Interactive visualization tools for topological exploration

Thesis (Ph.D.) - Indiana University, Computer Science, 1992This thesis concerns using computer graphics methods to visualize mathematical objects. Abstract mathematical concepts are extremely difficult to visualize, particularly when higher dimensions are involved; I therefore concentrate on subject areas such as the topology and geometry of four dimensions which provide a very challenging domain for visualization techniques. In the first stage of this research, I applied existing three-dimensional computer graphics techniques to visualize projected four-dimensional mathematical objects in an interactive manner. I carried out experiments with direct object manipulation and constraint-based interaction and implemented tools for visualizing mathematical transformations. As an application, I applied these techniques to visualizing the conjecture known as Fermat's Last Theorem. Four-dimensional objects would best be perceived through four-dimensional eyes. Even though we do not have four-dimensional eyes, we can use computer graphics techniques to simulate the effect of a virtual four-dimensional camera viewing a scene where four-dimensional objects are being illuminated by four-dimensional light sources. I extended standard three-dimensional lighting and shading methods to work in the fourth dimension. This involved replacing the standard "z-buffer" algorithm by a "w-buffer" algorithm for handling occlusion, and replacing the standard "scan-line" conversion method by a new "scan-plane" conversion method. Furthermore, I implemented a new "thickening" technique that made it possible to illuminate surfaces correctly in four dimensions. Our new techniques generate smoothly shaded, highlighted view-volume images of mathematical objects as they would appear from a four-dimensional viewpoint. These images reveal fascinating structures of mathematical objects that could not be seen with standard 3D computer graphics techniques. As applications, we generated still images and animation sequences for mathematical objects such as the Steiner surface, the four-dimensional torus, and a knotted 2-sphere. The images of surfaces embedded in 4D that have been generated using our methods are unique in the history of mathematical visualization. Finally, I adapted these techniques to visualize volumetric data (3D scalar fields) generated by other scientific applications. Compared to other volume visualization techniques, this method provides a new approach that researchers can use to look at and manipulate certain classes of volume data

Mask-ShadowGAN: Learning to Remove Shadows from Unpaired Data

This paper presents a new method for shadow removal using unpaired data, enabling us to avoid tedious annotations and obtain more diverse training samples. However, directly employing adversarial learning and cycle-consistency constraints is insufficient to learn the underlying relationship between the shadow and shadow-free domains, since the mapping between shadow and shadow-free images is not simply one-to-one. To address the problem, we formulate Mask-ShadowGAN, a new deep framework that automatically learns to produce a shadow mask from the input shadow image and then takes the mask to guide the shadow generation via re-formulated cycle-consistency constraints. Particularly, the framework simultaneously learns to produce shadow masks and learns to remove shadows, to maximize the overall performance. Also, we prepared an unpaired dataset for shadow removal and demonstrated the effectiveness of Mask-ShadowGAN on various experiments, even it was trained on unpaired data.Comment: Accepted to ICCV 201

Domain-incremental Cardiac Image Segmentation with Style-oriented Replay and Domain-sensitive Feature Whitening

Contemporary methods have shown promising results on cardiac image segmentation, but merely in static learning, i.e., optimizing the network once for all, ignoring potential needs for model updating. In real-world scenarios, new data continues to be gathered from multiple institutions over time and new demands keep growing to pursue more satisfying performance. The desired model should incrementally learn from each incoming dataset and progressively update with improved functionality as time goes by. As the datasets sequentially delivered from multiple sites are normally heterogenous with domain discrepancy, each updated model should not catastrophically forget previously learned domains while well generalizing to currently arrived domains or even unseen domains. In medical scenarios, this is particularly challenging as accessing or storing past data is commonly not allowed due to data privacy. To this end, we propose a novel domain-incremental learning framework to recover past domain inputs first and then regularly replay them during model optimization. Particularly, we first present a style-oriented replay module to enable structure-realistic and memory-efficient reproduction of past data, and then incorporate the replayed past data to jointly optimize the model with current data to alleviate catastrophic forgetting. During optimization, we additionally perform domain-sensitive feature whitening to suppress model's dependency on features that are sensitive to domain changes (e.g., domain-distinctive style features) to assist domain-invariant feature exploration and gradually improve the generalization performance of the network. We have extensively evaluated our approach with the M&Ms Dataset in single-domain and compound-domain incremental learning settings with improved performance over other comparison approaches.Comment: Accepted to IEEE Transactions on Medical Imagin