SearcharxivSearch

arXiv subjects

Youngho Yoon

Publications and source records attributed to Youngho Yoon.

At least 19 recordsLinked to original sources

FrozenDrive: Zero-Shot Text-Guided Driving Scene Generation and Data Augmentation with Parameter-Free Frozen Diffusion Model

Synthetic data for autonomous driving is surging, powered by diffusion models that promise scalable scene generation. Yet key obstacles remain, as enforcing multi-view and temporal consistency often relies on backbone fine-tuning or added layers, which erodes pre-trained knowledge and weakens text alignment. Models also stay close to the training distribution, struggling under adverse weather and unseen configurations, and fidelity favors frequent over rare classes. We address these gaps with FrozenDrive, a controllable generative framework that preserves a pretrained diffusion models knowledge while achieving strong consistency. FrozenDrive conditions on rich driving-stack signals and text prompts, and introduces knowledge-preserving spatio-temporal attention to impose cross-view alignment and temporal coherence in a single pass within a parameter-free frozen diffusion backbone. An additional object-focused constraint improves per-object fidelity for rare categories. Without any weather- or scene-specific fine-tuning, our model synthesizes globally coherent multi-view driving scenes from text, particularly under adverse and rare conditions, and surpasses prior baselines. On nuScenes, FrozenDrive augmented data significantly improves AD models performance, especially at night and in rain, demonstrating stronger robustness when trained with our scenario-targeted data.

cs.CV

Spectrum of cones of projective hypersurfaces with singularities isolated

Let $Z$ be a projective hypersurface such that its underlying reduced variety has only isolated singularities. In case its irreducible components have constant multiplicities, for instance if $\dim Z>1$, we show that the spectrum of its cone can be described by using the spectral numbers at singular points of the reduced hypersurface and the global degree. In the non-reduced plane curve case, assuming that the underlying reduced curve has only semi-weighted-homogeneous singularities, we express the spectrum of the cone in terms of the local weights and the weighted degrees and multiplicities of local irreducible components together with the degrees and multiplicities of global ones. These generalize a formula for reduced line arrangements. In the non-reduced ordinary (that is, semi-homogeneous) singularity case, the second formula is essentially equivalent to the one obtained by the third-named author.

math.AG

Robust Adverse Weather Removal via Spectral-based Spatial Grouping

Adverse weather conditions cause diverse and complex degradation patterns, driving the development of All-in-One (AiO) models. However, recent AiO solutions still struggle to capture diverse degradations, since global filtering methods like direct operations on the frequency domain fail to handle highly variable and localized distortions. To address these issue, we propose Spectral-based Spatial Grouping Transformer (SSGformer), a novel approach that leverages spectral decomposition and group-wise attention for multi-weather image restoration. SSGformer decomposes images into high-frequency edge features using conventional edge detection and low-frequency information via Singular Value Decomposition. We utilize multi-head linear attention to effectively model the relationship between these features. The fused features are integrated with the input to generate a grouping-mask that clusters regions based on the spatial similarity and image texture. To fully leverage this mask, we introduce a group-wise attention mechanism, enabling robust adverse weather removal and ensuring consistent performance across diverse weather conditions. We also propose a Spatial Grouping Transformer Block that uses both channel attention and spatial attention, effectively balancing feature-wise relationships and spatial dependencies. Extensive experiments show the superiority of our approach, validating its effectiveness in handling the varied and intricate adverse weather degradations.

cs.CV

Synchronizing Task Behavior: Aligning Multiple Tasks during Test-Time Training

Generalizing neural networks to unseen target domains is a significant challenge in real-world deployments. Test-time training (TTT) addresses this by using an auxiliary self-supervised task to reduce the domain gap caused by distribution shifts between the source and target. However, we find that when models are required to perform multiple tasks under domain shifts, conventional TTT methods suffer from unsynchronized task behavior, where the adaptation steps needed for optimal performance in one task may not align with the requirements of other tasks. To address this, we propose a novel TTT approach called Synchronizing Tasks for Test-time Training (S4T), which enables the concurrent handling of multiple tasks. The core idea behind S4T is that predicting task relations across domain shifts is key to synchronizing tasks during test time. To validate our approach, we apply S4T to conventional multi-task benchmarks, integrating it with traditional TTT protocols. Our empirical results show that S4T outperforms state-of-the-art TTT methods across various benchmarks.

