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Saikat Roy

Publications and source records attributed to Saikat Roy.

At least 37 records · Page 2Linked to original sources
arXiv2024

nnU-Net Revisited: A Call for Rigorous Validation in 3D Medical Image Segmentation

The release of nnU-Net marked a paradigm shift in 3D medical image segmentation, demonstrating that a properly configured U-Net architecture could still achieve state-of-the-art results. Despite this, the pursuit of novel architectures, and the respective claims of superior performance over the U-Net baseline, continued. In this study, we demonstrate that many of these recent claims fail to hold up when scrutinized for common validation shortcomings, such as the use of inadequate baselines, insufficient datasets, and neglected computational resources. By meticulously avoiding these pitfalls, we conduct a thorough and comprehensive benchmarking of current segmentation methods including CNN-based, Transformer-based, and Mamba-based approaches. In contrast to current beliefs, we find that the recipe for state-of-the-art performance is 1) employing CNN-based U-Net models, including ResNet and ConvNeXt variants, 2) using the nnU-Net framework, and 3) scaling models to modern hardware resources. These results indicate an ongoing innovation bias towards novel architectures in the field and underscore the need for more stringent validation standards in the quest for scientific progress.

cs.CV↗
arXiv2024

Orthogonality of bilinear forms and application to matrices

We characterize Birkhoff-James orthogonality of continuous vector-valued functions on a compact topological space. As an application of our investigation, Birkhoff-James orthogonality of real bilinear forms are studied. This allows us to present an elementary proof of the well-known Bhatia-Šemrl Theorem in the real case.

math.FA↗
arXiv2024

Skeleton Recall Loss for Connectivity Conserving and Resource Efficient Segmentation of Thin Tubular Structures

Accurately segmenting thin tubular structures, such as vessels, nerves, roads or concrete cracks, is a crucial task in computer vision. Standard deep learning-based segmentation loss functions, such as Dice or Cross-Entropy, focus on volumetric overlap, often at the expense of preserving structural connectivity or topology. This can lead to segmentation errors that adversely affect downstream tasks, including flow calculation, navigation, and structural inspection. Although current topology-focused losses mark an improvement, they introduce significant computational and memory overheads. This is particularly relevant for 3D data, rendering these losses infeasible for larger volumes as well as increasingly important multi-class segmentation problems. To mitigate this, we propose a novel Skeleton Recall Loss, which effectively addresses these challenges by circumventing intensive GPU-based calculations with inexpensive CPU operations. It demonstrates overall superior performance to current state-of-the-art approaches on five public datasets for topology-preserving segmentation, while substantially reducing computational overheads by more than 90%. In doing so, we introduce the first multi-class capable loss function for thin structure segmentation, excelling in both efficiency and efficacy for topology-preservation.

eess.IV↗
arXiv2024

MedNeXt: Transformer-driven Scaling of ConvNets for Medical Image Segmentation

There has been exploding interest in embracing Transformer-based architectures for medical image segmentation. However, the lack of large-scale annotated medical datasets make achieving performances equivalent to those in natural images challenging. Convolutional networks, in contrast, have higher inductive biases and consequently, are easily trainable to high performance. Recently, the ConvNeXt architecture attempted to modernize the standard ConvNet by mirroring Transformer blocks. In this work, we improve upon this to design a modernized and scalable convolutional architecture customized to challenges of data-scarce medical settings. We introduce MedNeXt, a Transformer-inspired large kernel segmentation network which introduces - 1) A fully ConvNeXt 3D Encoder-Decoder Network for medical image segmentation, 2) Residual ConvNeXt up and downsampling blocks to preserve semantic richness across scales, 3) A novel technique to iteratively increase kernel sizes by upsampling small kernel networks, to prevent performance saturation on limited medical data, 4) Compound scaling at multiple levels (depth, width, kernel size) of MedNeXt. This leads to state-of-the-art performance on 4 tasks on CT and MRI modalities and varying dataset sizes, representing a modernized deep architecture for medical image segmentation. Our code is made publicly available at: https://github.com/MIC-DKFZ/MedNeXt.

