Multilevel Image Thresholding

This paper proposes a novel membrane algorithm based on artificial protozoa optimizer (MAAPO) for global optimization problems. The artificial protozoa optimizer (APO) is adopted as the base meta-heuristic algorithm due to its novelty and competitive performance. MAAPO integrates two key innovations:(1) a membrane computing (MC) framework that introduces a parallel distributed paradigm to improve population diversity and search dynamics, and (2) an enhanced autotrophic model within APO that uses a roulette-based fitness-distance balance (RFDB) mechanism for adaptive reference point selection. These strategies collectively enhance the algorithm's exploration-exploitation balance and global search capabilities. To validate its performance, MAAPO is tested against 12 advanced algorithms on the CEC2017 test suite, and further applied to the multilevel thresholding image segmentation problem using Otsu and Kapur entropy as objective functions. The quality of segmented images is assessed using peak signal-to-noise ratio (PSNR), structural similarity index (SSIM), and feature similarity index (FSIM) metrics. Experimental results demonstrate that MAAPO outperforms its counterparts, delivering superior segmentation quality. This research on MAAPO contributes an effective enhancement strategy to meta-heuristic algorithms and introduces a novel, highly applicable approach for complex image segmentation tasks.

Pseudo-labeling is a strong paradigm for semi-supervised medical image segmentation, yet its effectiveness is highly sensitive to confidence thresholding. In abdominal multi-organ segmentation, a fixed global threshold is particularly suboptimal because organ classes differ substantially in size, appearance, and learning difficulty. In this work, we propose ThreshGuide, a class-aware threshold adaptation framework that uses labeled data to guide pseudo-label selection on unlabeled data. Built upon a standard teacher-student architecture, the teacher model evaluates labeled samples during training to estimate class-aware threshold targets by maximizing an error-aware F\b{eta} criterion that balances precision and coverage. These targets are then smoothed with an exponential moving average (EMA) and used to filter unlabeled voxels in a class-dependent manner. Experiments on FLARE2022 and AMOS2022 show that ThreshGuide performs competitively overall, yielding clear improvements specifically on hard-to-learn organs.

We study the problem of lossless compression of source code, motivated by the storage demands of large-scale software archives, such as Software Heritage (https://www.softwareheritage.org/). General-purpose compressors (e.g., zstd, bzip2) offer a good trade-off between compression ratio and speed, but fail to exploit all special regularities inherent in source code. Recent approaches leverage Large Language Models (LLMs) within Shannon's symbol-ranking framework, relying on a scheme in which the predicted rank can grow arbitrarily. While effective at reducing space, this setting incurs significant throughput degradation, and leaves open the question whether it is necessary to explicitly encode all ranks. In this work, we introduce LLM-based compressors deploying two novel symbol-ranking variants that bound predictions to the top-$T$ ranks ($T=1$ or $63$), with out-of-threshold symbols stored as exceptions and compressed jointly with the rank stream via general-purpose compressors. We conduct the first large-scale evaluation of LLM-based source code compression across 30 LLMs, including general-domain, code-specialized, and quantized models. Our $T$-bounded approach outperforms prior LLM-based compressors both in compression ratio (up to 37% relative improvement) and compression throughput (40% faster). Compared to general-purpose compressors (e.g., zstd, bzip2), we obtain up to 82% relative compression gain but at a lower speed, thus offering a new trade-off point in the compression-speed spectrum. We also show that these gains are stronger on source code than on natural language, suggesting an interesting indication, namely that source code exposes regularities captured by LLMs but missed by general-purpose exact-match-based compressors. We conclude by commenting on open problems that offer theoretical and practical avenues of research.

The segmentation of multiple degradations has been a challenging problem in the field of image segmentation. Existing level set approaches commonly adopt a length regularization term to constrain the geometric shape of the segmentation contour. However, the introduction of the length term often results in numerical instability and high computational cost. In this paper, we show that the length term is not essential under certain smoothness constraints, and theoretically prove that the presence of the length term affects the property of $|\nabla φ|=1$. Based on the finding, we define a class of smooth images, construct the grayscale level set, and propose a fast segmentation framework for degraded images, such as heavily noisy images and intensity inhomogeneous images. The framework transforms PDE evolution into one-dimensional threshold search, which has significant advantages in computational speed, especially on large-scale images. Experiments validate the segmentation performance of the proposed framework on various degraded images.

