Incremental Non-Rigid Structure-from-Motion with Unknown Focal Length

The perspective camera and the isometric surface prior have recently gathered increased attention for Non-Rigid Structure-from-Motion (NRSfM). Despite the recent progress, several challenges remain, particularly the computational complexity and the unknown camera focal length. In this paper we present a method for incremental Non-Rigid Structure-from-Motion (NRSfM) with the perspective camera model and the isometric surface prior with unknown focal length. In the template-based case, we provide a method to estimate four parameters of the camera intrinsics. For the template-less scenario of NRSfM, we propose a method to upgrade reconstructions obtained for one focal length to another based on local rigidity and the so-called Maximum Depth Heuristics (MDH). On its basis we propose a method to simultaneously recover the focal length and the non-rigid shapes. We further solve the problem of incorporating a large number of points and adding more views in MDH-based NRSfM and efficiently solve them with Second-Order Cone Programming (SOCP). This does not require any shape initialization and produces results orders of times faster than many methods. We provide evaluations on standard sequences with ground-truth and qualitative reconstructions on challenging YouTube videos. These evaluations show that our method performs better in both speed and accuracy than the state of the art.Comment: ECCV 201

Model-free Consensus Maximization for Non-Rigid Shapes

Many computer vision methods use consensus maximization to relate measurements containing outliers with the correct transformation model. In the context of rigid shapes, this is typically done using Random Sampling and Consensus (RANSAC) by estimating an analytical model that agrees with the largest number of measurements (inliers). However, small parameter models may not be always available. In this paper, we formulate the model-free consensus maximization as an Integer Program in a graph using `rules' on measurements. We then provide a method to solve it optimally using the Branch and Bound (BnB) paradigm. We focus its application on non-rigid shapes, where we apply the method to remove outlier 3D correspondences and achieve performance superior to the state of the art. Our method works with outlier ratio as high as 80\%. We further derive a similar formulation for 3D template to image matching, achieving similar or better performance compared to the state of the art.Comment: ECCV1

Eulerian on Lagrangian Cloth Simulation

This thesis introduces a novel Eulerian-on-Lagrangian (EoL) approach for simulating cloth. This approach allows for the simulation of traditionally difficult cloth scenarios, such as draping and sliding cloth over sharp features like the edge of a table. A traditional Lagrangian approach models a cloth as a series of connected nodes. These nodes are free to move in 3d space, but have difficulty with sliding over hard edges. The cloth cannot always bend smoothly around these edges, as motion can only occur at existing nodes. An EoL approach adds additional flexibility to a Lagrangian approach by constructing special Eulerian on Lagrangian nodes (EoL Nodes), where cloth material can pass through a fixed point. On contact with the edge of a box, EoL nodes are introduced directly on the edge. These nodes allow the cloth to bend exactly at the edge, and pass smoothly over the area while sliding. Using this ‘Eulerian-on-Lagrangian’ discretization, a set of rules for introducing and constraining EoL Nodes, and an adaptive remesher, This simulator allows cloth to move in a sliding motion over sharp edges. The current implementation is limited to cloth collision with static boxes, but the method presented can be expanded to include contact with more complicated meshes and dynamic rigid bodies

A Benchmark and Evaluation of Non-Rigid Structure from Motion

Non-Rigid structure from motion (NRSfM), is a long standing and central problem in computer vision, allowing us to obtain 3D information from multiple images when the scene is dynamic. A main issue regarding the further development of this important computer vision topic, is the lack of high quality data sets. We here address this issue by presenting of data set compiled for this purpose, which is made publicly available, and considerably larger than previous state of the art. To validate the applicability of this data set, and provide and investigation into the state of the art of NRSfM, including potential directions forward, we here present a benchmark and a scrupulous evaluation using this data set. This benchmark evaluates 16 different methods with available code, which we argue reasonably spans the state of the art in NRSfM. We also hope, that the presented and public data set and evaluation, will provide benchmark tools for further development in this field

