Lev Markhasin

Jiapeng Tang, Yinyu Nie, Lev Markhasin et al.

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.

Jiapeng Tang, Lev Markhasin, Bi Wang et al.

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.

Aicke Hinrichs, Lev Markhasin

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.

Lev Markhasin

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.

Shivangi Aneja, Lev Markhasin, Matthias Niessner

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.

Dmitriy Bilyk, Lev Markhasin

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.