eess.IV↗
arXiv2024

A numerical range approach to Birkhoff-James orthogonality with applications

The main aim of this paper is to provide characterizations of Birkhoff-James orthogonality (BJ-orthogonality in short) in a number of families of Banach spaces in terms of the elements of significant subsets of the unit ball of their dual spaces, which makes the characterizations more applicable. The tool to do so is a fine study of the abstract numerical range and its relation with the BJ-orthogonality. Among other results, we provide a characterization of BJ-orthogonality for spaces of vector-valued bounded functions in terms of the domain set and the dual of the target space, which is applied to get results for spaces of vector-valued continuous functions, uniform algebras, Lipschitz maps, injective tensor products, bounded linear operators with respect to the operator norm and to the numerical radius, multilinear maps, and polynomials. Next, we study possible extensions of the well-known Bhatia-Šemrl theorem on BJ-orthogonality of matrices, showing results in spaces of vector-valued continuous functions, compact linear operators on reflexive spaces, and finite Blaschke products. Finally, we find applications of our results to the study of spear vectors and spear operators. We show that no smooth point of a Banach space can be BJ-orthogonal to a spear vector of $Z$. As a consequence, if $X$ is a Banach space containing strongly exposed points and $Y$ is a smooth Banach space with dimension at least two, then there are no spear operators from $X$ to $Y$. Particularizing this result to the identity operator, we show that a smooth Banach space containing strongly exposed points has numerical index strictly smaller than one. These latter results partially solve some open problems.

math.FA↗
arXiv2023

The Eshelby problem in amorphous solids

The ``Eshelby problem" refers to the response of a 2-dimensional elastic sheet to cutting away a circle, deforming it into an ellipse, and pushing it back. The resulting response is dominated by the so-called ``Eshelby Kernel" which was derived for purely elastic (infinite) material, but has been employed extensively to model the redistribution of stress after plastic events in amorphous solids with finite boundaries. Here we discuss and solve the Eshelby problem directly for amorphous solids, taking into account possible screening effects and realistic boundary conditions. We find major modifications compared to the classical Eshelby solution. These modification are needed for modeling correctly the spatial responses to plastic events in amorphous solids.

cond-mat.mtrl-sci↗
arXiv2023

atTRACTive: Semi-automatic white matter tract segmentation using active learning

Accurately identifying white matter tracts in medical images is essential for various applications, including surgery planning and tract-specific analysis. Supervised machine learning models have reached state-of-the-art solving this task automatically. However, these models are primarily trained on healthy subjects and struggle with strong anatomical aberrations, e.g. caused by brain tumors. This limitation makes them unsuitable for tasks such as preoperative planning, wherefore time-consuming and challenging manual delineation of the target tract is typically employed. We propose semi-automatic entropy-based active learning for quick and intuitive segmentation of white matter tracts from whole-brain tractography consisting of millions of streamlines. The method is evaluated on 21 openly available healthy subjects from the Human Connectome Project and an internal dataset of ten neurosurgical cases. With only a few annotations, the proposed approach enables segmenting tracts on tumor cases comparable to healthy subjects (dice=0.71), while the performance of automatic methods, like TractSeg dropped substantially (dice=0.34) in comparison to healthy subjects. The method is implemented as a prototype named atTRACTive in the freely available software MITK Diffusion. Manual experiments on tumor data showed higher efficiency due to lower segmentation times compared to traditional ROI-based segmentation.

eess.IV↗
arXiv2023

Taming Detection Transformers for Medical Object Detection

The accurate detection of suspicious regions in medical images is an error-prone and time-consuming process required by many routinely performed diagnostic procedures. To support clinicians during this difficult task, several automated solutions were proposed relying on complex methods with many hyperparameters. In this study, we investigate the feasibility of DEtection TRansformer (DETR) models for volumetric medical object detection. In contrast to previous works, these models directly predict a set of objects without relying on the design of anchors or manual heuristics such as non-maximum-suppression to detect objects. We show by conducting extensive experiments with three models, namely DETR, Conditional DETR, and DINO DETR on four data sets (CADA, RibFrac, KiTS19, and LIDC) that these set prediction models can perform on par with or even better than currently existing methods. DINO DETR, the best-performing model in our experiments demonstrates this by outperforming a strong anchor-based one-stage detector, Retina U-Net, on three out of four data sets.