Learning and recovering 3D surface deformations

Recovering the 3D deformations of a non-rigid surface from a single viewpoint has applications in many domains such as sports, entertainment, and medical imaging. Unfortunately, without any knowledge of the possible deformations that the object of interest can undergo, it is severely under-constrained, and extremely different shapes can have very similar appearances when reprojected onto an image plane. In this thesis, we first exhibit the ambiguities of the reconstruction problem when relying on correspondences between a reference image for which we know the shape and an input image. We then propose several approaches to overcoming these ambiguities. The core idea is that some a priori knowledge about how a surface can deform must be introduced to solve them. We therefore present different ways to formulate that knowledge that range from very generic constraints to models specifically designed for a particular object or material. First, we propose generally applicable constraints formulated as motion models. Such models simply link the deformations of the surface from one image to the next in a video sequence. The obvious advantage is that they can be used independently of the physical properties of the object of interest. However, to be effective, they require the presence of texture over the whole surface, and, additionally, do not prevent error accumulation from frame to frame. To overcome these weaknesses, we propose to introduce statistical learning techniques that let us build a model from a large set of training examples, that is, in our case, known 3D deformations. The resulting model then essentially performs linear or non-linear interpolation between the training examples. Following this approach, we first propose a linear global representation that models the behavior of the whole surface. As is the case with all statistical learning techniques, the applicability of this representation is limited by the fact that acquiring training data is far from trivial. A large surface can undergo many subtle deformations, and thus a large amount of training data must be available to build an accurate model. We therefore propose an automatic way of generating such training examples in the case of inextensible surfaces. Furthermore, we show that the resulting linear global models can be incorporated into a closed-form solution to the shape recovery problem. This lets us not only track deformations from frame to frame, but also reconstruct surfaces from individual images. The major drawback of global representations is that they can only model the behavior of a specific surface, which forces us to re-train a new model for every new shape, even though it is made of a material observed before. To overcome this issue, and simultaneously reduce the amount of required training data, we propose local deformation models. Such models describe the behavior of small portions of a surface, and can be combined to form arbitrary global shapes. For this purpose, we study both linear and non-linear statistical learning methods, and show that, whereas the latter are better suited for traking deformations from frame to frame, the former can also be used for reconstruction from a single image

Unsupervised Monocular Depth Reconstruction of Non-Rigid Scenes

Monocular depth reconstruction of complex and dynamic scenes is a highly challenging problem. While for rigid scenes learning-based methods have been offering promising results even in unsupervised cases, there exists little to no literature addressing the same for dynamic and deformable scenes. In this work, we present an unsupervised monocular framework for dense depth estimation of dynamic scenes, which jointly reconstructs rigid and non-rigid parts without explicitly modelling the camera motion. Using dense correspondences, we derive a training objective that aims to opportunistically preserve pairwise distances between reconstructed 3D points. In this process, the dense depth map is learned implicitly using the as-rigid-as-possible hypothesis. Our method provides promising results, demonstrating its capability of reconstructing 3D from challenging videos of non-rigid scenes. Furthermore, the proposed method also provides unsupervised motion segmentation results as an auxiliary output

