Given an image dataset, we are often interested in finding data generative factors that encode semantic content independently from pose variables such as rotation and translation. However, current disentanglement approaches do not impose any specific structure on the learned latent representations. We propose a method for explicitly disentangling image rotation and translation from other unstructured latent factors in a variational autoencoder (VAE) framework. By formulating the generative model as a function of the spatial coordinate, we make the reconstruction error differentiable with respect to latent translation and rotation parameters. This formulation allows us to train a neural network to perform approximate inference on these latent variables while explicitly constraining them to only represent rotation and translation. We demonstrate that this framework, termed spatial-VAE, effectively learns latent representations that disentangle image rotation and translation from content and improves reconstruction over standard VAEs on several benchmark datasets, including applications to modeling continuous 2-D views of proteins from single particle electron microscopy and galaxies in astronomical images.

In many imaging modalities, objects of interest can occur in a variety of locations and poses (i.e. are subject to translations and rotations in 2d or 3d), but the location and pose of an object does not change its semantics (i.e. the object's essence). That is, the specific location and rotation of an airplane in satellite imagery, or the 3d rotation of a chair in a natural image, or the rotation of a particle in a cryo-electron micrograph, do not change the intrinsic nature of those objects. Here, we consider the problem of learning semantic representations of objects that are invariant to pose and location in a fully unsupervised manner. We address shortcomings in previous approaches to this problem by introducing TARGET-VAE, a translation and rotation group-equivariant variational autoencoder framework.

We introduce a solid harmonic wavelet scattering representation, invariant to rigid motion and stable to deformations, for regression and classification of 2D and 3D signals. Solid harmonic wavelets are computed by multiplying solid harmonic functions with Gaussian windows dilated at different scales. Invariant scattering coefficients are obtained by cascading such wavelet transforms with the complex modulus nonlinearity.

Humanoids operating in real-world workspaces must frequently execute task-driven, short-range movements to SE(2) target poses. To be practical, these transitions must be fast, robust, and energy efficient. While learning-based locomotion has made significant progress, most existing methods optimize for velocity-tracking rather than direct pose reaching, resulting in inefficient, marching-style behavior when applied to short-range tasks. In this work, we develop a reinforcement learning approach that directly optimizes humanoid locomotion for SE(2) targets. Central to this approach is a new constellation-based reward function that encourages natural and efficient target-oriented movement. To evaluate performance, we introduce a benchmarking framework that measures energy consumption, time-to-target, and footstep count on a distribution of SE(2) goals. Our results show that the proposed approach consistently outperforms standard methods and enables successful transfer from simulation to hardware, highlighting the importance of targeted reward design for practical short-range humanoid locomotion.

Precise needle alignment is essential for percutaneous needle insertion in robotic ultrasound-guided procedures. However, inherent challenges such as speckle noise, needle-like artifacts, and low image resolution make robust needle detection difficult, particularly when visibility is reduced or lost. In this paper, we propose a method to restore needle alignment when the ultrasound imaging plane and the needle insertion plane are misaligned. Unlike many existing approaches that rely heavily on needle visibility in ultrasound images, our method uses a more robust feature by periodically vibrating the needle using a mechanical system. Specifically, we propose a vibration-based energy metric that remains effective even when the needle is fully out of plane. Using this metric, we develop a control strategy to reposition the ultrasound probe in response to misalignments between the imaging plane and the needle insertion plane in both translation and rotation. Experiments conducted on ex-vivo porcine tissue samples using a dual-arm robotic ultrasound-guided needle insertion system demonstrate the effectiveness of the proposed approach. The experimental results show the translational error of 0.41$\pm$0.27 mm and the rotational error of 0.51$\pm$0.19 degrees.

In many imaging modalities, objects of interest can occur in a variety of locations and poses (i.e. are subject to translations and rotations in 2d or 3d), but the location and pose of an object does not change its semantics (i.e. the object's essence). That is, the specific location and rotation of an airplane in satellite imagery, or the 3d rotation of a chair in a natural image, or the rotation of a particle in a cryo-electron micrograph, do not change the intrinsic nature of those objects. Here, we consider the problem of learning semantic representations of objects that are invariant to pose and location in a fully unsupervised manner. We address shortcomings in previous approaches to this problem by introducing TARGET-VAE, a translation and rotation group-equivariant variational autoencoder framework. In comprehensive experiments, we show that TARGET-VAE learns disentangled representations without supervision that significantly improve upon, and avoid the pathologies of, previous methods.

Given an image dataset, we are often interested in finding data generative factors that encode semantic content independently from pose variables such as rotation and translation. However, current disentanglement approaches do not impose any specific structure on the learned latent representations. We propose a method for explicitly disentangling image rotation and translation from other unstructured latent factors in a variational autoencoder (VAE) framework. By formulating the generative model as a function of the spatial coordinate, we make the reconstruction error differentiable with respect to latent translation and rotation parameters. This formulation allows us to train a neural network to perform approximate inference on these latent variables while explicitly constraining them to only represent rotation and translation. We demonstrate that this framework, termed spatial-VAE, effectively learns latent representations that disentangle image rotation and translation from content and improves reconstruction over standard VAEs on several benchmark datasets, including applications to modeling continuous 2-D views of proteins from single particle electron microscopy and galaxies in astronomical images.

We introduce a solid harmonic wavelet scattering representation, invariant to rigid motion and stable to deformations, for regression and classification of 2D and 3D signals. Solid harmonic wavelets are computed by multiplying solid harmonic functions with Gaussian windows dilated at different scales. Invariant scattering coefficients are obtained by cascading such wavelet transforms with the complex modulus nonlinearity. We study an application of solid harmonic scattering invariants to the estimation of quantum molecular energies, which are also invariant to rigid motion and stable with respect to deformations. A multilinear regression over scattering invariants provides close to state of the art results over small and large databases of organic molecules.

Concentric Tube Robots (CTRs) have garnered significant interest within the surgical robotics community because of their flexibility, dexterity, and ease of miniaturization. However, mastering the unique kinematics and design principles of CTRs can be challenging for newcomers to the field. In this paper, we present an educational kit aimed at lowering the barriers to entry into concentric tube robot research. Our goal is to provide accessible learning resources for CTRs, bridging the knowledge gap between traditional robotic arms and these specialized devices. The proposed kit includes (1) An open-source design and assembly instructions for an economical (cost of materials $\approx$ 700 USD) modular CTR; (2) A set of self-study materials to learn the basics of CTR modeling and control, including automatically-graded assignments. To evaluate the effectiveness of our educational kit, we conducted a human subjects study involving first-year graduate students in engineering. Over a four-week period, participants -- none of whom had any prior knowledge of concentric tube robots -- successfully built their first CTR using the provided materials, implemented the robot's kinematics in MATLAB, and conducted a tip-tracking experiment with an optical tracking device. Our findings suggest that the proposed kit facilitates learning and hands-on experience with CTRs, and furthermore, it has the potential to help early-stage graduate students get rapidly started with CTR research. By disseminating these resources, we hope to broaden participation in concentric tube robot research to a wider a more diverse group of researchers.