clDice -- a Novel Topology-Preserving Loss Function for Tubular Structure Segmentation

Accurate segmentation of tubular, network-like structures, such as vessels, neurons, or roads, is relevant to many fields of research. For such structures, the topology is their most important characteristic; particularly preserving connectedness: in the case of vascular networks, missing a connected vessel entirely alters the blood-flow dynamics. We introduce a novel similarity measure termed centerlineDice (short clDice), which is calculated on the intersection of the segmentation masks and their (morphological) skeleta. We theoretically prove that clDice guarantees topology preservation up to homotopy equivalence for binary 2D and 3D segmentation. Extending this, we propose a computationally efficient, differentiable loss function (soft-clDice) for training arbitrary neural segmentation networks. We benchmark the soft-clDice loss on five public datasets, including vessels, roads and neurons (2D and 3D). Training on soft-clDice leads to segmentation with more accurate connectivity information, higher graph similarity, and better volumetric scores.Comment: * The authors Suprosanna Shit and Johannes C. Paetzold contributed equally to the wor

4D Match Trees for Non-rigid Surface Alignment

This paper presents a method for dense 4D temporal alignment of partial reconstructions of non-rigid surfaces observed from single or multiple moving cameras of complex scenes. 4D Match Trees are introduced for robust global alignment of non-rigid shape based on the similarity between images across sequences and views. Wide-timeframe sparse correspondence between arbitrary pairs of images is established using a segmentation-based feature detector (SFD) which is demonstrated to give improved matching of non-rigid shape. Sparse SFD correspondence allows the similarity between any pair of image frames to be estimated for moving cameras and multiple views. This enables the 4D Match Tree to be constructed which minimises the observed change in non-rigid shape for global alignment across all images. Dense 4D temporal correspondence across all frames is then estimated by traversing the 4D Match tree using optical flow initialised from the sparse feature matches. The approach is evaluated on single and multiple view images sequences for alignment of partial surface reconstructions of dynamic objects in complex indoor and outdoor scenes to obtain a temporally consistent 4D representation. Comparison to previous 2D and 3D scene flow demonstrates that 4D Match Trees achieve reduced errors due to drift and improved robustness to large non-rigid deformations

Mathematical Imaging and Surface Processing

Within the last decade image and geometry processing have become increasingly rigorous with solid foundations in mathematics. Both areas are research fields at the intersection of different mathematical disciplines, ranging from geometry and calculus of variations to PDE analysis and numerical analysis. The workshop brought together scientists from all these areas and a fruitful interplay took place. There was a lively exchange of ideas between geometry and image processing applications areas, characterized in a number of ways in this workshop. For example, optimal transport, first applied in computer vision is now used to define a distance measure between 3d shapes, spectral analysis as a tool in image processing can be applied in surface classification and matching, and so on. We have also seen the use of Riemannian geometry as a powerful tool to improve the analysis of multivalued images. This volume collects the abstracts for all the presentations covering this wide spectrum of tools and application domains

Data-driven 3D Reconstruction and View Synthesis of Dynamic Scene Elements

Our world is filled with living beings and other dynamic elements. It is important to record dynamic things and events for the sake of education, archeology, and culture inheritance. From vintage to modern times, people have recorded dynamic scene elements in different ways, from sequences of cave paintings to frames of motion pictures. This thesis focuses on two key computer vision techniques by which dynamic element representation moves beyond video capture: towards 3D reconstruction and view synthesis. Although previous methods on these two aspects have been adopted to model and represent static scene elements, dynamic scene elements present unique and difficult challenges for the tasks. This thesis focuses on three types of dynamic scene elements, namely 1) dynamic texture with static shape, 2) dynamic shapes with static texture, and 3) dynamic illumination of static scenes. Two research aspects will be explored to represent and visualize them: dynamic 3D reconstruction and dynamic view synthesis. Dynamic 3D reconstruction aims to recover the 3D geometry of dynamic objects and, by modeling the objects’ movements, bring 3D reconstructions to life. Dynamic view synthesis, on the other hand, summarizes or predicts the dynamic appearance change of dynamic objects – for example, the daytime-to-nighttime illumination of a building or the future movements of a rigid body. We first target the problem of reconstructing dynamic textures of objects that have (approximately) fixed 3D shape but time-varying appearance. Examples of such objects include waterfalls, fountains, and electronic billboards. Since the appearance of dynamic-textured objects can be random and complicated, estimating the 3D geometry of these objects from 2D images/video requires novel tools beyond the appearance-based point correspondence methods of traditional 3D computer vision. To perform this 3D reconstruction, we introduce a method that simultaneously 1) segments dynamically textured scene objects in the input images and 2) reconstructs the 3D geometry of the entire scene, assuming a static 3D shape for the dynamically textured objects. Compared to dynamic textures, the appearance change of dynamic shapes is due to physically defined motions like rigid body movements. In these cases, assumptions can be made about the object’s motion constraints in order to identify corresponding points on the object at different timepoints. For example, two points on a rigid object have constant distance between them in the 3D space, no matter how the object moves. Based on this assumption of local rigidity, we propose a robust method to correctly identify point correspondences of two images viewing the same moving object from different viewpoints and at different times. Dense 3D geometry could be obtained from the computed point correspondences. We apply this method on unsynchronized video streams, and observe that the number of inlier correspondences found by this method can be used as indicator for frame alignment among the different streams. To model dynamic scene appearance caused by illumination changes, we propose a framework to find a sequence of images that have similar geometric composition as a single reference image and also show a smooth transition in illumination throughout the day. These images could be registered to visualize patterns of illumination change from a single viewpoint. The final topic of this thesis involves predicting the movements of dynamic shapes in the image domain. Towards this end, we propose deep neural network architectures to predict future views of dynamic motions, such as rigid body movements and flowers blooming. Instead of predicting image pixels from the network, my methods predict pixel offsets and iteratively synthesize future views.Doctor of Philosoph