Foundation models such as CLIP have enabled open-vocabulary object detectors that generalise to novel categories via vision-language similarity. However, the confidence scores these detectors produce are not reliable localization probability estimates: they conflate visual scale and semantic query specificity with the true detection signal. Through controlled experiments on COCO across three foundation-model-based detectors (GroundingDINO, OWL-ViT, YOLO-World), with the scale-bias finding further replicated on LVIS (1,203 categories) using GroundingDINO, we show that s=cos(v,t) is a biased mixture of two effects. Scale bias (alpha = +0.064, r = 0.579, p = 1.29 x 10^-58) systematically inflates scores for large objects. Semantic bias (beta = -0.705, p = 5.23 x 10^-41) suppresses scores for generic queries. Both biases are structurally inevitable from CLIP's image-level pretraining. Threshold adjustment cannot remove them: oracle per-scale thresholding yields Delta F1 = +0.001 for small objects versus +0.102 for large. A parameter-free temperature scaling correction improves small-object Recall@10 by 19.6% (p < 0.01) without retraining. This comes at a modest, measurable cost to pooled-ranking precision, so the bias is partially, not freely, reversible at inference time. These findings reveal a fundamental limitation of adapting image-level foundation models to region-level detection tasks.

Efficient inference in Large Language Models (LLMs) requires deciding where computation can be reduced while preserving model quality. We study this problem through multilayer perceptron (MLP) activation sparsification and token-level conditional routing. We first propose Sensitivity-Aware Thresholding for Sparsity (SATS), a threshold calibration method to choose layerwise gate thresholds using a local MLP output sensitivity proxy rather than calibrating thresholds directly from activation percentiles. While SATS retains the existing mechanism of sparsifying MLP activations by thresholding gate activations, it replaces percentile-based calibration with a sensitivity-aware selection rule. We then introduce a lightweight token routing framework that dynamically selects between a base path and a modified path on a per-token basis, rather than applying the modified computation uniformly to all tokens. We evaluate both methods on multiple recent open-weight LLMs. Our results show that SATS improves over the threshold-based sparsification baseline at matched actual sparsity and that token routing yields a more favorable quality-throughput trade-off than static activation modification baselines. Overall, our results suggest that improved threshold calibration and token routing can improve the quality-throughput trade-off in LLMs.

Fayyazi et al. (2025) recently proposed FACTER, a model-agnostic framework designed to jointly enforce fairness and statistical coverage in LLM-based recommendation through conformal thresholding and iterative prompt repair. In this work, we conduct a reproducibility study of the FACTER framework across diverse architectures and dataset sparsity levels, evaluating both the original open-ended generation task and a constrained re-ranking extension. Under the strict reproduction, we observe a divergence in recommendation utility, which we trace to underspecified target-set evaluation in the original study. We then use the constrained re-ranking setting to evaluate FACTER when the candidate set is fixed, and introduce a static Fair Zero-Shot baseline to isolate the contribution of the iterative prompt repair loop. Our analysis shows that FACTER consistently reduces adaptive-threshold violation counts, but that these reductions are not consistently reflected under the fixed threshold or in global fairness metrics. In the constrained ranking setting, static fairness instructions achieve comparable semantic-parity outcomes to FACTER's dynamic repair loop, suggesting that the additional online repair mechanism provides limited benefit in this formulation. All code and reproduction artifacts are available at https://github.com/oscar-omlf/facter-repr.

Pervasive data contamination -- stemming from measurement errors, outliers, or adversarial corruption -- has motivated the development of robust statistical methods. In this context, we propose a two-stage Adversarial Contamination-resistant Iterative Hard Thresholding (AC-IHT) algorithm for high-dimensional regression with contamination. Our nonconvex algorithm achieves minimax near-optimal (up to logarithmic terms) estimation by iteratively updating the coefficient vector and the contamination vector with different thresholding scales. We further demonstrate that our AC-IHT estimator is signal-adaptive: under proper signal conditions, it adaptively attains a sharper estimation rate and more accurate support recovery. Moreover, it enjoys the strong oracle property, laying a theoretical foundation for asymptotic inference. Numerical experiments confirm its superior finite-sample performance. Finally, we discuss theoretical extensions of the proposed procedure to generalized linear models and to heavy-tailed noise settings.

