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WalkTheDog Cross-Morphology Motion Alignment via Phase Manifolds We present a new approach for understanding the periodicity structure and semantics of motion datasets, independently of the morphology and skeletal structure of characters. Unlike existing methods using an overly sparse high-dimensional latent, we propose a phase manifold consisting of multiple closed... curves, each corresponding to a latent amplitude. With our proposed vector quantized periodic autoencoder, we learn a shared phase manifold for multiple characters, such as a human and a dog, without any supervision. This is achieved by exploiting the discrete structure and a shallow network as bottlenecks, such that semantically similar motions are clustered into the same curve of the manifold, and the motions within the same component are aligned temporally by the phase variable. In combination with an improved motion matching framework, we demonstrate the manifold's capability of timing and semantics alignment in several applications, including motion retrieval, transfer and stylization.show more

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27,569 views • 2 years ago •via X (Twitter)

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We are pleased to present a new lateral-view animation of the leg in motion. As the limb moves through extension and flexion, the active muscle groups light up. Now the challenge: can you name every muscle active in each phase? Most people miss at least one. #anatomystandard

We are pleased to present a new lateral-view animation of the leg in motion. As the limb moves through extension and flexion, the active muscle groups light up. Now the challenge: can you name every muscle active in each phase? Most people miss at least one. #anatomystandard

Anatomy Standard

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Meta releases VGGSfM Visual Geometry Grounded Deep Structure From Motion Structure-from-motion (SfM) is a long-standing problem in the computer vision community, which aims to reconstruct the camera poses and 3D structure of a scene from a set of unconstrained 2D images. Classical frameworks solve this problem in an incremental manner by detecting and matching keypoints, registering images, triangulating 3D points, and conducting bundle adjustment. Recent research efforts have predominantly revolved around harnessing the power of deep learning techniques to enhance specific elements (e.g., keypoint matching), but are still based on the original, non-differentiable pipeline. Instead, we propose a new deep SfM pipeline VGGSfM, where each component is fully differentiable and thus can be trained in an end-to-end manner. To this end, we introduce new mechanisms and simplifications. First, we build on recent advances in deep 2D point tracking to extract reliable pixel-accurate tracks, which eliminates the need for chaining pairwise matches. Furthermore, we recover all cameras simultaneously based on the image and track features instead of gradually registering cameras. Finally, we optimise the cameras and triangulate 3D points via a differentiable bundle adjustment layer. We attain state-of-the-art performance on three popular datasets, CO3D, IMC Phototourism, and ETH3D.

Meta releases VGGSfM Visual Geometry Grounded Deep Structure From Motion Structure-from-motion (SfM) is a long-standing problem in the computer vision community, which aims to reconstruct the camera poses and 3D structure of a scene from a set of unconstrained 2D images. Classical frameworks solve this problem in an incremental manner by detecting and matching keypoints, registering images, triangulating 3D points, and conducting bundle adjustment. Recent research efforts have predominantly revolved around harnessing the power of deep learning techniques to enhance specific elements (e.g., keypoint matching), but are still based on the original, non-differentiable pipeline. Instead, we propose a new deep SfM pipeline VGGSfM, where each component is fully differentiable and thus can be trained in an end-to-end manner. To this end, we introduce new mechanisms and simplifications. First, we build on recent advances in deep 2D point tracking to extract reliable pixel-accurate tracks, which eliminates the need for chaining pairwise matches. Furthermore, we recover all cameras simultaneously based on the image and track features instead of gradually registering cameras. Finally, we optimise the cameras and triangulate 3D points via a differentiable bundle adjustment layer. We attain state-of-the-art performance on three popular datasets, CO3D, IMC Phototourism, and ETH3D.

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The Thomas attractor is a mathematical concept in dynamical systems theory representing a type of chaotic space phase that exhibits cyclic symmetry. It was named after René Thomas, the mathematician who introduced it in 1979. The system is strictly related to the Lorenz attractor another famous chaotic evolutionary space manifold. The 3D Thomas attractor is represented by the combination of three differential equations where the symmetry is invariant under rotations of 120° (or 2π/3 radians) around the x y z axis which are the space coordinates, plus μ (mu) that is a parameter controlling the behavior. The attractor is characterized by a chaotic tendency and it’s sensitive to initial conditions, meaning that as μ increases, the motion undergoes period-doubling bifurcations leading to chaos. A good visualization of this spacetime manifold is a twisted, spiral-shaped structure with 3-fold symmetry where each spiral arm is symmetric with respect to the central axis, like the one displayed below. The chaotic evolution of this attractor demonstrates the geometric beauty and complexity of unpredictable systems.

