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We study how to optimize the latent space of neural shape generators that map latent codes to 3D deformable shapes. The key focus is to look at a deformable shape generator from a differential geometry perspective. We define a Riemannian metric based on as-rigid-as-possible and as-conformal-as-possible deformation energies. Under this metric, we study two desired properties of the latent space: 1) straight-line interpolations in latent codes follow geodesic curves; 2) latent codes disentangle pose and shape variations at different scales. Strictly enforcing the geometric interpolation property, however, only applies if the metric matrix is a constant. We show how to achieve this property approximately by enforcing that geodesic interpolations are axis-aligned, i.e., interpolations along coordinate axis follow geodesic curves. In addition, we introduce a novel approach that decouples pose and shape variations via generalized eigendecomposition. We also study efficient regularization terms for learning deformable shape generators, e.g., that promote smooth interpolations. Experimental results on benchmark datasets show that our approach leads to interpretable latent codes, improves the generalizability of synthetic shapes, and enhances performance in geodesic interpolation and geodesic shooting.
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Abstract Contemporary approaches to instance segmentation in cell science use 2D or 3D convolutional networks depending on the experiment and data structures. However, limitations in microscopy systems or efforts to prevent phototoxicity commonly require recording sub-optimally sampled data that greatly reduces the utility of such 3D data, especially in crowded sample space with significant axial overlap between objects. In such regimes, 2D segmentations are both more reliable for cell morphology and easier to annotate. In this work, we propose the projection enhancement network (PEN), a novel convolutional module which processes the sub-sampled 3D data and produces a 2D RGB semantic compression, and is trained in conjunction with an instance segmentation network of choice to produce 2D segmentations. Our approach combines augmentation to increase cell density using a low-density cell image dataset to train PEN, and curated datasets to evaluate PEN. We show that with PEN, the learned semantic representation in CellPose encodes depth and greatly improves segmentation performance in comparison to maximum intensity projection images as input, but does not similarly aid segmentation in region-based networks like Mask-RCNN. Finally, we dissect the segmentation strength against cell density of PEN with CellPose on disseminated cells from side-by-side spheroids. We present PEN as a data-driven solution to form compressed representations of 3D data that improve 2D segmentations from instance segmentation networks.