Ron Kimmel

Hao Liu, Xue-Cheng Tai, Ron Kimmel et al. · gatech

One classical approach to regularize color is to tream them as two dimensional surfaces embedded in a five dimensional spatial-chromatic space. In this case, a natural regularization term arises as the image surface area. Choosing the chromatic coordinates as dominating over the spatial ones, the image spatial coordinates could be thought of as a paramterization of the image surface manifold in a three dimensional color space. Minimizing the area of the image manifold leads to the Beltrami flow or mean curvature flow of the image surface in the 3D color space, while minimizing the elastica of the image surface yields an additional interesting regularization. Recently, the authors proposed a color elastica model, which minimizes both the surface area and elastica of the image manifold. In this paper, we propose to modify the color elastica and introduce two new models for color image regularization. The revised measures are motivated by the relations between the color elastica model, Euler's elastica model and the total variation model for gray level images. Compared to our previous color elastica model, the new models are direct extensions of Euler's elastica model to color images. The proposed models are nonlinear and challenging to minimize. To overcome this difficulty, two operator-splitting methods are suggested. Specifically, nonlinearities are decoupled by introducing new vector- and matrix-valued variables. Then, the minimization problems are converted to solving initial value problems which are time-discretized by operator splitting. Each subproblem, after splitting either, has a closed-form solution or can be solved efficiently. The effectiveness and advantages of the proposed models are demonstrated by comprehensive experiments. The benefits of incorporating the elastica of the image surface as regularization terms compared to common alternatives are empirically validated.

Oshri Halimi, Fabian Prada, Tuur Stuyck et al.

Virtual telepresence is the future of online communication. Clothing is an essential part of a person's identity and self-expression. Yet, ground truth data of registered clothes is currently unavailable in the required resolution and accuracy for training telepresence models for realistic cloth animation. Here, we propose an end-to-end pipeline for building drivable representations for clothing. The core of our approach is a multi-view patterned cloth tracking algorithm capable of capturing deformations with high accuracy. We further rely on the high-quality data produced by our tracking method to build a Garment Avatar: an expressive and fully-drivable geometry model for a piece of clothing. The resulting model can be animated using a sparse set of views and produces highly realistic reconstructions which are faithful to the driving signals. We demonstrate the efficacy of our pipeline on a realistic virtual telepresence application, where a garment is being reconstructed from two views, and a user can pick and swap garment design as they wish. In addition, we show a challenging scenario when driven exclusively with body pose, our drivable garment avatar is capable of producing realistic cloth geometry of significantly higher quality than the state-of-the-art.

Roy Velich, Ron Kimmel

We propose a learning paradigm for the numerical approximation of differential invariants of planar curves. Deep neural-networks' (DNNs) universal approximation properties are utilized to estimate geometric measures. The proposed framework is shown to be a preferable alternative to axiomatic constructions. Specifically, we show that DNNs can learn to overcome instabilities and sampling artifacts and produce consistent signatures for curves subject to a given group of transformations in the plane. We compare the proposed schemes to alternative state-of-the-art axiomatic constructions of differential invariants. We evaluate our models qualitatively and quantitatively and propose a benchmark dataset to evaluate approximation models of differential invariants of planar curves.

David Bensaïd, Amit Bracha, Ron Kimmel

Evaluating the similarity of non-rigid shapes with significant partiality is a fundamental task in numerous computer vision applications. Here, we propose a novel axiomatic method to match similar regions across shapes. Matching similar regions is formulated as the alignment of the spectra of operators closely related to the Laplace-Beltrami operator (LBO). The main novelty of the proposed approach is the consideration of differential operators defined on a manifold with multiple metrics. The choice of a metric relates to fundamental shape properties while considering the same manifold under different metrics can thus be viewed as analyzing the underlying manifold from different perspectives. Specifically, we examine the scale-invariant metric and the corresponding scale-invariant Laplace-Beltrami operator (SI-LBO) along with the regular metric and the regular LBO. We demonstrate that the scale-invariant metric emphasizes the locations of important semantic features in articulated shapes. A truncated spectrum of the SI-LBO consequently better captures locally curved regions and complements the global information encapsulated in the truncated spectrum of the regular LBO. We show that matching these dual spectra outperforms competing axiomatic frameworks when tested on standard benchmarks. We introduced a new dataset and compare the proposed method with the state-of-the-art learning based approach in a cross-database configuration. Specifically, we show that, when trained on one data set and tested on another, the proposed axiomatic approach which does not involve training, outperforms the deep learning alternative.

Saar Huberman, Amit Bracha, Ron Kimmel

A common approach to compute distances on continuous surfaces is by considering a discretized polygonal mesh approximating the surface and estimating distances on the polygon. We show that exact geodesic distances restricted to the polygon are at most second-order accurate with respect to the distances on the corresponding continuous surface. By order of accuracy we refer to the convergence rate as a function of the average distance between sampled points. Next, a higher-order accurate deep learning method for computing geodesic distances on surfaces is introduced. Traditionally, one considers two main components when computing distances on surfaces: a numerical solver that locally approximates the distance function, and an efficient causal ordering scheme by which surface points are updated. Classical minimal path methods often exploit a dynamic programming principle with quasi-linear computational complexity in the number of sampled points. The quality of the distance approximation is determined by the local solver that is revisited in this paper. To improve state of the art accuracy, we consider a neural network-based local solver which implicitly approximates the structure of the continuous surface. We supply numerical evidence that the proposed learned update scheme provides better accuracy compared to the best possible polyhedral approximations and previous learning-based methods. The result is a third-order accurate solver with a bootstrapping-recipe for further improvement.

