arXiv subjects

Lev Markhasin

Publications and source records attributed to Lev Markhasin.

15 recordsLinked to original sources

arXiv2025

EgoAnimate: Generating Human Animations from Egocentric top-down Views

An ideal digital telepresence experience requires accurate replication of a person's body, clothing, and movements. To capture and transfer these movements into virtual reality, the egocentric (first-person) perspective can be adopted, which enables the use of a portable and cost-effective device without front-view cameras. However, this viewpoint introduces challenges such as occlusions and distorted body proportions. There are few works reconstructing human appearance from egocentric views, and none use a generative prior-based approach. Some methods create avatars from a single egocentric image during inference, but still rely on multi-view datasets during training. To our knowledge, this is the first study using a generative backbone to reconstruct animatable avatars from egocentric inputs. Based on Stable Diffusion, our method reduces training burden and improves generalizability. Inspired by methods such as SiTH and MagicMan, which perform 360-degree reconstruction from a frontal image, we introduce a pipeline that generates realistic frontal views from occluded top-down images using ControlNet and a Stable Diffusion backbone. Our goal is to convert a single top-down egocentric image into a realistic frontal representation and feed it into an image-to-motion model. This enables generation of avatar motions from minimal input, paving the way for more accessible and generalizable telepresence systems.

cs.CV↗

arXiv2024

QMC integration based on arbitrary (t,m,s)-nets yields optimal convergence rates on several scales of function spaces

We study the integration problem over the $s$-dimensional unit cube on four types of Banach spaces of integrands. First we consider Haar wavelet spaces, consisting of functions whose Haar wavelet coefficients exhibit a certain decay behavior measured by a parameter $\alpha >0$. We study the worst case error of integration over the norm unit ball and provide upper error bounds for quasi-Monte Carlo (QMC) cubature rules based on arbitrary $(t,m,s)$-nets as well as matching lower error bounds for arbitrary cubature rules. These results show that using arbitrary $(t,m,s)$-nets as sample points yields the best possible rate of convergence. Afterwards we study spaces of integrands of fractional smoothness $\alpha \in (0,1)$ and state a sharp Koksma-Hlawka-type inequality. More precisely, we show that on those spaces the worst case error of integration is equal to the corresponding fractional discrepancy. Those spaces can be continuously embedded into tensor product Bessel potential spaces, also known as Sobolev spaces of dominated mixed smoothness, with the same set of parameters. The latter spaces can be embedded into suitable Besov spaces of dominating mixed smoothness $\alpha$, which in turn can be embedded into the Haar wavelet spaces with the same set of parameters. Therefore our upper error bounds on Haar wavelet spaces for QMC cubatures based on $(t,m,s)$-nets transfer (with possibly different constants) to the corresponding spaces of integrands of fractional smoothness and to Sobolev and Besov spaces of dominating mixed smoothness. Moreover, known lower error bounds for periodic Sobolev and Besov spaces of dominating mixed smoothness show that QMC integration based on arbitrary $(t,m,s)$-nets yields the best possible convergence rate on periodic as well as on non-periodic Sobolev and Besov spaces of dominating smoothness.

math.NA↗

arXiv2023

DPHMs: Diffusion Parametric Head Models for Depth-based Tracking

We introduce Diffusion Parametric Head Models (DPHMs), a generative model that enables robust volumetric head reconstruction and tracking from monocular depth sequences. While recent volumetric head models, such as NPHMs, can now excel in representing high-fidelity head geometries, tracking and reconstructing heads from real-world single-view depth sequences remains very challenging, as the fitting to partial and noisy observations is underconstrained. To tackle these challenges, we propose a latent diffusion-based prior to regularize volumetric head reconstruction and tracking. This prior-based regularizer effectively constrains the identity and expression codes to lie on the underlying latent manifold which represents plausible head shapes. To evaluate the effectiveness of the diffusion-based prior, we collect a dataset of monocular Kinect sequences consisting of various complex facial expression motions and rapid transitions. We compare our method to state-of-the-art tracking methods and demonstrate improved head identity reconstruction as well as robust expression tracking.