cs.CV↗
arXiv2023

Dilation and Birkhoff-James orthogonality

We study the interaction between unitary $ρ$-dilations of a pair of Hilbert space operators and Birkhoff-James orthogonality. We prove that for two orthogonal operators $T,A$ if $\|T\|=ρ$, then $U_T \perp_B U_A$ for any unitary $ρ$-dilations $U_T$ of $T$ and $U_A$ of $A$ acting on a common space. We characterize $\varepsilon$-approximate Birkhoff-James orthogonality for complex Hilbert space operators. Then find a sharp bound on $\varepsilon$ such that $T \perp_B A$ implies that $U_T \perp_B^{\varepsilon} U_A$ for any unitary $ρ$-dilations $U_T, U_A$ of $T$ and $A$ respectively. The Schäffer unitary dilations of a pair of contractions $T,A$ are not orthogonal in general. We construct Schäffer-type unitary dilations for contractions which are pairwise orthogonal.

math.FA↗
arXiv2023

Dipole Screening in Pure Shear Strain Protocols of Amorphous Solids

When amorphous solids are subjected to simple or pure strain, they exhibit elastic increase in stress, punctuated by plastic events that become denser (in strain) upon increasing the system size. It is customary to assume in theoretical models that the stress released in each plastic event is redistributed according to the linear Eshelby kernel, causing avalanches of additional stress release. Here we demonstrate that contrary to the uniform affine strain resulting from simple or pure strain, each plastic event is associated with a non-uniform strain that gives rise to a displacement field that contains quadrupolar and dipolar charges that typically screen the linear elastic phenomenology and introduce anomalous length-scales and influence the form of the stress redistribution. An important question that opens up is how to take this into account in elasto-plastic models of shear induced phenomena like shear-banding.

cond-mat.soft↗
arXiv2023

Energy dissipation in high speed impact on granular media

In this work, we thoroughly investigate the impact process on the granular media in the limit when the ratio of the impact velocity to the acoustic speed becomes of the order of 0.01-1, which is far greater than the existing literature (0.0001-0.001). We show that the energy dissipation is largely due to the energy cost associated with the exploration between different metastable states via large scale reorganization of the force chain network. In this regime, the conventional drag force models break down, and the drag force can not be decomposed into a depth dependent static pressure and a depth independent inertial drag as proposed in the existing literature. The high dynamical stress generates acoustic pulses, which propagate longer distances rather than decaying exponentially, as observed in the previous works. In the latter stage of the impact process, the boundary also plays an essential role in the reorganization of the force chains as the reflected acoustic pulses interact with the original impact pulses. Furthermore, we study the scaling of the early stage peak forces with the impact velocity and find that spatial dimensionality strongly influences the scaling.

cond-mat.soft↗
arXiv2023

SAM.MD: Zero-shot medical image segmentation capabilities of the Segment Anything Model

Foundation models have taken over natural language processing and image generation domains due to the flexibility of prompting. With the recent introduction of the Segment Anything Model (SAM), this prompt-driven paradigm has entered image segmentation with a hitherto unexplored abundance of capabilities. The purpose of this paper is to conduct an initial evaluation of the out-of-the-box zero-shot capabilities of SAM for medical image segmentation, by evaluating its performance on an abdominal CT organ segmentation task, via point or bounding box based prompting. We show that SAM generalizes well to CT data, making it a potential catalyst for the advancement of semi-automatic segmentation tools for clinicians. We believe that this foundation model, while not reaching state-of-the-art segmentation performance in our investigations, can serve as a highly potent starting point for further adaptations of such models to the intricacies of the medical domain. Keywords: medical image segmentation, SAM, foundation models, zero-shot learning

eess.IV↗
arXiv2023

Transformer Utilization in Medical Image Segmentation Networks

Owing to success in the data-rich domain of natural images, Transformers have recently become popular in medical image segmentation. However, the pairing of Transformers with convolutional blocks in varying architectural permutations leaves their relative effectiveness to open interpretation. We introduce Transformer Ablations that replace the Transformer blocks with plain linear operators to quantify this effectiveness. With experiments on 8 models on 2 medical image segmentation tasks, we explore -- 1) the replaceable nature of Transformer-learnt representations, 2) Transformer capacity alone cannot prevent representational replaceability and works in tandem with effective design, 3) The mere existence of explicit feature hierarchies in transformer blocks is more beneficial than accompanying self-attention modules, 4) Major spatial downsampling before Transformer modules should be used with caution.

cs.CV↗
arXiv2022

Geometry of nowhere vanishing, point separating sub-algebras of $\mathcal{H}ol(Γ\cup\text{Int}(Γ))$ and zeros of Holomorphic functions