Assaf Singer, Noam Rotstein, Amir Mann et al.

Diffusion-based video generation can create realistic videos, yet existing image- and text-based conditioning fails to offer precise motion control. Prior methods for motion-conditioned synthesis typically require model-specific fine-tuning, which is computationally expensive and restrictive. We introduce Time-to-Move (TTM), a training-free, plug-and-play framework for motion- and appearance-controlled video generation with image-to-video (I2V) diffusion models. Our key insight is to use crude reference animations obtained through user-friendly manipulations such as cut-and-drag or depth-based reprojection. Motivated by SDEdit's use of coarse layout cues for image editing, we treat the crude animations as coarse motion cues and adapt the mechanism to the video domain. We preserve appearance with image conditioning and introduce dual-clock denoising, a region-dependent strategy that enforces strong alignment in motion-specified regions while allowing flexibility elsewhere, balancing fidelity to user intent with natural dynamics. This lightweight modification of the sampling process incurs no additional training or runtime cost and is compatible with any backbone. Extensive experiments on object and camera motion benchmarks show that TTM matches or exceeds existing training-based baselines in realism and motion control. Beyond this, TTM introduces a unique capability: precise appearance control through pixel-level conditioning, exceeding the limits of text-only prompting. Visit our project page for video examples and code: https://time-to-move.github.io/.

Amit Bracha, Thomas Dagès, Ron Kimmel

While dealing with matching shapes to their parts, we often apply a tool known as functional maps. The idea is to translate the shape matching problem into "convenient" spaces by which matching is performed algebraically by solving a least squares problem. Here, we argue that such formulations, though popular in this field, introduce errors in the estimated match when partiality is invoked. Such errors are unavoidable even for advanced feature extraction networks, and they can be shown to escalate with increasing degrees of shape partiality, adversely affecting the learning capability of such systems. To circumvent these limitations, we propose a novel approach for partial shape matching. Our study of functional maps led us to a novel method that establishes direct correspondence between partial and full shapes through feature matching bypassing the need for functional map intermediate spaces. The Gromov Distance between metric spaces leads to the construction of the first part of our loss functions. For regularization we use two options: a term based on the area preserving property of the mapping, and a relaxed version that avoids the need to resort to functional maps. The proposed approach shows superior performance on the SHREC'16 dataset, outperforming existing unsupervised methods for partial shape matching.Notably, it achieves state-of-the-art results on the SHREC'16 HOLES benchmark, superior also compared to supervised methods. We demonstrate the benefits of the proposed unsupervised method when applied to a new dataset PFAUST for part-to-full shape correspondence.

Roman Rabinovich, Ibrahim Jubran, Aaron Wetzler et al.

This paper presents a novel beacon light coding protocol, which enables fast and accurate identification of the beacons in an image. The protocol is provably robust to a predefined set of detection and decoding errors, and does not require any synchronization between the beacons themselves and the optical sensor. A detailed guide is then given for developing an optical tracking and localization system, which is based on the suggested protocol and readily available hardware. Such a system operates either as a standalone system for recovering the six degrees of freedom of fast moving objects, or integrated with existing SLAM pipelines providing them with error-free and easily identifiable landmarks. Based on this guide, we implemented a low-cost positional tracking system which can run in real-time on an IoT board. We evaluate our system's accuracy and compare it to other popular methods which utilize the same optical hardware, in experiments where the ground truth is known. A companion video containing multiple real-world experiments demonstrates the accuracy, speed, and applicability of the proposed system in a wide range of environments and real-world tasks. Open source code is provided to encourage further development of low-cost localization systems integrating the suggested technology at its navigation core.

Thomas Dagès, Simon Weber, Daniel Cremers et al.

Manifold learning is a fundamental task at the core of data analysis and visualisation. It aims to capture the simple underlying structure of complex high-dimensional data by preserving pairwise dissimilarities in low-dimensional embeddings. Traditional methods rely on symmetric Riemannian geometry, thus forcing symmetric dissimilarities and embedding spaces, e.g. Euclidean. However, this discards in practice valuable asymmetric information inherent to the non-uniformity of data samples. We suggest to harness this asymmetry by switching to Finsler geometry, an asymmetric generalisation of Riemannian geometry, and propose a Finsler manifold learning pipeline that constructs asymmetric dissimilarities and embeds in a Finsler space. This greatly broadens the applicability of existing asymmetric embedders beyond traditionally directed data to any data. We also modernise asymmetric embedders by generalising current reference methods to asymmetry, like Finsler t-SNE and Finsler Umap. On controlled synthetic and large real datasets, we show that our asymmetric pipeline reveals valuable information lost in the traditional pipeline, e.g. density hierarchies, and consistently provides superior quality embeddings than their Euclidean counterparts.