cs.CV↗

arXiv2023

DiffuScene: Denoising Diffusion Models for Generative Indoor Scene Synthesis

We present DiffuScene for indoor 3D scene synthesis based on a novel scene configuration denoising diffusion model. It generates 3D instance properties stored in an unordered object set and retrieves the most similar geometry for each object configuration, which is characterized as a concatenation of different attributes, including location, size, orientation, semantics, and geometry features. We introduce a diffusion network to synthesize a collection of 3D indoor objects by denoising a set of unordered object attributes. Unordered parametrization simplifies and eases the joint distribution approximation. The shape feature diffusion facilitates natural object placements, including symmetries. Our method enables many downstream applications, including scene completion, scene arrangement, and text-conditioned scene synthesis. Experiments on the 3D-FRONT dataset show that our method can synthesize more physically plausible and diverse indoor scenes than state-of-the-art methods. Extensive ablation studies verify the effectiveness of our design choice in scene diffusion models.

cs.CV↗

arXiv2022

Neural Shape Deformation Priors

We present Neural Shape Deformation Priors, a novel method for shape manipulation that predicts mesh deformations of non-rigid objects from user-provided handle movements. State-of-the-art methods cast this problem as an optimization task, where the input source mesh is iteratively deformed to minimize an objective function according to hand-crafted regularizers such as ARAP. In this work, we learn the deformation behavior based on the underlying geometric properties of a shape, while leveraging a large-scale dataset containing a diverse set of non-rigid deformations. Specifically, given a source mesh and desired target locations of handles that describe the partial surface deformation, we predict a continuous deformation field that is defined in 3D space to describe the space deformation. To this end, we introduce transformer-based deformation networks that represent a shape deformation as a composition of local surface deformations. It learns a set of local latent codes anchored in 3D space, from which we can learn a set of continuous deformation functions for local surfaces. Our method can be applied to challenging deformations and generalizes well to unseen deformations. We validate our approach in experiments using the DeformingThing4D dataset, and compare to both classic optimization-based and recent neural network-based methods.

cs.CV↗

arXiv2021

TAFIM: Targeted Adversarial Attacks against Facial Image Manipulations

Face manipulation methods can be misused to affect an individual's privacy or to spread disinformation. To this end, we introduce a novel data-driven approach that produces image-specific perturbations which are embedded in the original images. The key idea is that these protected images prevent face manipulation by causing the manipulation model to produce a predefined manipulation target (uniformly colored output image in our case) instead of the actual manipulation. In addition, we propose to leverage differentiable compression approximation, hence making generated perturbations robust to common image compression. In order to prevent against multiple manipulation methods simultaneously, we further propose a novel attention-based fusion of manipulation-specific perturbations. Compared to traditional adversarial attacks that optimize noise patterns for each image individually, our generalized model only needs a single forward pass, thus running orders of magnitude faster and allowing for easy integration in image processing stacks, even on resource-constrained devices like smartphones.

cs.CV↗

arXiv2016

Discrepancy of second order digital sequences in function spaces with dominating mixed smoothness

The discrepancy function measures the deviation of the empirical distribution of a point set in $[0,1]^d$ from the uniform distribution. In this paper, we study the classical discrepancy function with respect to the BMO and exponential Orlicz norms, as well as Sobolev, Besov and Triebel-Lizorkin norms with dominating mixed smoothness. We give sharp bounds for the discrepancy function under such norms with respect to infinite sequences.

math.NT↗

arXiv2016

Optimal $L_p$-discrepancy bounds for second order digital sequences

The $L_p$-discrepancy is a quantitative measure for the irregularity of distribution modulo one of infinite sequences. In 1986 Proinov proved for all $p>1$ a lower bound for the $L_p$-discrepancy of general infinite sequences in the $d$-dimensional unit cube, but it remained an open question whether this lower bound is best possible in the order of magnitude until recently. In 2014 Dick and Pillichshammer gave a first construction of an infinite sequence whose order of $L_2$-discrepancy matches the lower bound of Proinov. Here we give a complete solution to this problem for all finite $p > 1$. We consider so-called order $2$ digital $(t,d)$-sequences over the finite field with two elements and show that such sequences achieve the optimal order of $L_p$-discrepancy simultaneously for all $p \in (1,\infty)$.

math.NT↗

arXiv2015

Optimal quasi-Monte Carlo rules on order 2 digital nets for the numerical integration of multivariate periodic functions

We investigate quasi-Monte Carlo rules for the numerical integration of multivariate periodic functions from Besov spaces $S^r_{p,q}B(\mathbb{T}^d)$ with dominating mixed smoothness $1/p<r<2$. We show that order 2 digital nets achieve the optimal rate of convergence $N^{-r} (\log N)^{(d-1)(1-1/q)}$. The logarithmic term does not depend on $r$ and hence improves the known bound provided by J. Dick for the special case of Sobolev spaces $H^r_{\text{mix}}(\mathbb{T}^d)$. Secondly, the rate of convergence is independent of the integrability $p$ of the Besov space, which allows for sacrificing integrability in order to gain Besov regularity. Our method combines characterizations of periodic Besov spaces with dominating mixed smoothness via Faber bases with sharp estimates of Haar coefficients for the discrepancy function of higher order digital nets. Moreover, we provide numerical computations which indicate that this bound also holds for the case $r=2$.