cs.LG

Tjurina spectrum and graded symmetry of missing spectral numbers

For a hypersurface isolated singularity defined by a convergent power series $f$, the Steenbrink spectrum can be defined as the Poincar\'e polynomial of the graded quotients of the $V$-filtration on the Jacobian ring of $f$. The Tjurina subspectrum is defined by replacing the Jacobian ring with its quotient by the image of the multiplication by $f$. We prove that their difference (consisting of missing spectral numbers) has a canonical graded symmetry. This follows from the self-duality of the Jacobian ring, which is compatible with the action of $f$ as well as the $V$-filtration. It implies for instance that the number of missing spectral numbers which are smaller than $(n{+}1)/2$ (with $n$ the number of variables) is bounded by $[(\mu{-}\tau)/2]$. We can moreover improve the estimate of Brian\c{c}on-Skoda exponent in the semisimple monodromy case.

math.AG

GMT: Enhancing Generalizable Neural Rendering via Geometry-Driven Multi-Reference Texture Transfer

Novel view synthesis (NVS) aims to generate images at arbitrary viewpoints using multi-view images, and recent insights from neural radiance fields (NeRF) have contributed to remarkable improvements. Recently, studies on generalizable NeRF (G-NeRF) have addressed the challenge of per-scene optimization in NeRFs. The construction of radiance fields on-the-fly in G-NeRF simplifies the NVS process, making it well-suited for real-world applications. Meanwhile, G-NeRF still struggles in representing fine details for a specific scene due to the absence of per-scene optimization, even with texture-rich multi-view source inputs. As a remedy, we propose a Geometry-driven Multi-reference Texture transfer network (GMT) available as a plug-and-play module designed for G-NeRF. Specifically, we propose ray-imposed deformable convolution (RayDCN), which aligns input and reference features reflecting scene geometry. Additionally, the proposed texture preserving transformer (TP-Former) aggregates multi-view source features while preserving texture information. Consequently, our module enables direct interaction between adjacent pixels during the image enhancement process, which is deficient in G-NeRF models with an independent rendering process per pixel. This addresses constraints that hinder the ability to capture high-frequency details. Experiments show that our plug-and-play module consistently improves G-NeRF models on various benchmark datasets.

cs.CV

Some remarks on the generalized Hertling conjecture for Tjurina spectrum

We study the original version of the generalized Hertling conjecture on the variance of the Tjurina spectral numbers, which was proposed by Shi, Wang, and Zuo, and provide a sufficient condition for the original conjecture to fail, employing a theorem of Hertling in an essential way. We calculate certain examples using some codes in Singular.

math.AG

Spectrum of non-degenerate functions with simplicial Newton polytopes

We show a precise proof of Steenbrink's formula for the spectrum of convenient Newton non-degenerate functions, and prove the symmetry of combinatorial polynomials in the simplicial case. Combined with the modified Steenbrink conjecture for spectral pairs (that is, weighted spectrum) which is recently proved in that case, this simplifies quite a lot of their calculations in such a case. We also introduce the $Γ$-spectrum of simplicial convenient non-degenerate functions as a first approximation of the spectrum, generalizing Arnold's picture in the 2 variable case. Analyzing their difference, we can find simple formulas for weighted spectrum in the 3 or 4 variable case. This is proved by using the symmetry of combinatorial polynomials, and fails in the non-simplicial case. Combining these with the Yomdin-Steenbrink formula for the spectrum, we can prove a formula for the spectrum of certain non-isolated surface singularities with simplicial non-degenerate Newton boundaries. As a byproduct of these arguments, we find an example where the Yomdin-Steenbrink formula for spectral pairs does not hold because of fusions of compact faces under projections.