Yaniv Wolf, Amit Bracha, Ron Kimmel

Recently, 3D Gaussian Splatting (3DGS) has emerged as an efficient approach for accurately representing scenes. However, despite its superior novel view synthesis capabilities, extracting the geometry of the scene directly from the Gaussian properties remains a challenge, as those are optimized based on a photometric loss. While some concurrent models have tried adding geometric constraints during the Gaussian optimization process, they still produce noisy, unrealistic surfaces. We propose a novel approach for bridging the gap between the noisy 3DGS representation and the smooth 3D mesh representation, by injecting real-world knowledge into the depth extraction process. Instead of extracting the geometry of the scene directly from the Gaussian properties, we instead extract the geometry through a pre-trained stereo-matching model. We render stereo-aligned pairs of images corresponding to the original training poses, feed the pairs into a stereo model to get a depth profile, and finally fuse all of the profiles together to get a single mesh. The resulting reconstruction is smoother, more accurate and shows more intricate details compared to other methods for surface reconstruction from Gaussian Splatting, while only requiring a small overhead on top of the fairly short 3DGS optimization process. We performed extensive testing of the proposed method on in-the-wild scenes, obtained using a smartphone, showcasing its superior reconstruction abilities. Additionally, we tested the method on the Tanks and Temples and DTU benchmarks, achieving state-of-the-art results.

Roy Velich, Arkadi Piven, David Bensaïd et al.

We introduce a novel framework that directly learns a spectral basis for shape and manifold analysis from unstructured data, eliminating the need for traditional operator selection, discretization, and eigensolvers. Grounded in optimal-approximation theory, we train a network to decompose an implicit approximation operator by minimizing the reconstruction error in the learned basis over a chosen distribution of probe functions. For suitable distributions, they can be seen as an approximation of the Laplacian operator and its eigendecomposition, which are fundamental in geometry processing. Furthermore, our method recovers in a unified manner not only the spectral basis, but also the implicit metric's sampling density and the eigenvalues of the underlying operator. Notably, our unsupervised method makes no assumption on the data manifold, such as meshing or manifold dimensionality, allowing it to scale to arbitrary datasets of any dimension. On point clouds lying on surfaces in 3D and high-dimensional image manifolds, our approach yields meaningful spectral bases, that can resemble those of the Laplacian, without explicit construction of an operator. By replacing the traditional operator selection, construction, and eigendecomposition with a learning-based approach, our framework offers a principled, data-driven alternative to conventional pipelines. This opens new possibilities in geometry processing for unstructured data, particularly in high-dimensional spaces.

Navve Wasserman, Noam Rotstein, Roy Ganz et al.

Image editing has advanced significantly with the introduction of text-conditioned diffusion models. Despite this progress, seamlessly adding objects to images based on textual instructions without requiring user-provided input masks remains a challenge. We address this by leveraging the insight that removing objects (Inpaint) is significantly simpler than its inverse process of adding them (Paint), attributed to inpainting models that benefit from segmentation mask guidance. Capitalizing on this realization, by implementing an automated and extensive pipeline, we curate a filtered large-scale image dataset containing pairs of images and their corresponding object-removed versions. Using these pairs, we train a diffusion model to inverse the inpainting process, effectively adding objects into images. Unlike other editing datasets, ours features natural target images instead of synthetic ones while ensuring source-target consistency by construction. Additionally, we utilize a large Vision-Language Model to provide detailed descriptions of the removed objects and a Large Language Model to convert these descriptions into diverse, natural-language instructions. Our quantitative and qualitative results show that the trained model surpasses existing models in both object addition and general editing tasks. Visit our project page for the released dataset and trained models at https://rotsteinnoam.github.io/Paint-by-Inpaint.

Noam Rotstein, Gal Yona, Daniel Silver et al.

Recent advances in image editing, driven by image diffusion models, have shown remarkable progress. However, significant challenges remain, as these models often struggle to follow complex edit instructions accurately and frequently compromise fidelity by altering key elements of the original image. Simultaneously, video generation has made remarkable strides, with models that effectively function as consistent and continuous world simulators. In this paper, we propose merging these two fields by utilizing image-to-video models for image editing. We reformulate image editing as a temporal process, using pretrained video models to create smooth transitions from the original image to the desired edit. This approach traverses the image manifold continuously, ensuring consistent edits while preserving the original image's key aspects. Our approach achieves state-of-the-art results on text-based image editing, demonstrating significant improvements in both edit accuracy and image preservation. Visit our project page at https://rotsteinnoam.github.io/Frame2Frame.

Amit Bracha, Thomas Dagès, Ron Kimmel

When matching parts of a surface to its whole, a fundamental question arises: Which points should be included in the matching process? The issue is intensified when using isometry to measure similarity, as it requires the validation of whether distances measured between pairs of surface points should influence the matching process. The approach we propose treats surfaces as manifolds equipped with geodesic distances, and addresses the partial shape matching challenge by introducing a novel criterion to meticulously search for consistent distances between pairs of points. The new criterion explores the relation between intrinsic geodesic distances between the points, geodesic distances between the points and surface boundaries, and extrinsic distances between boundary points measured in the embedding space. It is shown to be less restrictive compared to previous measures and achieves state-of-the-art results when used as a loss function in training networks for partial shape matching.

David Bensaïd, Noam Rotstein, Roy Velich et al.

