arXiv subjects

Ujjwal Mishra

Publications and source records attributed to Ujjwal Mishra.

3 recordsLinked to original sources

arXiv2026

Curves of constant width and Lebesgue's covering problem

A universal cover is a convex set in the plane that contains a congruent copy of every planar set of diameter one. Lebesgue asked in 1914 for one of least area, and the value is not known. We prove that every convex universal cover has area at least 0.8344, improving on 0.832, published in 2005, and 0.833, in a 2026 preprint, both of which come from a disc together with an equilateral triangle and a regular pentagon. Our test sets are instead curves of constant width: the disc, the Reuleaux triangle and the Reuleaux pentagon. Each contains the regular polygon it is built on, so the family is strictly larger at the same number of bodies and the same number of placement parameters, and we show that the classical configuration admits an arrangement whose hull has area below 0.8336, so no bound drawn from those three sets by this argument reaches ours. Curves of constant width were proposed for this role, and explored numerically, by Gibbs in 2014; what is added here is a proof. It consists of an analytic reduction followed by one finite computation. The reduction bounds the hull area from below over an entire box of placements at once, by eroding each Reuleaux polygon to a fixed set contained in every placement that box allows. The computation is an exhaustive subdivision of the resulting five-dimensional space, recorded as a certificate of 486,799,600 nodes and checked by a verifier independent of the search, with a rigorous bound on its floating point error some thousands of times smaller than the margin the verification attains.

cs.CG↗

arXiv2026

Improvise, Adapt, Overcome -- Telescopic Adapters for Efficient Fine-tuning of Vision Language Models in Medical Imaging

Adapting Vision Language Segmentation Models (VLSMs) to medical imaging domains requires significant computational overhead when using conventional fine-tuning approaches. Existing Parameter-Efficient Fine-Tuning (PEFT) methods apply uniform adapter dimensions across all transformer layers, leading to suboptimal parameter allocation and reduced adaptation efficiency. We introduce Telescopic Adapters, a novel PEFT framework that employs depth-aware scaling to progressively increase adapter capacity from shallow to deep transformer layers. Our method integrates lightweight bottleneck modules within CLIPSeg's vision and text encoders, with adapter dimensions dynamically scaled based on layer depth and semantic relevance. Using only 613k trainable parameters--244x fewer than end-to-end fine-tuning, Telescopic Adapters achieve superior performance across five diverse medical datasets spanning polyp segmentation, skin lesion detection, and breast ultrasound imaging. Comprehensive ablation studies demonstrate that deeper layers require substantially more adaptation capacity than shallow layers, validating our telescopic scaling hypothesis. Our approach establishes a new paradigm for efficient medical VLSM fine-tuning, enabling deployment in resource-constrained clinical environments while maintaining competitive segmentation accuracy. Our source code is publicly available at https://github.com/Ujjwal238/Telescopic_adapters

cs.CV↗

arXiv2026

GRAD-Former: Gated Robust Attention-based Differential Transformer for Change Detection

Change detection (CD) in remote sensing aims to identify semantic differences between satellite images captured at different times. While deep learning has significantly advanced this field, existing approaches based on convolutional neural networks (CNNs), transformers and Selective State Space Models (SSMs) still struggle to precisely delineate change regions. In particular, traditional transformer-based methods suffer from quadratic computational complexity when applied to very high-resolution (VHR) satellite images and often perform poorly with limited training data, leading to under-utilization of the rich spatial information available in VHR imagery. We present GRAD-Former, a novel framework that enhances contextual understanding while maintaining efficiency through reduced model size. The proposed framework consists of a novel encoder with Adaptive Feature Relevance and Refinement (AFRAR) module, fusion and decoder blocks. AFRAR integrates global-local contextual awareness through two proposed components: the Selective Embedding Amplification (SEA) module and the Global-Local Feature Refinement (GLFR) module. SEA and GLFR leverage gating mechanisms and differential attention, respectively, which generates multiple softmax heaps to capture important features while minimizing the captured irreverent features. Multiple experiments across three challenging CD datasets (LEVIR-CD, CDD, DSIFN-CD) demonstrate GRAD-Former's superior performance compared to existing approaches. Notably, GRAD-Former outperforms the current state-of-the-art models across all the metrics and all the datasets while using fewer parameters. Our framework establishes a new benchmark for remote sensing change detection performance. Our code will be released at: https://github.com/Ujjwal238/GRAD-Former

cs.CV↗