Data Augmentation for Leaf Segmentation and Counting Tasks in Rosette Plants

Deep learning techniques involving image processing and data analysis are constantly evolving. Many domains adapt these techniques for object segmentation, instantiation and classification. Recently, agricultural industries adopted those techniques in order to bring automation to farmers around the globe. One analysis procedure required for automatic visual inspection in this domain is leaf count and segmentation. Collecting labeled data from field crops and greenhouses is a complicated task due to the large variety of crops, growth seasons, climate changes, phenotype diversity, and more, especially when specific learning tasks require a large amount of labeled data for training. Data augmentation for training deep neural networks is well established, examples include data synthesis, using generative semi-synthetic models, and applying various kinds of transformations. In this paper we propose a method that preserves the geometric structure of the data objects, thus keeping the physical appearance of the data-set as close as possible to imaged plants in real agricultural scenes. The proposed method provides state of the art results when applied to the standard benchmark in the field, namely, the ongoing Leaf Segmentation Challenge hosted by Computer Vision Problems in Plant Phenotyping.

Deep Eikonal Solvers

A deep learning approach to numerically approximate the solution to the Eikonal equation is introduced. The proposed method is built on the fast marching scheme which comprises of two components: a local numerical solver and an update scheme. We replace the formulaic local numerical solver with a trained neural network to provide highly accurate estimates of local distances for a variety of different geometries and sampling conditions. Our learning approach generalizes not only to flat Euclidean domains but also to curved surfaces enabled by the incorporation of certain invariant features in the neural network architecture. We show a considerable gain in performance, validated by smaller errors and higher orders of accuracy for the numerical solutions of the Eikonal equation computed on different surfaces The proposed approach leverages the approximation power of neural networks to enhance the performance of numerical algorithms, thereby, connecting the somewhat disparate themes of numerical geometry and learning.

Learning to Optimize Multigrid PDE Solvers

Constructing fast numerical solvers for partial differential equations (PDEs) is crucial for many scientific disciplines. A leading technique for solving large-scale PDEs is using multigrid methods. At the core of a multigrid solver is the prolongation matrix, which relates between different scales of the problem. This matrix is strongly problem-dependent, and its optimal construction is critical to the efficiency of the solver. In practice, however, devising multigrid algorithms for new problems often poses formidable challenges. In this paper we propose a framework for learning multigrid solvers. Our method learns a (single) mapping from discretized PDEs to prolongation operators for a broad class of 2D diffusion problems. We train a neural network once for the entire class of PDEs, using an efficient and unsupervised loss function. Our tests demonstrate improved convergence rates compared to the widely used Black-Box multigrid scheme, suggesting that our method successfully learned rules for constructing prolongation matrices.

Synthesizing facial photometries and corresponding geometries using generative adversarial networks

Artificial data synthesis is currently a well studied topic with useful applications in data science, computer vision, graphics and many other fields. Generating realistic data is especially challenging since human perception is highly sensitive to non realistic appearance. In recent times, new levels of realism have been achieved by advances in GAN training procedures and architectures. These successful models, however, are tuned mostly for use with regularly sampled data such as images, audio and video. Despite the successful application of the architecture on these types of media, applying the same tools to geometric data poses a far greater challenge. The study of geometric deep learning is still a debated issue within the academic community as the lack of intrinsic parametrization inherent to geometric objects prohibits the direct use of convolutional filters, a main building block of today's machine learning systems. In this paper we propose a new method for generating realistic human facial geometries coupled with overlayed textures. We circumvent the parametrization issue by imposing a global mapping from our data to the unit rectangle. We further discuss how to design such a mapping to control the mapping distortion and conserve area within the mapped image. By representing geometric textures and geometries as images, we are able to use advanced GAN methodologies to generate new geometries. We address the often neglected topic of relation between texture and geometry and propose to use this correlation to match between generated textures and their corresponding geometries. We offer a new method for training GAN models on partially corrupted data. Finally, we provide empirical evidence demonstrating our generative model's ability to produce examples of new identities independent from the training data while maintaining a high level of realism, two traits that are often at odds.

Mo-Net: Flavor the Moments in Learning to Classify Shapes

A fundamental question in learning to classify 3D shapes is how to treat the data in a way that would allow us to construct efficient and accurate geometric processing and analysis procedures. Here, we restrict ourselves to networks that operate on point clouds. There were several attempts to treat point clouds as non-structured data sets by which a neural network is trained to extract discriminative properties. The idea of using 3D coordinates as class identifiers motivated us to extend this line of thought to that of shape classification by comparing attributes that could easily account for the shape moments. Here, we propose to add polynomial functions of the coordinates allowing the network to account for higher order moments of a given shape. Experiments on two benchmarks show that the suggested network is able to provide more accurate results and at the same token learn more efficiently in terms of memory and computational complexity.

