Fig. 1. Extraction results of building based on the classification verification principle. (a) Original remote sensing image #1; (b) building extraction results by classification of image #1; (c) original remote sensing image #2; (d) building extraction results by classification of image #2

Fig. 2. Polygon fitting contour results using different circumscribed rectangles. (a) Polygon fitting result; (b) minimum-outsourcing rectangle result; (c) minimum-area circumscribed rectangle result; (d) best-fitting circumscribed rectangle result

Fig. 3. Flow chart of preliminary optimization of building outline

Fig. 4. Schematic diagram of building outline. (a) Outline point diagram; (b) Hausdorff distance calculation diagram

Fig. 5. Principle and effect diagram of building contour initial optimization

Fig. 6. Intermediate results of preliminary optimization of building outline in image # 1. (a) Polygon fitting result; (b) best-fitting circumscribed rectangle; (c) contour preliminary optimization results; (d) ground truth contours of buildings

Fig. 7. Diagram of corner regularization. (a) Schematic diagram of the regularization process; (b) optimization flow chart

Fig. 8. Schematic diagram of corner judgment. (a) θ∈T; (b) θ?T

Fig. 9. Results of corner elimination by feature analysis. (a) Corner detection result; (b) result of removing corners after analysis; (c) Shi--Tomasi algorithm deep optimization; (d) ground truth contours of buildings

Fig. 10. Results comparison between initial optimization and deep regularization. (a) Original remote sensing image #3; (b) preliminary optimization result for image #3; (c) deep optimization result for image #3; (d) original remote sensing image #4; (e) preliminary optimization result for image #4; (f) deep optimization result for image #4

Fig. 11. Flow chart of building outline optimization

Fig. 12. Original remote sensing image. (a) Image #5; (b) image #6; (c) image #7; (d) image #8

Fig. 13. Result graphs when the coefficient r is different values. (a) Initial result; (b) r=0.8; (c) r=1.0; (d) r=1.2

Fig. 14. Accuracy line chart when coefficient r is different

Fig. 15. Optimization results of image # 5 under different image extraction methods. (a) Extraction result 1 by BP neural network classification verification method; (b) optimized the contour by our method for extraction result 1; (c) extraction result 2 by offset shadow classification verification method; (d) optimized the contour by our method for extraction result 2

Fig. 16. Optimization results of image # 6 under different image extraction methods. (a) Extraction result 1 by BP neural network classification verification method; (b) optimized the contour by our method for extraction result 1; (c) extraction result 2 by offset shadow classification verification method; (d) optimized the contour by our method for extraction result 2

Fig. 17. Comparison of optimized extraction results of image #7. (a) Image #7; (b) ground truth contour of buildings; (c) extracted initial result by offset shadow verification; (d) optimization result by method in Ref. [13]; (e) reference method optimization result by method in Ref. [26]; (f) contour optimization result of our method

Fig. 18. Comparison of optimized extraction results of image #8. (a) Image #8; (b) ground truth contour of buildings; (c) extracted initial resuls by offset shadow verification; (d) optimization result by method in Ref. [13]; (e) optimization result by method in Ref. [26]; (f) contour optimization result by our method

Fig. 19. Comparison of three optimization methods