Low-Rank Adaptation (LoRA) has significantly advanced parameter-efficient fine-tuning of large pretrained models. LoRA augments the pre-trained weights of a model by adding the product of two smaller matrices that together form a low-rank matrix update. Recent research has shown that scale disparities between these two matrices often cause unstable training dynamics, leading to suboptimal performance. In this paper, we propose SingLoRA, which reformulates low-rank adaptation by learning the weights update as a decomposition of a single low-rank matrix multiplied by its transpose. This simple design inherently removes inter-matrix scale conflicts, ensuring stable optimization, and roughly halves the parameter count. We analyze SingLoRA within the infinite-width neural network framework, showing that it guarantees stable feature learning by construction. Extensive experiments on multiple tasks validate these benefits. In common sense reasoning, fine-tuning LLama 7B on MNLI with SingLoRA achieves 91.3% accuracy - surpassing LoRA (89.1%) and LoRA+ (90.2%) - while using only 60% of their parameter budget. In image generation, fine-tuning Stable Diffusion with SingLoRA significantly improves image fidelity on DreamBooth, achieving a DINO similarity score of 0.151, compared to scores of 0.148 and 0.143 for DoRA and LoRA, respectively.

Thomas Dagès, Simon Weber, Ya-Wei Eileen Lin et al.

Dimensionality reduction is a fundamental task that aims to simplify complex data by reducing its feature dimensionality while preserving essential patterns, with core applications in data analysis and visualisation. To preserve the underlying data structure, multi-dimensional scaling (MDS) methods focus on preserving pairwise dissimilarities, such as distances. They optimise the embedding to have pairwise distances as close as possible to the data dissimilarities. However, the current standard is limited to embedding data in Riemannian manifolds. Motivated by the lack of asymmetry in the Riemannian metric of the embedding space, this paper extends the MDS problem to a natural asymmetric generalisation of Riemannian manifolds called Finsler manifolds. Inspired by Euclidean space, we define a canonical Finsler space for embedding asymmetric data. Due to its simplicity with respect to geodesics, data representation in this space is both intuitive and simple to analyse. We demonstrate that our generalisation benefits from the same theoretical convergence guarantees. We reveal the effectiveness of our Finsler embedding across various types of non-symmetric data, highlighting its value in applications such as data visualisation, dimensionality reduction, directed graph embedding, and link prediction.

Gal Yona, Roy Velich, Ron Kimmel et al.

Classical shape descriptors such as Heat Kernel Signature (HKS), Wave Kernel Signature (WKS), and Signature of Histograms of OrienTations (SHOT), while widely used in shape analysis, exhibit sensitivity to mesh connectivity, sampling patterns, and topological noise. While differential geometry offers a promising alternative through its theory of differential invariants, which are theoretically guaranteed to be robust shape descriptors, the computation of these invariants on discrete meshes often leads to unstable numerical approximations, limiting their practical utility. We present a self-supervised learning approach for extracting geometric features from 3D surfaces. Our method combines synthetic data generation with a neural architecture designed to learn sampling-invariant features. By integrating our features into existing shape correspondence frameworks, we demonstrate improved performance on standard benchmarks including FAUST, SCAPE, TOPKIDS, and SHREC'16, showing particular robustness to topological noise and partial shapes.

Daniel Silver, Ron Kimmel

In the field of video compression, the pursuit for better quality at lower bit rates remains a long-lasting goal. Recent developments have demonstrated the potential of Implicit Neural Representation (INR) as a promising alternative to traditional transform-based methodologies. Video INRs can be roughly divided into frame-wise and pixel-wise methods according to the structure the network outputs. While the pixel-based methods are better for upsampling and parallelization, frame-wise methods demonstrated better performance. We introduce CoordFlow, a novel pixel-wise INR for video compression. It yields state-of-the-art results compared to other pixel-wise INRs and on-par performance compared to leading frame-wise techniques. The method is based on the separation of the visual information into visually consistent layers, each represented by a dedicated network that compensates for the layer's motion. When integrated, a byproduct is an unsupervised segmentation of video sequence. Objects motion trajectories are implicitly utilized to compensate for visual-temporal redundancies. Additionally, the proposed method provides inherent video upsampling, stabilization, inpainting, and denoising capabilities.

Noam Rotstein, David Bensaid, Shaked Brody et al.

The advent of vision-language pre-training techniques enhanced substantial progress in the development of models for image captioning. However, these models frequently produce generic captions and may omit semantically important image details. This limitation can be traced back to the image-text datasets; while their captions typically offer a general description of image content, they frequently omit salient details. Considering the magnitude of these datasets, manual reannotation is impractical, emphasizing the need for an automated approach. To address this challenge, we leverage existing captions and explore augmenting them with visual details using "frozen" vision experts including an object detector, an attribute recognizer, and an Optical Character Recognizer (OCR). Our proposed method, FuseCap, fuses the outputs of such vision experts with the original captions using a large language model (LLM), yielding comprehensive image descriptions. We automatically curate a training set of 12M image-enriched caption pairs. These pairs undergo extensive evaluation through both quantitative and qualitative analyses. Subsequently, this data is utilized to train a captioning generation BLIP-based model. This model outperforms current state-of-the-art approaches, producing more precise and detailed descriptions, demonstrating the effectiveness of the proposed data-centric approach. We release this large-scale dataset of enriched image-caption pairs for the community.

Roy Velich, Ron Kimmel

We propose a learning paradigm for numerical approximation of differential invariants of planar curves. Deep neural-networks' (DNNs) universal approximation properties are utilized to estimate geometric measures. The proposed framework is shown to be a preferable alternative to axiomatic constructions. Specifically, we show that DNNs can learn to overcome instabilities and sampling artifacts and produce numerically-stable signatures for curves subject to a given group of transformations in the plane. We compare the proposed schemes to alternative state-of-the-art axiomatic constructions of group invariant arc-lengths and curvatures.