math.NA↗

arXiv2014

BMO and exponential Orlicz space estimates of the discrepancy function in arbitrary dimension

In the current paper we obtain discrepancy estimates in exponential Orlicz and BMO spaces in arbitrary dimension $d \ge 3$. In particular, we use dyadic harmonic analysis to prove that for the so-called digital nets of order $2$ the BMO${}^d$ and $\exp \big( L^{2/(d-1)} \big)$ norms of the discrepancy function are bounded above by $(\log N)^{\frac{d-1}{2}}$. The latter bound has been recently conjectured in several papers and is consistent with the best known low-discrepancy constructions. Such estimates play an important role as an intermediate step between the well-understood $L_p$ bounds and the notorious open problem of finding the precise $L_\infty$ asymptotics of the discrepancy function in higher dimensions, which is still elusive.

math.FA↗

arXiv2014

L_p- and S_{p,q}^rB-discrepancy of (order 2) digital nets

Dick proved that all order $2$ digital nets satisfy optimal upper bounds of the $L_2$-discrepancy. We give an alternative proof for this fact using Haar bases. Furthermore, we prove that all digital nets satisfy optimal upper bounds of the $S_{p,q}^r B$-discrepancy for a certain parameter range and enlarge that range for order $2$ digitals nets. $L_p$-, $S_{p,q}^r F$- and $S_p^r H$-discrepancy is considered as well.

math.NA↗

arXiv2013

Discrepancy and integration in function spaces with dominating mixed smoothness

Optimal lower bounds for discrepancy in Besov spaces with dominating mixed smoothness are known from the work of Triebel. Hinrichs proved upper bounds in the plane. In this work we systematically analyse the problem, starting with a survey of discrepancy results and the calculation of the best known constant in Roth's Theorem. We give a larger class of point sets satisfying the optimal upper bounds than already known from Hinrichs for the plane and solve the problem in arbitrary dimension for certain parameters considering a celebrated constructions by Chen and Skriganov which are known to achieve optimal $L_2$-norm of the discrepancy function. Since those constructions are $b$-adic, we give $b$-adic characterizations of the spaces. Finally results for Triebel-Lizorkin and Sobolev spaces with dominating mixed smoothness and for the integration error are concluded.

math.NA↗

arXiv2012

Quasi-Monte Carlo methods for integration of functions with dominating mixed smoothness in arbitrary dimension

In a celebrated construction, Chen and Skriganov gave explicit examples of point sets achieving the best possible $L_2$-norm of the discrepancy function. We consider the discrepancy function of the Chen-Skriganov point sets in Besov spaces with dominating mixed smoothness and show that they also achieve the best possible rate in this setting. The proof uses a $b$-adic generalization of the Haar system and corresponding characterizations of the Besov space norm. Results for further function spaces and integration errors are concluded.

math.NA↗

arXiv2011

Discrepancy of generalized Hammersley type point sets in Besov spaces of dominating mixed smoothness

The symmetrized Hammersley point set is known to achieve the best possible rate for the $L_2$-norm of the discrepancy function. Also lower bounds for the norm in Besov spaces of dominating mixed smoothness are known. In this paper a large class of point sets which are generalizations of the Hammersley type point sets are proved to asymptotically achieve the known lower bound of the Besov norm. The proof uses a $b$-adic generalization of the Haar system. This result can be regarded as a preparation for the proof in arbitrary dimension.

math.NA↗

arXiv2010

On lower bounds for the L_2-discrepancy

The L_2-discrepancy measures the irregularity of the distribution of a finite point set. In this note we prove lower bounds for the L_2 discrepancy of arbitrary N-point sets. Our main focus is on the two-dimensional case. Asymptotic upper and lower estimates of the L_2-discrepancy in dimension 2 are well-known and are of the sharp order sqrt(log N). Nevertheless the gap in the constants between the best known lower and upper bounds is unsatisfactory large for a two-dimensional problem. Our lower bound improves upon this situation considerably. The main method is an adaption of the method of K. F. Roth using the Fourier coefficients of the discrepancy function with respect to the Haar basis.

math.NA↗