math.AG

Briançon-Skoda exponents and the maximal root of reduced Bernstein-Sato polynomials

For a holomorphic function $f$ on a complex manifold $X$, the Briançon-Skoda exponent $e^{\rm BS}(f)$ is the smallest integer $k$ with $f^k\in(\partial f)$ (replacing $X$ with a neighborhood of $f^{-1}(0)$), where $(\partial f)$ denotes the Jacobian ideal of $f$. It is shown that $e^{\rm BS}(f)\le d_X$ $(:=\dim X)$ by Brian\c con-Skoda. We prove that $e^{\rm BS}(f)\le[d_X-2\widetildeα_f]+1$ with $-\widetildeα_f$ the maximal root of the reduced Bernstein-Sato polynomial $b_f(s)/(s+1)$, assuming the latter exists (shrinking $X$ if necessary). This implies for instance that $e^{\rm BS}(f)\le d_X-2$ in the case $f^{-1}(0)$ has only rational singularities, that is, if $\widetildeα_f>1$.

math.CV

Higher Du Bois singularities of hypersurfaces

For a complex algebraic variety $X$, we introduce higher $p$-Du Bois singularity by imposing canonical isomorphisms between the sheaves of Kähler differential forms $Ω_X^q$ and the shifted graded pieces of the Du Bois complex $\underlineΩ_X^q$ for $q\le p$. If $X$ is a reduced hypersurface, we show that higher $p$-Du~Bois singularity coincides with higher $p$-log canonical singularity, generalizing a well-known theorem for $p=0$. The assertion that $p$-log canonicity implies $p$-Du Bois has been proved by Mustata, Olano, Popa, and Witaszek quite recently as a corollary of two theorems asserting that the sheaves of reflexive differential forms $Ω_X^{[q]}$ ($q\le p$) coincide with $Ω_X^q$ and $\underlineΩ_X^q$ respectively, and these are shown by calculating the depth of the latter two sheaves. We construct explicit isomorphisms between $Ω_X^q$ and $\underlineΩ_X^q$ applying the acyclicity of a Koszul complex in a certain range. We also improve some non-vanishing assertion shown by them using mixed Hodge modules and the Tjurina subspectrum in the isolated singularity case. This is useful for instance to estimate the lower bound of the maximal root of the reduced Bernstein-Sato polynomial in the case where a quotient singularity is a hypersurface and its singular locus has codimension at most 4.

math.AG

Hodge ideals and spectrum of isolated hypersurface singularities

We introduce Hodge ideal spectrum for isolated hypersurface singularities to see the difference between the Hodge ideals and the microlocal $V$-filtration modulo the Jacobian ideal. Via the Tjurina subspectrum, we can compare the Hodge ideal spectrum with the Steenbrink spectrum which can be defined by the microlocal $V$-filtration. As a consequence of a formula of Mustata and Popa, these two spectra coincide in the weighted homogeneous case. We prove sufficient conditions for their coincidence and non-coincidence in some non-weighted-homogeneous cases where the defining function is semi-weighted-homogeneous or with non-degenerate Newton boundary in most cases. We also show that the convenience condition can be avoided in a formula of Zhang for the non-degenerate case, and present an example where the Hodge ideals are not weakly decreasing even modulo the Jacobian ideal.

math.AG

SphereSR: 360° Image Super-Resolution with Arbitrary Projection via Continuous Spherical Image Representation

The 360°imaging has recently gained great attention; however, its angular resolution is relatively lower than that of a narrow field-of-view (FOV) perspective image as it is captured by using fisheye lenses with the same sensor size. Therefore, it is beneficial to super-resolve a 360°image. Some attempts have been made but mostly considered the equirectangular projection (ERP) as one of the way for 360°image representation despite of latitude-dependent distortions. In that case, as the output high-resolution(HR) image is always in the same ERP format as the low-resolution (LR) input, another information loss may occur when transforming the HR image to other projection types. In this paper, we propose SphereSR, a novel framework to generate a continuous spherical image representation from an LR 360°image, aiming at predicting the RGB values at given spherical coordinates for super-resolution with an arbitrary 360°image projection. Specifically, we first propose a feature extraction module that represents the spherical data based on icosahedron and efficiently extracts features on the spherical surface. We then propose a spherical local implicit image function (SLIIF) to predict RGB values at the spherical coordinates. As such, SphereSR flexibly reconstructs an HR image under an arbitrary projection type. Experiments on various benchmark datasets show that our method significantly surpasses existing methods.