Amit Bracha, Noam Rotstein, David Bensaïd et al.

Depth estimation is a cornerstone of a vast number of applications requiring 3D assessment of the environment, such as robotics, augmented reality, and autonomous driving to name a few. One prominent technique for depth estimation is stereo matching which has several advantages: it is considered more accessible than other depth-sensing technologies, can produce dense depth estimates in real-time, and has benefited greatly from the advances of deep learning in recent years. However, current techniques for depth estimation from stereoscopic images still suffer from a built-in drawback. To reconstruct depth, a stereo matching algorithm first estimates the disparity map between the left and right images before applying a geometric triangulation. A simple analysis reveals that the depth error is quadratically proportional to the object's distance. Therefore, constant disparity errors are translated to large depth errors for objects far from the camera. To mitigate this quadratic relation, we propose a simple but effective method that uses a refinement network for depth estimation. We show analytical and empirical results suggesting that the proposed learning procedure reduces this quadratic relation. We evaluate the proposed refinement procedure on well-known benchmarks and datasets, like Sceneflow and KITTI datasets, and demonstrate significant improvements in the depth accuracy metric.

Ron Slossberg, Ibrahim Jubran, Ron Kimmel

Many methods have been proposed over the years to tackle the task of facial 3D geometry and texture recovery from a single image. Such methods often fail to provide high-fidelity texture without relying on 3D facial scans during training. In contrast, the complementary task of 3D facial generation has not received as much attention. As opposed to the 2D texture domain, where GANs have proven to produce highly realistic facial images, the more challenging 3D geometry domain has not yet caught up to the same levels of realism and diversity. In this paper, we propose a novel unified pipeline for both tasks, generation of both geometry and texture, and recovery of high-fidelity texture. Our texture model is learned, in an unsupervised fashion, from natural images as opposed to scanned texture maps. To the best of our knowledge, this is the first such unified framework independent of scanned textures. Our novel training pipeline incorporates a pre-trained 2D facial generator coupled with a deep feature manipulation methodology. By applying precise 3DMM fitting, we can seamlessly integrate our modeled textures into synthetically generated background images forming a realistic composition of our textured model with background, hair, teeth, and body. This enables us to apply transfer learning from the domain of 2D image generation, thus, benefiting greatly from the impressive results obtained in this domain. We provide a comprehensive study on several recent methods comparing our model in generation and reconstruction tasks. As the extensive qualitative, as well as quantitative analysis, demonstrate, we achieve state-of-the-art results for both tasks.

Noam Rotstein, Amit Bracha, Ron Kimmel

Reconstruction of geometric structures from images using supervised learning suffers from limited available amount of accurate data. One type of such data is accurate real-world RGB-D images. A major challenge in acquiring such ground truth data is the accurate alignment between RGB images and the point cloud measured by a depth scanner. To overcome this difficulty, we consider a differential optimization method that aligns a colored point cloud with a given color image through iterative geometric and color matching. In the proposed framework, the optimization minimizes the photometric difference between the colors of the point cloud and the corresponding colors of the image pixels. Unlike other methods that try to reduce this photometric error, we analyze the computation of the gradient on the image plane and propose a different direct scheme. We assume that the colors produced by the geometric scanner camera and the color camera sensor are different and therefore characterized by different chromatic acquisition properties. Under these multimodal conditions, we find the transformation between the camera image and the point cloud colors. We alternately optimize for aligning the position of the point cloud and matching the different color spaces. The alignments produced by the proposed method are demonstrated on both synthetic data with quantitative evaluation and real scenes with qualitative results.

Benjamin Groisser, Alon Wolf, Ron Kimmel

The proliferation of 3D scanning technology has driven a need for methods to interpret geometric data, particularly for human subjects. In this paper we propose an elegant fusion of regression (bottom-up) and generative (top-down) methods to fit a parametric template model to raw scan meshes. Our first major contribution is an intrinsic convolutional mesh U-net architecture that predicts pointwise correspondence to a template surface. Soft-correspondence is formulated as coordinates in a newly-constructed Cartesian space. Modeling correspondence as Euclidean proximity enables efficient optimization, both for network training and for the next step of the algorithm. Our second contribution is a generative optimization algorithm that uses the U-net correspondence predictions to guide a parametric Iterative Closest Point registration. By employing pre-trained human surface parametric models we maximally leverage domain-specific prior knowledge. The pairing of a mesh-convolutional network with generative model fitting enables us to predict correspondence for real human surface scans including occlusions, partialities, and varying genus (e.g. from self-contact). We evaluate the proposed method on the FAUST correspondence challenge where we achieve 20% (33%) improvement over state of the art methods for inter- (intra-) subject correspondence.

Ibrahim Jubran, Alaa Maalouf, Ron Kimmel et al.