The Thomas attractor is a mathematical concept in dynamical systems theory representing a type of chaotic space phase that exhibits cyclic symmetry. It was named after René Thomas, the mathematician who introduced it in 1979. The system is strictly related to the Lorenz attractor another famous chaotic evolutionary space manifold. The 3D Thomas attractor is represented by the combination of three differential equations where the symmetry is invariant under rotations of 120° (or 2π/3 radians) around the x y z axis which are the space coordinates, plus μ (mu) that is a parameter controlling the behavior. The attractor is characterized by a chaotic tendency and it’s sensitive to initial conditions, meaning that as μ increases, the motion undergoes period-doubling bifurcations leading to chaos. A good visualization of this spacetime manifold is a twisted, spiral-shaped structure with 3-fold symmetry where each spiral arm is symmetric with respect to the central axis, like the one displayed below. The chaotic evolution of this attractor demonstrates the geometric beauty and complexity of unpredictable systems.

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A closed outline shaped like the Greek letter pi can be rebuilt as the path of a point carried by a chain of rotating circles, each circle matching one frequency component through its radius and phase, so that successive circles refine the match to the original curve.

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Abu Obeida in a previous speech: We bless the operations of the sincere brothers, Ansar Allah, in dear Yemen, and their announcement of a new phase of confrontation with the enemy and support for Gaza, despite the blind, unjust threats and alliances.

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The Hidden Language of Diffusion Models paper page: tackle the challenge of understanding concept representations in text-to-image models by decomposing an input text prompt into a small set of interpretable elements. This is achieved by learning a pseudo-token that is a sparse weighted combination of tokens from the model's vocabulary, with the objective of reconstructing the images generated for the given concept. Applied over the state-of-the-art Stable Diffusion model, this decomposition reveals non-trivial and surprising structures in the representations of concepts. For example, we find that some concepts such as "a president" or "a composer" are dominated by specific instances (e.g., "Obama", "Biden") and their interpolations. Other concepts, such as "happiness" combine associated terms that can be concrete ("family", "laughter") or abstract ("friendship", "emotion"). In addition to peering into the inner workings of Stable Diffusion, our method also enables applications such as single-image decomposition to tokens, bias detection and mitigation, and semantic image manipulation

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Fighter jet pilot demonstrates centripetal force, a concept that Isaac Newton discovered between 1676 and 1677. However, the concept of centripetal force was not actually discovered in a single event or by a single individual but rather evolved over time through the works of multiple scientists and thinkers. Here is a brief history of the development of our understanding of centripetal force: Ancient Greece: The ancient Greeks, particularly philosophers such as Aristotle and later Archimedes, made observations and formulated theories about the motion of objects. However, they did not have a clear understanding of centripetal force as a distinct concept. Islamic Scholars: During the Islamic Golden Age, scholars such as Ibn Sina (Avicenna) and Ibn Bajjah (Avempace) made significant contributions to the understanding of motion. They discussed the idea of impetus, a precursor to the concept of centripetal force. Johannes Kepler: In the 17th century, Johannes Kepler, a German astronomer and mathematician, formulated his laws of planetary motion. Kepler's laws described the motion of planets around the sun and the concept of elliptical orbits. Although Kepler did not explicitly mention centripetal force, his work laid the foundation for later developments. Isaac Newton: In the late 17th century, Sir Isaac Newton, an English physicist and mathematician, published his groundbreaking work, "Mathematical Principles of Natural Philosophy" (also known as the Principia). In this work, Newton presented his laws of motion and the universal law of gravitation. Newton's laws, particularly the second law of motion, provided a mathematical understanding of centripetal force. He demonstrated that an object moving in a curved path experiences an inward force acting towards the center of the curve, which is now known as centripetal force. Further Developments: Following Newton's work, subsequent scientists, such as Jean le Rond d'Alembert and Daniel Bernoulli, expanded on the understanding of centripetal force in the context of mechanics and fluid dynamics. It's important to note that the discovery and understanding of centripetal force were gradual processes that involved the contributions of numerous individuals over centuries. The concept became firmly established with the development of Newtonian physics and its laws of motion.

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What if I told you any shape can be broken down into circles? This visualization demonstrates the stunning power of the Fourier Transform. By using a series of rotating vectors—known as epicycles—we can reconstruct complex, continuous paths from simple circular motions. Each circle represents a specific frequency, phase, and amplitude. When these rotating arrows are added together, the resulting "tip" traces out the intricate outline you see here. It’s where pure mathematics meets digital art, proving that even the most complex designs are just a symphony of oscillations. Credit: mathswithmuza

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