cs.CV

Pixel-wise Deep Image Stitching

Image stitching aims at stitching the images taken from different viewpoints into an image with a wider field of view. Existing methods warp the target image to the reference image using the estimated warp function, and a homography is one of the most commonly used warping functions. However, when images have large parallax due to non-planar scenes and translational motion of a camera, the homography cannot fully describe the mapping between two images. Existing approaches based on global or local homography estimation are not free from this problem and suffer from undesired artifacts due to parallax. In this paper, instead of relying on the homography-based warp, we propose a novel deep image stitching framework exploiting the pixel-wise warp field to handle the large-parallax problem. The proposed deep image stitching framework consists of two modules: Pixel-wise Warping Module (PWM) and Stitched Image Generating Module (SIGMo). PWM employs an optical flow estimation model to obtain pixel-wise warp of the whole image, and relocates the pixels of the target image with the obtained warp field. SIGMo blends the warped target image and the reference image while eliminating unwanted artifacts such as misalignments, seams, and holes that harm the plausibility of the stitched result. For training and evaluating the proposed framework, we build a large-scale dataset that includes image pairs with corresponding pixel-wise ground truth warp and sample stitched result images. We show that the results of the proposed framework are qualitatively superior to those of the conventional methods, especially when the images have large parallax. The code and the proposed dataset will be publicly available soon.

cs.CV

Intersection cohomology of pure sheaf spaces using Kirwan's desingularization

Let $\mathbf{M}_n$ be the Simpson compactification of twisted ideal sheaves $\mathcal{I}_{L,Q}(1)$ where $Q$ is a rank $4$ quardric hypersurface in $\mathbb{P}^n$ and $L$ is a linear subspace of dimension $n-2$. This paper calculates the intersection Poincaré polynomial of $\mathbf{M}_n$ using Kirwan's desingularization method. We obtain the intersection Poincaré polynomial of the moduli space for one-dimensional sheaves on del Pezzo surfaces of degree $\geq 8$ by considering wall-crossings of stable pairs and complexes.

math.AG

Spectrum of Projective Plane Curve Arrangements with Ordinary Singularities

The Hodge spectrum is an important analytic invariant of singularities encoding the Hodge filtration and the monodromy of the Milnor fiber. Explicit formulas exist for only a few cases. In this article the main result is a combinatorial formula for homogeneous polynomials in three variables whose reduced one define projective curve arrangements having only ordinary multiple points.

math.AG

On the explicit calculation of Hirzebruch-Milnor classes of hyperplane arrangements

The Hirzebruch-Milnor class is given by the difference between the homology Hirzebruch characteristic class and the virtual one. It is known that the Hirzebruch-Milnor class for a certain singular hypersurface can be calculated by using the Hodge spectrum of each stratum of singular locus. So far there is no explicit calculation of this invariant for any non-trivial examples, and we calculate this invariant by two different ways for low dimmensional hyperplane arrangements.

math.AG

Rank one local systems and forms of degree one

Cohomology support loci of rank one local systems of a smooth quasiprojective complex algebraic variety are finite unions of torsion-translated complex subtori of the character variety of the fundamental group. Tangent spaces of the character variety are (partially) represented by logarithmic 1-forms. In this paper, we give a relation between cohomology support loci and the natural strata of 1-forms given by the dimension of the vanishing locus. This relation generalizes the one for the projective case due to Green and Lazarsfeld and also generalizes the partial relation due to Dimca in the quasi-projective case.

math.AG