The goal of the \emph{alignment problem} is to align a (given) point cloud $P = \{p_1,\cdots,p_n\}$ to another (observed) point cloud $Q = \{q_1,\cdots,q_n\}$. That is, to compute a rotation matrix $R \in \mathbb{R}^{3 \times 3}$ and a translation vector $t \in \mathbb{R}^{3}$ that minimize the sum of paired distances $\sum_{i=1}^n D(Rp_i-t,q_i)$ for some distance function $D$. A harder version is the \emph{registration problem}, where the correspondence is unknown, and the minimum is also over all possible correspondence functions from $P$ to $Q$. Heuristics such as the Iterative Closest Point (ICP) algorithm and its variants were suggested for these problems, but none yield a provable non-trivial approximation for the global optimum. We prove that there \emph{always} exists a "witness" set of $3$ pairs in $P \times Q$ that, via novel alignment algorithm, defines a constant factor approximation (in the worst case) to this global optimum. We then provide algorithms that recover this witness set and yield the first provable constant factor approximation for the: (i) alignment problem in $O(n)$ expected time, and (ii) registration problem in polynomial time. Such small witness sets exist for many variants including points in $d$-dimensional space, outlier-resistant cost functions, and different correspondence types. Extensive experimental results on real and synthetic datasets show that our approximation constants are, in practice, close to $1$, and up to x$10$ times smaller than state-of-the-art algorithms.

Sagi Levanon, Oshry Markovich, Itamar Gozlan et al.

Prediction of stress conditions is important for monitoring plant growth stages, disease detection, and assessment of crop yields. Multi-modal data, acquired from a variety of sensors, offers diverse perspectives and is expected to benefit the prediction process. We present several methods and strategies for abiotic stress prediction in banana plantlets, on a dataset acquired during a two and a half weeks period, of plantlets subject to four separate water and fertilizer treatments. The dataset consists of RGB and thermal images, taken once daily of each plant. Results are encouraging, in the sense that neural networks exhibit high prediction rates (over $90\%$ amongst four classes), in cases where there are hardly any noticeable features distinguishing the treatments, much higher than field experts can supply.

Hao Liu, Xue-Cheng Tai, Ron Kimmel et al.

Models related to the Euler's elastica energy have proven to be useful for many applications including image processing. Extending elastica models to color images and multi-channel data is a challenging task, as stable and consistent numerical solvers for these geometric models often involve high order derivatives. Like the single channel Euler's elastica model and the total variation (TV) models, geometric measures that involve high order derivatives could help when considering image formation models that minimize elastic properties. In the past, the Polyakov action from high energy physics has been successfully applied to color image processing. Here, we introduce an addition to the Polyakov action for color images that minimizes the color manifold curvature. The color image curvature is computed by applying of the Laplace-Beltrami operator to the color image channels. When reduced to gray-scale images, while selecting appropriate scaling between space and color, the proposed model minimizes the Euler's elastica operating on the image level sets. Finding a minimizer for the proposed nonlinear geometric model is a challenge we address in this paper. Specifically, we present an operator-splitting method to minimize the proposed functional. The non-linearity is decoupled by introducing three vector-valued and matrix-valued variables. The problem is then converted into solving for the steady state of an associated initial-value problem. The initial-value problem is time-split into three fractional steps, such that each sub-problem has a closed form solution, or can be solved by fast algorithms. The efficiency and robustness of the proposed method are demonstrated by systematic numerical experiments.

Luca Cosmo, Antonio Norelli, Oshri Halimi et al.

In this paper, we advocate the adoption of metric preservation as a powerful prior for learning latent representations of deformable 3D shapes. Key to our construction is the introduction of a geometric distortion criterion, defined directly on the decoded shapes, translating the preservation of the metric on the decoding to the formation of linear paths in the underlying latent space. Our rationale lies in the observation that training samples alone are often insufficient to endow generative models with high fidelity, motivating the need for large training datasets. In contrast, metric preservation provides a rigorous way to control the amount of geometric distortion incurring in the construction of the latent space, leading in turn to synthetic samples of higher quality. We further demonstrate, for the first time, the adoption of differentiable intrinsic distances in the backpropagation of a geodesic loss. Our geometric priors are particularly relevant in the presence of scarce training data, where learning any meaningful latent structure can be especially challenging. The effectiveness and potential of our generative model is showcased in applications of style transfer, content generation, and shape completion.

Amir Livne, Alex Bronstein, Ron Kimmel et al.

Some face recognition methods are designed to utilize geometric information extracted from depth sensors to overcome the weaknesses of single-image based recognition technologies. However, the accurate acquisition of the depth profile is an expensive and challenging process. Here, we introduce a novel method that learns to recognize faces from stereo camera systems without the need to explicitly compute the facial surface or depth map. The raw face stereo images along with the location in the image from which the face is extracted allow the proposed CNN to improve the recognition task while avoiding the need to explicitly handle the geometric structure of the face. This way, we keep the simplicity and cost efficiency of identity authentication from a single image, while enjoying the benefits of geometric data without explicitly reconstructing it. We demonstrate that the suggested method outperforms both existing single-image and explicit depth based methods on large-scale benchmarks, and even capable of recognize spoofing attacks. We also provide an ablation study that shows that the suggested method uses the face locations in the left and right images to encode informative features that improve the overall performance.

Oshri Halimi, Ido Imanuel, Or Litany et al.

According to Aristotle, a philosopher in Ancient Greece, "the whole is greater than the sum of its parts". This observation was adopted to explain human perception by the Gestalt psychology school of thought in the twentieth century. Here, we claim that observing part of an object which was previously acquired as a whole, one could deal with both partial matching and shape completion in a holistic manner. More specifically, given the geometry of a full, articulated object in a given pose, as well as a partial scan of the same object in a different pose, we address the problem of matching the part to the whole while simultaneously reconstructing the new pose from its partial observation. Our approach is data-driven, and takes the form of a Siamese autoencoder without the requirement of a consistent vertex labeling at inference time; as such, it can be used on unorganized point clouds as well as on triangle meshes. We demonstrate the practical effectiveness of our model in the applications of single-view deformable shape completion and dense shape correspondence, both on synthetic and real-world geometric data, where we outperform prior work on these tasks by a large margin.