Self-supervised Learning of Dense Shape Correspondence

We introduce the first completely unsupervised correspondence learning approach for deformable 3D shapes. Key to our model is the understanding that natural deformations (such as changes in pose) approximately preserve the metric structure of the surface, yielding a natural criterion to drive the learning process toward distortion-minimizing predictions. On this basis, we overcome the need for annotated data and replace it by a purely geometric criterion. The resulting learning model is class-agnostic, and is able to leverage any type of deformable geometric data for the training phase. In contrast to existing supervised approaches which specialize on the class seen at training time, we demonstrate stronger generalization as well as applicability to a variety of challenging settings. We showcase our method on a wide selection of correspondence benchmarks, where we outperform other methods in terms of accuracy, generalization, and efficiency.

Specular-to-Diffuse Translation for Multi-View Reconstruction

Most multi-view 3D reconstruction algorithms, especially when shape-from-shading cues are used, assume that object appearance is predominantly diffuse. To alleviate this restriction, we introduce S2Dnet, a generative adversarial network for transferring multiple views of objects with specular reflection into diffuse ones, so that multi-view reconstruction methods can be applied more effectively. Our network extends unsupervised image-to-image translation to multi-view "specular to diffuse" translation. To preserve object appearance across multiple views, we introduce a Multi-View Coherence loss (MVC) that evaluates the similarity and faithfulness of local patches after the view-transformation. Our MVC loss ensures that the similarity of local correspondences among multi-view images is preserved under the image-to-image translation. As a result, our network yields significantly better results than several single-view baseline techniques. In addition, we carefully design and generate a large synthetic training data set using physically-based rendering. During testing, our network takes only the raw glossy images as input, without extra information such as segmentation masks or lighting estimation. Results demonstrate that multi-view reconstruction can be significantly improved using the images filtered by our network. We also show promising performance on real world training and testing data.

Sparse Approximation of 3D Meshes using the Spectral Geometry of the Hamiltonian Operator

The discrete Laplace operator is ubiquitous in spectral shape analysis, since its eigenfunctions are provably optimal in representing smooth functions defined on the surface of the shape. Indeed, subspaces defined by its eigenfunctions have been utilized for shape compression, treating the coordinates as smooth functions defined on the given surface. However, surfaces of shapes in nature often contain geometric structures for which the general smoothness assumption may fail to hold. At the other end, some explicit mesh compression algorithms utilize the order by which vertices that represent the surface are traversed, a property which has been ignored in spectral approaches. Here, we incorporate the order of vertices into an operator that defines a novel spectral domain. We propose a method for representing 3D meshes using the spectral geometry of the Hamiltonian operator, integrated within a sparse approximation framework. We adapt the concept of a potential function from quantum physics and incorporate vertex ordering information into the potential, yielding a novel data-dependent operator. The potential function modifies the spectral geometry of the Laplacian to focus on regions with finer details of the given surface. By sparsely encoding the geometry of the shape using the proposed data-dependent basis, we improve compression performance compared to previous results that use the standard Laplacian basis and spectral graph wavelets.

Parametric Manifold Learning Via Sparse Multidimensional Scaling

We propose a metric-learning framework for computing distance-preserving maps that generate low-dimensional embeddings for a certain class of manifolds. We employ Siamese networks to solve the problem of least squares multidimensional scaling for generating mappings that preserve geodesic distances on the manifold. In contrast to previous parametric manifold learning methods we show a substantial reduction in training effort enabled by the computation of geodesic distances in a farthest point sampling strategy. Additionally, the use of a network to model the distance-preserving map reduces the complexity of the multidimensional scaling problem and leads to an improved non-local generalization of the manifold compared to analogous non-parametric counterparts. We demonstrate our claims on point-cloud data and on image manifolds and show a numerical analysis of our technique to facilitate a greater understanding of the representational power of neural networks in modeling manifold data.

Efficient Deformable Shape Correspondence via Kernel Matching

We present a method to match three dimensional shapes under non-isometric deformations, topology changes and partiality. We formulate the problem as matching between a set of pair-wise and point-wise descriptors, imposing a continuity prior on the mapping, and propose a projected descent optimization procedure inspired by difference of convex functions (DC) programming. Surprisingly, in spite of the highly non-convex nature of the resulting quadratic assignment problem, our method converges to a semantically meaningful and continuous mapping in most of our experiments, and scales well. We provide preliminary theoretical analysis and several interpretations of the method.