High Quality Compatible Triangulations with Inconsistent Rotation and Shape Self-occlusion Enhancement for Planar Shape Morphing


Student thesis: Doctoral Thesis

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  • Zhiguang LIU

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Award date7 Sept 2016


Planar shape morphing, also known as metamorphosis or shape blending, is the gradual transformation of one shape into another. Shape morphing techniques have been used widely in animation and special effects packages, such as Adobe After Effects and HTML5. With these morphing methods, we can transform a human to a bird or some other objects that people may never experience in real life. Thus, we want to build an interactive system that blends the human silhouette and other shapes such that the users can see these interesting transformations. To build such a system, (1) we need to employ compatible triangulation method to compute the correspondence between two shapes. (2) we need to apply shape interpolation method to transform one shape to another. (3) we need to use posture reconstruction method to address the transformation that involves self-occlusion.
Computing compatible triangulation can build the one-to-one correspondence between both the boundary and interior of two shapes. In this thesis, we propose a new method to compute compatible triangulation of two polygons in order to create a smooth geometric transformation between them. Compared with existing methods, our approach creates triangulations of better quality, that is, triangulations with fewer long thin triangles and Steiner points. This results in visually appealing morphing when transforming the shape from one to another. Our method consists of three stages. First, we use the common valid vertex pair to uniquely decompose the source and target polygons into pairs of sub-polygon, in which each concave sub-polygon is triangulated. Second, within each sub-polygon pair, we map the triangulation of a concave sub-polygon onto the corresponding sub-polygon using linear transformation, thereby generating the compatible meshes between the source and the target. Third, we refine the compatible meshes, which can create better quality planar shape morphing with detailed textures.
Shape interpolation algorithms determine the path that transforms the source shape into the target one. Traditional image space interpolation methods use different features, points or line segments for example, to discretize the image. To achieve realistic morphing results, users need to carefully draw the corresponding features on both the source and target images. Previous work has shown that rigid shape interpolation methods can maximize the rigidity of a blended shape, which results in sensible transformations. However, the rigid shape interpolation approaches will suffer from inconsistent rotations whenever the rotation is more than π. We offer an efficient algorithm that gives a unique rotation assignment with minimum rotation angle. We create a graph with each original rotation angle as one vertex of the graph. During the searching process, we fix any jump that is larger than π by adding or subtracting multiple 2π. All the correct rotations in the thesis are generated by this efficient scheme.
It is still challenging to accurately recognize postures from a single depth camera due to the inherently noisy data derived from depth images and self-occluding action performed by the user. In this thesis, we propose a new real-time probabilistic framework to enhance the accuracy of live captured postures that belong to one of the action classes in the database. We adopt the Gaussian Process model as a prior to leverage the position data obtained from Kinect and marker-based motion capture system. We also incorporate a temporal consistency term into the optimization framework to constrain the velocity variations between successive frames. To ensure that the reconstructed posture resembles the accurate parts of the observed posture, we embed a set of joint reliability measurements into the optimization framework. A major drawback of Gaussian Process is its cubic learning complexity when dealing with a large database due to the inverse of a covariance matrix. To solve the problem, we propose a new method based on a local mixture of Gaussian Processes, in which Gaussian Processes are defined in local regions of the state space. Due to the significantly decreased sample size in each local Gaussian Process, the learning time is greatly reduced. At the same time, the prediction speed is enhanced as the weighted mean prediction for a given sample is determined by the nearby local models only. Our system also allows incrementally updating a specific local Gaussian Process in real time, which enhances the likelihood of adapting to run-time postures that are different from those in the database.
Experimental results show that our method can create compatible meshes of higher quality compared with existing methods, which facilitates smoother morphing process. The proposed algorithm is robust and computationally efficient. Our posture reconstruction system can generate high quality postures even under severe self-occlusion situations. Our system can be applied to produce convincing transformations such as interactive 2D animation creation and special effects in movies.