Gautam Pai, Mor Joseph-Rivlin, Ron Kimmel

A majority of shape correspondence frameworks are based on devising pointwise and pairwise constraints on the correspondence map. The functional maps framework allows for formulating these constraints in the spectral domain. In this paper, we develop a functional map framework for the shape correspondence problem by constructing pairwise constraints using point-wise descriptors. Our core observation is that, every point-wise descriptor allows for the construction a pairwise kernel operator whose low frequency eigenfunctions depict regions of similar descriptor values at various scales of frequency. By aggregating the pairwise information from the descriptor and the intrinsic geometry of the surface encoded in the heat kernel, we construct a hybrid kernel and call it the bilateral operator. Analogous to the edge preserving bilateral filter in image processing, the action of the bilateral operator on a function defined over the manifold yields a descriptor dependent local smoothing of that function. By forcing the correspondence map to commute with the Bilateral operator, we show that we can maximally exploit the information from a given set of pointwise descriptors in a functional map framework.

Dmitry Kuznichov, Alon Zvirin, Yaron Honen et al.

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.

Moshe Lichtenstein, Gautam Pai, Ron Kimmel

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.

Daniel Greenfeld, Meirav Galun, Ron Kimmel et al.

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 a family of parameterized PDEs to prolongation operators. We train a neural network once for the entire class of PDEs, using an efficient and unsupervised loss function. Experiments on a broad class of 2D diffusion problems demonstrate improved convergence rates compared to the widely used Black-Box multigrid scheme, suggesting that our method successfully learned rules for constructing prolongation matrices.

Gil Shamai, Ron Slossberg, Ron Kimmel

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.

Mor Joseph-Rivlin, Alon Zvirin, Ron Kimmel

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 state of the art results and at the same token learn more efficiently in terms of memory and computational complexity.

Oshri Halimi, Or Litany, Emanuele Rodolà et al.

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.

Shihao Wu, Hui Huang, Tiziano Portenier et al.

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.

Gautam Pai, Ronen Talmon, Alex Bronstein et al.

This paper explores a fully unsupervised deep learning approach for computing distance-preserving maps that generate low-dimensional embeddings for a certain class of manifolds. We use the Siamese configuration to train a neural network to solve the problem of least squares multidimensional scaling for generating maps that approximately preserve geodesic distances. By training with only a few landmarks, we show a significantly improved local and nonlocal generalization of the isometric mapping as compared to analogous non-parametric counterparts. Importantly, the combination of a deep-learning framework with a multidimensional scaling objective enables a numerical analysis of network architectures to aid in understanding their representation power. This provides a geometric perspective to the generalizability of deep learning.

Zorah Lähner, Matthias Vestner, Amit Boyarski et al.

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.

Yoni Choukroun, Gautam Pai, Ron Kimmel

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.

Ran Breuer, Ron Kimmel

Facial expressions play a significant role in human communication and behavior. Psychologists have long studied the relationship between facial expressions and emotions. Paul Ekman et al., devised the Facial Action Coding System (FACS) to taxonomize human facial expressions and model their behavior. The ability to recognize facial expressions automatically, enables novel applications in fields like human-computer interaction, social gaming, and psychological research. There has been a tremendously active research in this field, with several recent papers utilizing convolutional neural networks (CNN) for feature extraction and inference. In this paper, we employ CNN understanding methods to study the relation between the features these computational networks are using, the FACS and Action Units (AU). We verify our findings on the Extended Cohn-Kanade (CK+), NovaEmotions and FER2013 datasets. We apply these models to various tasks and tests using transfer learning, including cross-dataset validation and cross-task performance. Finally, we exploit the nature of the FER based CNN models for the detection of micro-expressions and achieve state-of-the-art accuracy using a simple long-short-term-memory (LSTM) recurrent neural network (RNN).

Matan Sela, Elad Richardson, Ron Kimmel

It has been recently shown that neural networks can recover the geometric structure of a face from a single given image. A common denominator of most existing face geometry reconstruction methods is the restriction of the solution space to some low-dimensional subspace. While such a model significantly simplifies the reconstruction problem, it is inherently limited in its expressiveness. As an alternative, we propose an Image-to-Image translation network that jointly maps the input image to a depth image and a facial correspondence map. This explicit pixel-based mapping can then be utilized to provide high quality reconstructions of diverse faces under extreme expressions, using a purely geometric refinement process. In the spirit of recent approaches, the network is trained only with synthetic data, and is then evaluated on in-the-wild facial images. Both qualitative and quantitative analyses demonstrate the accuracy and the robustness of our approach.

Ron Slossberg, Aaron Wetzler, Ron Kimmel

Stereo reconstruction from rectified images has recently been revisited within the context of deep learning. Using a deep Convolutional Neural Network to obtain patch-wise matching cost volumes has resulted in state of the art stereo reconstruction on classic datasets like Middlebury and Kitti. By introducing this cost into a classical stereo pipeline, the final results are improved dramatically over non-learning based cost models. However these pipelines typically include hand engineered post processing steps to effectively regularize and clean the result. Here, we show that it is possible to take a more holistic approach by training a fully end-to-end network which directly includes regularization in the form of a densely connected Conditional Random Field (CRF) that acts as a prior on inter-pixel interactions. We demonstrate that our approach on both synthetic and real world datasets outperforms an alternative end-to-end network and compares favorably to more hand engineered approaches.

