-like symbolic deductive logic is missing. In this paper, we argue that any complex symbolic computation can be broken down to a sequence of finite Fundamental Computation Transformations (FCT), which are grounded as certain mathematical expression computation transformations. The entire computation sequence represents a full human understandable symbolic deduction process. Instead of studying on different end-to-end neural network applications, this paper focuses on approximating FCT which further build up symbolic deductive logic. To better mimic symbolic computations with math expression transformations, we propose a novel tree representation learning architecture GATE (Graph Aggregation Transformer Encoder) for math expressions. We generate a large-scale math expression transformation dataset for training purpose and collect a real-world dataset for validation. Experiments demonstrate the feasibility of producing step-by-step human-like symbolic deduction sequences with the proposed approach, which outperforms other neural network approaches and heuristic approaches.