We study $ \mathcal{H}ol(Γ\cup\text{Int}(Γ)) $, the normed algebra of all holomorphic functions defined on some simply connected neighbourhood of a simple closed curve $Γ$ in $\mathbb{C} $, equipped with the supremum norm on $ Γ$. We explore the geometry of nowhere vanishing, point separating sub-algebras of $ \mathcal{H}ol(Γ\cup \text{Int}(Γ)) $. We characterize the extreme points and the exposed points of the unit balls of the said sub-algebras for $Γ$ analytic. We also characterize the smoothness of an element in these sub-algebras by using Birkhoff-James orthogonality techniques without any restriction on $Γ$. As a culmination of our study, we assimilate the geometry of the aforesaid sub-algebras with some classical concepts of complex analysis and establish a connection between Birkhoff-James orthogonality and zeros of holomorphic functions.

math.FA↗
arXiv2022

Micro-mechanical insights into the stress transmission in strongly aggregating colloidal gel

Predicting the mechanical response of the soft gel materials under external deformation is of paramount importance in many areas, such as foods, pharmaceuticals, solid-liquid separations, cosmetics, aerogels and drug delivery. Most of the understanding of the elasticity of gel materials is based on the concept of fractal scaling with very little microscopic insights. Previous experimental observations strongly suggest that the gel material loses the fractal correlations upon deformation and the range of packing fraction up to which the fractal scaling can be applied is very limited. Also, correctly implementing the fractal modeling requires identifying the elastic backbone, which is a formidable task. So far, there is no clear understanding of the gel elasticity at high packing fraction and the correct length scale that governs its mechanical response. In this work, we undertake extensive numerical simulations to elucidate the different aspects of stress transmission in the gel materials. We observe the existence of two percolating networks of compressive and tensile normal forces close to the gel point. We also find that the probability distribution for the compressive and tensile part normalized by their respective mean shows universal behavior irrespective of varied interaction potential, thermal energy and particle size distribution. Interestingly, there are also large number of contacts with zero normal force, and consequently, a peak in the normal force distribution is observed at $f_n\approx0$ even at higher pressure. We also identify the critical internal state parameters such as mean normal force, force anisotropies and the average coordination number and propose simple constitutive relations that relate the different components of the stress to the internal state parameters. The agreement between our model prediction and the simulation observation is excellent.

cond-mat.soft↗
arXiv2022

Experimental and Numerical Verification of Anomalous Screening Theory in Granular Matter

The concept of mechanical screening is widely applied in solid-state systems. Examples include nucleation of defects in crystalline materials, scars and pleats in curved crystals, wrinkles in strongly confined thin sheets, and cell-rearrangements in biological tissue. Available theories of such screening usually contain a crucial ingredient, which is the existence of an ordered reference state, with respect to which screening elements nucleate to release stresses. In contradistinction, amorphous materials in which a unique reference state does not exist, nevertheless exhibits plastic events that act as screening geometric charges with significant implications on the mechanical response. In a recent paper [Phys. Rev. E 104, 024904] it was proposed that mechanical strains in amorphous solids can be either weakly or strongly screened by the formation of low or high density of plastic events. At low densities the screening effect is reminiscent of the role of dipoles in dielectrics, in only renormalizing the elastic moduli. The effect of high density screening has no immediate electrostatic analog and is expected to change qualitatively the mechanical response, as seen for example in the displacement field. On the basis of experiments and simulations, we show that in granular matter, strong screening results in significant deviation from elasticity theory. The theoretical analysis, which accounts for an emergent inherent length scale, the experimental measurements and the numerical simulations of frictional granular amorphous assemblies are in agreement with each other, and provide a strong support for the novel continuum theory.

cond-mat.dis-nn↗
arXiv2022

Birkhoff-James Orthogonality and Its Local Symmetry in Some Sequence Spaces

We study Birkhoff-James orthogonality and its local symmetry in some sequence spaces namely $\ell_p,$ for $1\leq p\leq\infty$, $p\neq2$, $c$, $c_0$ and $c_{00}$. Using the characterization of the local symmetry of Birkhoff-James orthogonality, we characterize isometries of each of these spaces onto itself and obtain the Banach-Lamperti theorem for onto operators on the sequence spaces.

math.FA↗