Browsing by Author "Amirkhanov, Aleksandr"

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    ManyLands: A Journey Across 4D Phase Space of Trajectories
    (The Eurographics Association and John Wiley & Sons Ltd., 2019) Amirkhanov, Aleksandr; Kosiuk, Ilona; Szmolyan, Peter; Amirkhanov, Artem; Mistelbauer, Gabriel; Gröller, Eduard; Raidou, Renata Georgia; Lee, Jehee and Theobalt, Christian and Wetzstein, Gordon
    Mathematical models of ordinary differential equations are used to describe and understand biological phenomena. These models are dynamical systems that often describe the time evolution of more than three variables, i.e., their dynamics take place in a multi-dimensional space, called the phase space. Currently, mathematical domain scientists use plots of typical trajectories in the phase space to analyze the qualitative behavior of dynamical systems. These plots are called phase portraits and they perform well for 2D and 3D dynamical systems. However, for 4D, the visual exploration of trajectories becomes challenging, as simple subspace juxtaposition is not sufficient. We propose ManyLands to support mathematical domain scientists in analyzing 4D models of biological systems. By describing the subspaces as Lands, we accompany domain scientists along a continuous journey through 4D HyperLand, 3D SpaceLand, and 2D FlatLand, using seamless transitions. The Lands are also linked to 1D TimeLines. We offer an additional dissected view of trajectories that relies on small-multiple compass-alike pictograms for easy navigation across subspaces and trajectory segments of interest. We show three use cases of 4D dynamical systems from cell biology and biochemistry. An informal evaluation with mathematical experts confirmed that ManyLands helps them to visualize and analyze complex 4D dynamics, while facilitating mathematical experiments and simulations.
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    Smoke Surfaces of 4D Biological Dynamical Systems
    (The Eurographics Association, 2023) Schindler, Marwin; Amirkhanov, Aleksandr; Raidou, Renata Georgia; Hansen, Christian; Procter, James; Renata G. Raidou; Jönsson, Daniel; Höllt, Thomas
    To study biological phenomena, mathematical biologists often employ modeling with ordinary differential equations. A system of ordinary differential equations that describes the state of a phenomenon as a moving point in space across time is known as a dynamical system. This moving point emerges from the initial condition of the system and is referred to as a trajectory that ''lives'' in phase space, i.e., a space that defines all possible states of the system. In our previous work, we proposed Many- Lands [AKS*19]-an approach to explore and analyze typical trajectories of 4D dynamical systems, using smooth, animated transitions to navigate through phase space. However, in ManyLands the comparison of multiple trajectories emerging from different initial conditions does not scale well, due to overdrawing that clutters the view. We extend ManyLands to support the comparative visualization of multiple trajectories of a 4D dynamical system, making use of smoke surfaces. In this way, the sensitivity of the dynamical system to its initialization can be investigated. The 4D smoke surfaces can be further projected onto lower-dimensional subspaces (3D and 2D) with seamless animated transitions. We showcase the capabilities of our approach using two 4D dynamical systems from biology [Gol11, KJS06] and a 4D dynamical system exhibiting chaotic behavior [Bou15].
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    Visual Analytics in Dental Aesthetics
    (The Eurographics Association and John Wiley & Sons Ltd., 2020) Amirkhanov, Aleksandr; Bernhard, Matthias; Karimov, Alexey; Stiller, Sabine; Geier, Andreas; Gröller, Eduard; Mistelbauer, Gabriel; Eisemann, Elmar and Jacobson, Alec and Zhang, Fang-Lue
    Dental healthcare increasingly employs computer-aided design software, to provide patients with high-quality dental prosthetic devices. In modern dental reconstruction, dental technicians address the unique anatomy of each patient individually, by capturing the dental impression and measuring the mandibular movements. Subsequently, dental technicians design a custom denture that fits the patient from a functional point of view. The current workflow does not include a systematic analysis of aesthetics, and dental technicians rely only on an aesthetically pleasing mock-up that they discuss with the patient, and on their experience. Therefore, the final denture aesthetics remain unknown until the dental technicians incorporate the denture into the patient. In this work, we present a solution that integrates aesthetics analysis into the functional workflow of dental technicians. Our solution uses a video recording of the patient, to preview the denture design at any stage of the denture design process. We present a teeth pose estimation technique that enables denture preview and a set of linked visualizations that support dental technicians in the aesthetic design of dentures. These visualizations assist dental technicians in choosing the most aesthetically fitting preset from a library of dentures, in identifying the suitable denture size, and in adjusting the denture position. We demonstrate the utility of our system with four use cases, explored by a dental technician. Also, we performed a quantitative evaluation for teeth pose estimation, and an informal usability evaluation, with positive outcomes concerning the integration of aesthetics analysis into the functional workflow.
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    WithTeeth: Denture Preview in Augmented Reality
    (The Eurographics Association, 2018) Amirkhanov, Aleksandr; Amirkhanov, Artem; Bernhard, Matthias; Toth, Zsolt; Stiller, Sabine; Geier, Andreas; Gröller, Eduard; Mistelbauer, Gabriel; Beck, Fabian and Dachsbacher, Carsten and Sadlo, Filip
    Dentures are prosthetic devices replacing missing or damaged teeth, often used for dental reconstruction. Dental reconstruction improves the functional state and aesthetic appearance of teeth. State-of-the-art methods used by dental technicians typically do not include the aesthetic analysis, which often leads to unsatisfactory results for patients. In this paper, we present a virtual mirror approach for a dental treatment preview in augmented reality. Different denture presets are visually evaluated and compared by switching them on the fly. Our main goals are to provide a virtual dental treatment preview to facilitate early feedback, and hence to build the confidence and trust of patients in the outcome. The workflow of our algorithm is as follows. First, the face is detected and 2D facial landmarks are extracted. Then, 3D pose estimation of upper and lower jaws is performed and high-quality 3D models of the upper and lower dentures are fitted. The fitting uses the occlusal plane angle as determined mnually by dental technicians. To provide a realistic impression of the virtual teeth, the dentures are rendered with motion blur. We demonstrate the robustness and visual quality of our approach by comparing the results of a webcam to a DSLR camera under natural, as well as controlled lighting conditions.