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## Introduction

In composing hand-drawn 3D urban maps, the most common design problem is to avoid overlaps between geographic features such as roads and buildings by displacing them consistently over the map domain. Nonetheless, automating this map design process is still a challenging task because we have to maximally retain the 3D depth perception inherent in pairs of parallel lines embedded in the original layout of such geographic features. This paper presents a novel approach to disoccluding important geographic features when creating 3D urban maps for enhancing their visual readability. This is accomplished by formulating the design criteria as a constrained optimization problem based on the linear programming approach. Our mathematical formulation allows us to systematically eliminate occlusions of landmark roads and buildings, and further controls the degree of local 3D map deformation by devising an objective function to be minimized. Various design examples together with a user study are presented to demonstrate the robustness and feasibility of the proposed approach.

## Constraints

There are five design criteria decided to be employed for improving the map readability, including Fixed orientation (Figure 1(a)), Relative position (Figure 1(b)), Scale limits (Figure 1(c)), Minimum displacement (Figure 1(d)), and Occlusion avoidance (Figure 1(e)),

Figure 1: Five design criteria.

Note that the first three criteria are employed for keeping the con- sistency in the arrangement of geographic features and formulated as hard constraints, while the last two are introduced as soft constraints for enhancing the reality and readability of 3D urban maps, respectively.

## Result

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Result 1: Side-by-side comparison between an ordinary perspective view (left) and its optimally distorted version with our approach (right). Note that we can successfully avoid the occlusions of important route to the destination (drawn in orange) while accentuating the 3D appearance of the landmark buildings. (Kikuna, Yokohama, Japan.)

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Result 2: A complicated 3D urban environment where a sharply curved route is disoccluded. An ordinary perspective image (left) and its optimized version (right). (Suwazaka, Yokohama, Japan.)

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Result 3: An optimized layout of a 3D urban map where all the routes are selected as landmarks. An ordinary perspective image (left) and its optimized version (right). (Nishi-Kamata, Tokyo, Japan.)

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Result 4: An optimized layout of a 3D urban map while landmark buildings are emphasized. An ordinary perspective image (left) and its optimized version (right). (Okurayama, Yokohama, Japan.)

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Result 5: Additional space for annotating roads has been introduced into a 3D urban map. An ordinary perspective image (left) and its optimized version (right). Note that we set Wr = 50 in this case. (Endo-machi, Kawasaki, Japan.)

## Paper

Daichi Hirono, Hsiang-Yun Wu, Masatoshi Arikawa and Shigeo Takahashi, Constrained Optimization for Disoccluding Geographic Landmarks in 3D Urban Maps, in Proceedings of the 6th IEEE Pacific Visualization Symposium (PacificVis 2013), pp. 17-24, 2013. Paper-preprint (PDF, 12.3MB) Video (MOV, 40.5MB)

## Acknowledgments

3D urban models of Japan provided by ZENRIN CO., LTD and digital road map databases of Japan provided by Sumitomo Electric Industries, Ltd are used as the joint research (No. 398) using spatial data provided by Center for Spatial Information Science, the University of Tokyo. This work has been partially supported by JSPS under Grants-in-Aid for Scientific Research (B) No. 24330033.