Robotic manipulation of cloth: mechanical modeling and perception

(Eng) In this work we study various mathematical problems arising from the robotic manipulation of cloth. First, we develop a locking-free continuous model for the physical simulation of inextensible textiles. We present a novel 'finite element' discretization of our inextensibility constraints which results in a unified treatment of triangle and quadrilateral meshings of the cloth. Next, we explain how to incorporate contacts, self-collisions and friction into the equations of motion, so that frictional forces and inextensibility and collision constraints may be integrated implicitly and without any decoupling. We develop an efficient 'active-set' solver tailored to our non-linear problem which takes into account past active constraints to accelerate the resolution of unresolved contacts and moreover can be initialized from any non-necessarily feasible point. Then, we embark ourselves in the empirical validation of the developed model. We record in a laboratory setting --with depth cameras and motion capture systems-- the motions of seven types of textiles (including e.g. cotton, denim and polyester) of various sizes and at different speeds and end up with more than 80 recordings. The scenarios considered are all dynamic and involve rapid shaking and twisting of the textiles, collisions with frictional objects and even strong hits with a long stick. We then, compare the recorded textiles with the simulations given by our inextensible model, and find that on average the mean error is of the order of 1 cm even for the largest sizes (DIN A2) and the most challenging scenarios. Furthermore, we also tackle other problems relevant to robotic cloth manipulation, such as cloth perception and classification of its states. We present a reconstruction algorithm based on Morse theory that proceeds directly from a point-cloud to obtain a cellular decomposition of a surface with or without boundary: the results are a piecewise parametrization of the cloth surface as a union of Morse cells. From the cellular decomposition the topology of the surface can be then deduced immediately. Finally, we study the configuration space of a piece of cloth: since the original state of a piece of cloth is flat, the set of possible states under the inextensible assumption is the set of developable surfaces isometric to a fixed one. We prove that a generic simple, closed, piecewise regular curve in space can be the boundary of only finitely many developable surfaces with nonvanishing mean curvature. Inspired on this result we introduce the dGLI cloth coordinates, a low-dimensional representation of the state of a piece of cloth based on a directional derivative of the Gauss Linking Integral. These coordinates --computed from the position of the cloth's boundary-- allow to distinguish key qualitative changes in folding sequences.(Esp) En este trabajo estudiamos varios problemas matemáticos relacionados con la manipulación robótica de textiles. En primer lugar, desarrollamos un modelo continuo libre de 'locking' para la simulación física de textiles inextensibles. Presentamos una novedosa discretización usando 'elementos finitos' de nuestras restricciones de inextensibilidad resultando en un tratamiento unificado de mallados triangulares y cuadrangulares de la tela. A continuación, explicamos cómo incorporar contactos, autocolisiones y fricción en las ecuaciones de movimiento, de modo que las fuerzas de fricción y las restricciones de inextensibilidad y colisiones puedan integrarse implícitamente y sin ningún desacoplamiento. Desarrollamos un 'solver' de tipo 'conjunto-activo' adaptado a nuestro problema no lineal que tiene en cuenta las restricciones activas pasadas para acelerar la resolución de los contactos no resueltos y, además, puede inicializarse desde cualquier punto no necesariamente factible. Posteriormente, nos embarcamos en la validación empírica del modelo desarrollado. Grabamos en un entorno de laboratorio -con cámaras de profundidad y sistemas de captura de movimiento- los movimientos de siete tipos de textiles (entre los que se incluyen, por ejemplo, algodón, tela vaquera y poliéster) de varios tamaños y a diferentes velocidades, terminando con más de 80 grabaciones. Los escenarios considerados son todos dinámicos e implican sacudidas y torsiones rápidas de los textiles, colisiones con obstáculos e incluso golpes con una varilla cilíndrica. Finalmente, comparamos las grabaciones con las simulaciones dadas por nuestro modelo inextensible, y encontramos que, de media, el error es del orden de 1 cm incluso para las telas más grandes (DIN A2) y los escenarios más complicados. Además, también abordamos otros problemas relevantes para la manipulación robótica de telas, como son la percepción y la clasificación de sus estados. Presentamos un algoritmo de reconstrucción basado en la teoría de Morse que procede directamente de una nube de puntos para obtener una descomposición celular de una superficie con o sin borde: los resultados son una parametrización a trozos de la superficie de la tela como una unión de celdas de Morse. A partir de la descomposición celular puede deducirse inmediatamente la topología de la superficie. Por último, estudiamos el espacio de configuración de un trozo de tela: dado que el estado original de la tela es plano, el conjunto de estados posibles bajo la hipótesis de inextensibilidad es el conjunto de superficies desarrollables isométricas a una fija. Demostramos que una curva genérica simple, cerrada y regular a trozos en el espacio puede ser el borde de un número finito de superficies desarrollables con curvatura media no nula. Inspirándonos en este resultado, introducimos las coordenadas dGLI, una representación de dimensión baja del estado de un pedazo de tela basada en una derivada direccional de la integral de enlazamiento de Gauss. Estas coordenadas -calculadas a partir de la posición del borde de la tela- permiten distinguir cambios cualitativos clave en distintas secuencias de plegado.Postprint (published version

