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基於單影像之六自由度物體姿態估測

為了解決3D vector graph的問題，作者洪金利 這樣論述：

Dealing with the object pose estimation from a single RGB image is very challenging since 6 degree-of-freedom (6DoF) parameters have to be predicted without using the spatial depth information. Since direct regression of the pose parameters by using the deep neural network was reportedly poor and t

hen attaching with the refinement module to improve the accuracy causes much time consumption, in this work, we propose several techniques of top-down or bottom-up approaches to predict indirect feature maps instead from which single or multiple object poses can be recovered by using sophisticated p

ost-processing algorithms.Since there are four possible scenarios where single/multiple objects in the same/different classes can appear in the image, the corresponding output feature maps are predicted differently. For a single object scenario, unit-vector fields are predicted. These features are c

omposed of many unit-vectors pointing from pixels within the object mask to the pre-defined 2D object keypoints where their corresponding 3D object keypoints are distributed optimally on the 3D object surface based on the keypoint distances and object surface curvatures. From some pairs of the predi

cted unit-vectors, 2D projected keypoints can be voted and determined, so that PnP algorithm can be applied to estimate the pose. To deal with multiple objects even in the same or different classes, sufficient and informative output feature maps need to be predicted. Different from object keypoints,

6D coordinate maps which form the main features can be considered as a bunch of 3D point clouds for pose parameter calculation when their 2D-3D correspondences are also established. 6D coordinate maps contains two parts: front- and rear-view 3D coordinate maps. 3D coordinate map is actually a 2D ma

p where each pixel records 3D coordinates of a point in the object CAD model which projects to that 2D pixel location. Via 3D/6D coordinate maps, instance 2D-3D correspondences of a large point set can be built and PnP algorithm combined with RANSAC scheme to overcome the outliers or noise can be us

ed to estimate multiple object poses. Even though in this case, 2D object keypoints can no longer be used to estimate multiple poses, they can be defined as single/multiple reference points for identifying all object instance masks even in the presence of heavy occlusion. We are also interested in o

vercoming some problems related to the missing information and symmetry ambiguity encountered when generating the ground truth of 6D coordinate maps.Our studies show that our single pose estimation method using unit-vector fields can achieve an outstanding accuracy if compared to other top-down stat

e-of-the-art methods without including refinement modules. It has a good algorithm to identify the designated object keypoints from which the predicted feature maps are trained with the effective loss functions, but it has a slower inference speed when multiple object poses are taken into considerat

ion. On the other hand, our 6D coordinate maps, combining with the information from two opposite views, are capable of providing more constraints for network optimization and hence helpful for pose estimation accuracy. Our methods using 6D coordinate maps can achieve great performances if compared t

o other multiple object pose estimation methods.

數學形態學導出多參數持續同調之層狀結構

為了解決3D vector graph的問題，作者胡全燊 這樣論述：

Topological Data Analysis (TDA), a fast-growing research topic in applied topology, uses techniques in algebraic topology to capture features from data. Its importance has been discovered in many areas, such as medical image processing, molecular biology, machine learning, and pattern recognition.

Persistent homology (PH) is vital in topological data analysis that detects local changes in filtered topological spaces. It measures the robustness and significance of homological objects in spaces' deformation, such as connected components, loops, or higher dimensional voids. In Morse theory, filt

ered spaces for persistent homology usually rely on a single parameter, such as the sublevel set filtration of height functions. Recently, as a generalization of persistent homology, computational topologists began to be interested in multi-parameter persistent homology. Multi-parameter persistent h

omology (or multi-parameter persistence) is an algebraic structure established on a multi-parametrized network of topological spaces and has more fruitful geometric information than persistent homology. So far, finding methods to extract features in multi-parameter persistence is still an open and

concentrating topic in TDA. Also, examples of multi-parameter filtration are still rare and limited. The three principal contributions of this dissertation are as follows. First, we combined persistent homology features (persistence statistics and persistence curves) and machine learning models for

analyzing medical images. We found that adding topological information into machine learning models can improve recognition accuracy and stability. Second, unlike traditional construction for multi-parameter filtrations in Euclidean spaces, we propose a framework for constructing multi-parameter fi

ltrations from digital images through mathematical morphology and discrete geometry. Multi-parameter persistence derived from mathematical morphology is more efficient for computing and contains intuitive geometric attributes of objects, such as the sizes or robustness of local objects in digital im

ages. We involve these features to remove the salt and pepper noise in digital images as an application. Compared with current denoise algorithms, the proposed approach has a more stable accuracy and keeps the topological structures of original data. The third part of this dissertation focuses on us

ing sheaf theory to analyze the lifespans of objects in multi-parameter persistence. The multi-parameter persistence has a natural sheaf structure by equipping the Alexandrov topology on the based partially ordered set. This sheaf structure uncovers the gluing properties of local image regions in th

e multi-parameter filtration. We referred to these properties as a fingerprint of the filtration and applied them for the character recognition task. Finally, we propose using sheaf operators to define ultrametric norms on local spaces in multi-parameter persistence. Like persistence barcodes, this

metric provides finer geometric and topological quantities.