Improving quality of knee segmentation by 3D shape matching using deep functional maps

• Κύριος συγγραφέας: Φίλιπ, Κωνσταντίνος-Ειρηναίος
• Άλλοι συγγραφείς: Μουστάκας, Κωνσταντίνος
• Μορφή: Thesis
• Γλώσσα: English
• Έκδοση: 2019
• Θέματα: Deep functional maps; 3D shape matching; Knee modeling; Statistical shape models; Γεωμετρικά σχήματα; Προσομοίωση γονάτου; Μοντέλα πολλαπλών σχημάτων; 616.707 5

The reconstruction of geometric shapes plays an important role in many biomedical applications. A characteristic example is the patient-specific, computer-aided intervention and treatment, which requires the generation of explicitly represented geometric models of anatomical structures depicted in medical images. In the past few decades, there has been a lot of effort to automate the procedure of geometric model construction, since the manual segmentation of 3D images can be timeconsuming and irreproducible. However, most automatic segmentation algorithms are inherently sensitive to image artifacts and noise, resulting in invalid geometric representations. The fundamental hypothesis, pursued in this thesis, is that the aforementioned problems can be resolved by incorporating the a-priori knowledge of the shape of biological structures. The basic idea is to capture the essential variations contained in a given population of a certain class of geometric objects through Statistical Shape Models (SSMs), and restrict the result of a reconstruction algorithm to the space spanned by them. We extend the discussion to the construction of multiple - shape models, in which the relationship between the neighboring anatomical components is described through Canonical Correlation Analysis. A fundamental prerequisite for performing statistical shape analysis on a set of objects is the identification of corresponding points on their associated surfaces. In this thesis, we address the correspondence problem using the recently proposed Functional Maps framework, which is a generalization of the notion of point-to-point shape correspondence, describing how mappings act on real-valued functions defined on shapes. Additionally, we show that, by incorporating techniques from the deep learning theory into the Functional Maps framework, we can further enhance the ability of SSMs to better capture the shape variations within the given dataset. We present the applicability of our methods on real 3D medical data of the human knee. In particular, we construct 3D models of the knee complex that can be transferred across any image modality, and demonstrate their application for improving the quality of automated segmentation methods and conducting inference about missing shapes.