Robotic manipulation of cloth: mechanical modeling and perception

(Eng) In this work we study various mathematical problems arising from the robotic manipulation of cloth. First, we develop a locking-free continuous model for the physical simulation of inextensible textiles. We present a novel 'finite element' discretization of our inextensibility constraints which results in a unified treatment of triangle and quadrilateral meshings of the cloth. Next, we explain how to incorporate contacts, self-collisions and friction into the equations of motion, so that frictional forces and inextensibility and collision constraints may be integrated implicitly and without any decoupling. We develop an efficient 'active-set' solver tailored to our non-linear problem which takes into account past active constraints to accelerate the resolution of unresolved contacts and moreover can be initialized from any non-necessarily feasible point. Then, we embark ourselves in the empirical validation of the developed model. We record in a laboratory setting --with depth cameras and motion capture systems-- the motions of seven types of textiles (including e.g. cotton, denim and polyester) of various sizes and at different speeds and end up with more than 80 recordings. The scenarios considered are all dynamic and involve rapid shaking and twisting of the textiles, collisions with frictional objects and even strong hits with a long stick. We then, compare the recorded textiles with the simulations given by our inextensible model, and find that on average the mean error is of the order of 1 cm even for the largest sizes (DIN A2) and the most challenging scenarios. Furthermore, we also tackle other problems relevant to robotic cloth manipulation, such as cloth perception and classification of its states. We present a reconstruction algorithm based on Morse theory that proceeds directly from a point-cloud to obtain a cellular decomposition of a surface with or without boundary: the results are a piecewise parametrization of the cloth surface as a union of Morse cells. From the cellular decomposition the topology of the surface can be then deduced immediately. Finally, we study the configuration space of a piece of cloth: since the original state of a piece of cloth is flat, the set of possible states under the inextensible assumption is the set of developable surfaces isometric to a fixed one. We prove that a generic simple, closed, piecewise regular curve in space can be the boundary of only finitely many developable surfaces with nonvanishing mean curvature. Inspired on this result we introduce the dGLI cloth coordinates, a low-dimensional representation of the state of a piece of cloth based on a directional derivative of the Gauss Linking Integral. These coordinates --computed from the position of the cloth's boundary-- allow to distinguish key qualitative changes in folding sequences.(Esp) En este trabajo estudiamos varios problemas matemáticos relacionados con la manipulación robótica de textiles. En primer lugar, desarrollamos un modelo continuo libre de 'locking' para la simulación física de textiles inextensibles. Presentamos una novedosa discretización usando 'elementos finitos' de nuestras restricciones de inextensibilidad resultando en un tratamiento unificado de mallados triangulares y cuadrangulares de la tela. A continuación, explicamos cómo incorporar contactos, autocolisiones y fricción en las ecuaciones de movimiento, de modo que las fuerzas de fricción y las restricciones de inextensibilidad y colisiones puedan integrarse implícitamente y sin ningún desacoplamiento. Desarrollamos un 'solver' de tipo 'conjunto-activo' adaptado a nuestro problema no lineal que tiene en cuenta las restricciones activas pasadas para acelerar la resolución de los contactos no resueltos y, además, puede inicializarse desde cualquier punto no necesariamente factible. Posteriormente, nos embarcamos en la validación empírica del modelo desarrollado. Grabamos en un entorno de laboratorio -con cámaras de profundidad y sistemas de captura de movimiento- los movimientos de siete tipos de textiles (entre los que se incluyen, por ejemplo, algodón, tela vaquera y poliéster) de varios tamaños y a diferentes velocidades, terminando con más de 80 grabaciones. Los escenarios considerados son todos dinámicos e implican sacudidas y torsiones rápidas de los textiles, colisiones con obstáculos e incluso golpes con una varilla cilíndrica. Finalmente, comparamos las grabaciones con las simulaciones dadas por nuestro modelo inextensible, y encontramos que, de media, el error es del orden de 1 cm incluso para las telas más grandes (DIN A2) y los escenarios más complicados. Además, también abordamos otros problemas relevantes para la manipulación robótica de telas, como son la percepción y la clasificación de sus estados. Presentamos un algoritmo de reconstrucción basado en la teoría de Morse que procede directamente de una nube de puntos para obtener una descomposición celular de una superficie con o sin borde: los resultados son una parametrización a trozos de la superficie de la tela como una unión de celdas de Morse. A partir de la descomposición celular puede deducirse inmediatamente la topología de la superficie. Por último, estudiamos el espacio de configuración de un trozo de tela: dado que el estado original de la tela es plano, el conjunto de estados posibles bajo la hipótesis de inextensibilidad es el conjunto de superficies desarrollables isométricas a una fija. Demostramos que una curva genérica simple, cerrada y regular a trozos en el espacio puede ser el borde de un número finito de superficies desarrollables con curvatura media no nula. Inspirándonos en este resultado, introducimos las coordenadas dGLI, una representación de dimensión baja del estado de un pedazo de tela basada en una derivada direccional de la integral de enlazamiento de Gauss. Estas coordenadas -calculadas a partir de la posición del borde de la tela- permiten distinguir cambios cualitativos clave en distintas secuencias de plegado