Gautam Pai, Aaron Wetzler, Ron Kimmel

We propose a metric learning framework for the construction of invariant geometric functions of planar curves for the Eucledian and Similarity group of transformations. We leverage on the representational power of convolutional neural networks to compute these geometric quantities. In comparison with axiomatic constructions, we show that the invariants approximated by the learning architectures have better numerical qualities such as robustness to noise, resiliency to sampling, as well as the ability to adapt to occlusion and partiality. Finally, we develop a novel multi-scale representation in a similarity metric learning paradigm.

Elad Richardson, Matan Sela, Roy Or-El et al.

Reconstructing the detailed geometric structure of a face from a given image is a key to many computer vision and graphics applications, such as motion capture and reenactment. The reconstruction task is challenging as human faces vary extensively when considering expressions, poses, textures, and intrinsic geometries. While many approaches tackle this complexity by using additional data to reconstruct the face of a single subject, extracting facial surface from a single image remains a difficult problem. As a result, single-image based methods can usually provide only a rough estimate of the facial geometry. In contrast, we propose to leverage the power of convolutional neural networks to produce a highly detailed face reconstruction from a single image. For this purpose, we introduce an end-to-end CNN framework which derives the shape in a coarse-to-fine fashion. The proposed architecture is composed of two main blocks, a network that recovers the coarse facial geometry (CoarseNet), followed by a CNN that refines the facial features of that geometry (FineNet). The proposed networks are connected by a novel layer which renders a depth image given a mesh in 3D. Unlike object recognition and detection problems, there are no suitable datasets for training CNNs to perform face geometry reconstruction. Therefore, our training regime begins with a supervised phase, based on synthetic images, followed by an unsupervised phase that uses only unconstrained facial images. The accuracy and robustness of the proposed model is demonstrated by both qualitative and quantitative evaluation tests.

Yoni Choukroun, Alon Shtern, Alex Bronstein et al.

Many shape analysis methods treat the geometry of an object as a metric space that can be captured by the Laplace-Beltrami operator. In this paper, we propose to adapt the classical Hamiltonian operator from quantum mechanics to the field of shape analysis. To this end we study the addition of a potential function to the Laplacian as a generator for dual spaces in which shape processing is performed. We present a general optimization approach for solving variational problems involving the basis defined by the Hamiltonian using perturbation theory for its eigenvectors. The suggested operator is shown to produce better functional spaces to operate with, as demonstrated on different shape analysis tasks.

Matan Sela, Nadav Toledo, Yaron Honen et al.

Sleep apnea is a syndrome that is characterized by sudden breathing halts while sleeping. One of the common treatments involves wearing a mask that delivers continuous air flow into the nostrils so as to maintain a steady air pressure. These masks are designed for an average facial model and are often difficult to adjust due to poor fit to the actual patient. The incompatibility is characterized by gaps between the mask and the face, which deteriorates the impermeability of the mask and leads to air leakage. We suggest a fully automatic approach for designing a personalized nasal mask interface using a facial depth scan. The interfaces generated by the proposed method accurately fit the geometry of the scanned face, and are easy to manufacture. The proposed method utilizes cheap commodity depth sensors and 3D printing technologies to efficiently design and manufacture customized masks for patients suffering from sleep apnea.

Matan Sela, Ron Kimmel

Independent component analysis (ICA) is a method for recovering statistically independent signals from observations of unknown linear combinations of the sources. Some of the most accurate ICA decomposition methods require searching for the inverse transformation which minimizes different approximations of the Mutual Information, a measure of statistical independence of random vectors. Two such approximations are the Kernel Generalized Variance or the Kernel Canonical Correlation which has been shown to reach the highest performance of ICA methods. However, the computational effort necessary just for computing these measures is cubic in the sample size. Hence, optimizing them becomes even more computationally demanding, in terms of both space and time. Here, we propose a couple of alternative novel measures based on randomized features of the samples - the Randomized Generalized Variance and the Randomized Canonical Correlation. The computational complexity of calculating the proposed alternatives is linear in the sample size and provide a controllable approximation of their Kernel-based non-random versions. We also show that optimization of the proposed statistical properties yields a comparable separation error at an order of magnitude faster compared to Kernel-based measures.

Alex Bronstein, Yoni Choukroun, Ron Kimmel et al.

The L1 norm has been tremendously popular in signal and image processing in the past two decades due to its sparsity-promoting properties. More recently, its generalization to non-Euclidean domains has been found useful in shape analysis applications. For example, in conjunction with the minimization of the Dirichlet energy, it was shown to produce a compactly supported quasi-harmonic orthonormal basis, dubbed as compressed manifold modes. The continuous L1 norm on the manifold is often replaced by the vector l1 norm applied to sampled functions. We show that such an approach is incorrect in the sense that it does not consistently discretize the continuous norm and warn against its sensitivity to the specific sampling. We propose two alternative discretizations resulting in an iteratively-reweighed l2 norm. We demonstrate the proposed strategy on the compressed modes problem, which reduces to a sequence of simple eigendecomposition problems not requiring non-convex optimization on Stiefel manifolds and producing more stable and accurate results.