2026-04-10T16:43:58Z https://ipsj.ixsq.nii.ac.jp/oai

oai:ipsj.ixsq.nii.ac.jp:00231366 2025-01-19T10:43:57Z 6164:6165:6630:11448

Quantitative Evaluation of Local Distortion in Historical Maps by Using the Nabla Operator Quantitative Evaluation of Local Distortion in Historical Maps by Using the Nabla Operator Miura, Takeshi Takeshi, Miura historical map, map distortion, vector analysis, nabla operator It is well known that geometric local distortion is often seen in historical maps. To quantitatively evaluate the tendency of the above distortion, a method in which a historical map is transformed by the Euclidean regression to fit its size, direction and location to those of a present map is often used. In the above method, the historical map is moved so that the centroid of its control points coincides with that of the present map. However, there is actually no guarantee that the centroid position of the fitted historical map necessarily coincides with that of the present map. In this study, a new method to evaluate the local distortion of historical maps is proposed. It spatially uniformly detects local distortions, irrespective of whether the detected point is close to the centroid or not. Specifically, the distribution of point-position differences between the historical and present maps is regarded as a vector field, and the nabla operator known as a vector differential operator is applied to the field. As a result, the divergence and rotation of local distortions are extracted. The experimental results show the effectiveness of the proposed method. It is well known that geometric local distortion is often seen in historical maps. To quantitatively evaluate the tendency of the above distortion, a method in which a historical map is transformed by the Euclidean regression to fit its size, direction and location to those of a present map is often used. In the above method, the historical map is moved so that the centroid of its control points coincides with that of the present map. However, there is actually no guarantee that the centroid position of the fitted historical map necessarily coincides with that of the present map. In this study, a new method to evaluate the local distortion of historical maps is proposed. It spatially uniformly detects local distortions, irrespective of whether the detected point is close to the centroid or not. Specifically, the distribution of point-position differences between the historical and present maps is regarded as a vector field, and the nabla operator known as a vector differential operator is applied to the field. As a result, the divergence and rotation of local distortions are extracted. The experimental results show the effectiveness of the proposed method. 情報処理学会 2023-12-02 eng conference paper https://ipsj.ixsq.nii.ac.jp/records/231366 じんもんこん2023論文集 2023 219 224 https://ipsj.ixsq.nii.ac.jp/record/231366/files/IPSJ-CH2023031.pdf application/pdf 2.1 MB 2025-12-02