Event cameras asynchronously report brightness changes with microsecond-level temporal resolution, but real event data remain difficult to collect at scale because specialized sensors, careful synchronization, and task-specific annotations are required. Event-camera simulation is therefore important to event-based vision tasks. Most practical simulators build on contrast-threshold event generation, some with additional filtering, stochastic noise, or hand-tuned sensor parameters. While effective, such formulations often simplify the temporal structure produced by the lifecycle of each pixel, which can distort event timing and weaken downstream transfer. We introduce FracEvent, an event simulator that models this pixel-level lifecycle with fractional-relaxation voltage dynamics. Given a log-intensity trajectory, FracEvent drives a compact stack of relaxation modes, combines their responses into a voltage state, emits ON/OFF events by localizing threshold crossings on the continuous voltage trajectory, and updates the reference while retaining the underlying memory modes. This retained state links residual voltage response to later event timing. We evaluate FracEvent through event-stream comparison and downstream transfer on image reconstruction and optical flow estimation. Across multiple datasets, FracEvent improves the temporal structure of generated events and achieves stronger downstream-transfer results than competing simulator baselines, showing its practical value for event-camera simulation.

Selective prediction with distribution-free risk control promises that, with confidence 1-delta over the calibration draw, the error rate of accepted inputs stays below a user budget alpha. We audit this promise on signal-domain detectors -- machine anomalous-sound detection (ASD) and AI-generated-image forensics -- for four calibration rules: uncertified empirical thresholding (NAIVE) and certified Hoeffding, Clopper-Pearson (CP), and betting (WSR) upper confidence bounds. We report three findings. (i) NAIVE thresholding, common in practice, exceeds its declared budget in 49-73% of synthetic trials (n=200 calibration points) and in up to 68% of real-data splits: a false sense of safety rather than a broken theorem, since the rule never had a certificate. (ii) Tightness matters: CP and WSR certify substantial coverage where Hoeffding certifies none, with zero observed budget overruns under exchangeable splits. (iii) Under grouped deployment (unseen machine types or generators), certified rules overrun in 9-30% of trials -- far above delta -- showing the failure lies in the broken exchangeability premise, not in the bounds; a conservative per-group threshold restores validity at a severe coverage cost.

The most widely used RANSAC variants score candidate models by counting inliers or summing per-point scores that saturate beyond a residual threshold. Every such score requires a user-supplied parameter that is a function of the inlier scale, which must itself be estimated from contaminated data. We remove this dependence by reversing the usual order of inference: rather than estimating the scale and then scoring against it, we marginalize the inlier scale analytically in closed form under a conjugate Inverse-Gamma prior for a fixed inlier partition, then optimize over partitions. A single closed-form expression spans the non-informative Jeffreys limit and informative empirical-Bayes priors, so the same score adapts across data-rich and data-scarce regimes without any change to the algorithm. The proposed RANSAC score is the first in which the inlier scale is genuinely absent from the formula. The score admits O(N log N ) computation via sort-and-sweep. On a benchmark of nearly 70 000 image pairs spanning different two-view estimation problems and both engineered and learned feature pipelines, the proposed score exceeds the state of the art (RANSAC, MSAC, GaU, MAGSAC): it stays nearly flat under threshold miscalibration where baselines degrade, reaches near-optimal accuracy from as few as two validation pairs where baselines need ont he order of 100 times more,. and tightens its prior regularization as validation data grows scarce.

Local Hyper-Flow Diffusion (HFD) gives an edge-size-independent Cheeger-type guarantee for seeded clustering in general submodular hypergraphs, but existing HFD solvers do not keep intermediate computation local at every iteration. We introduce Thresholded Local HFD (TL-HFD), a first-order method that maintains an active region around the seeds, performs projected subgradient updates on that region and its immediate boundary, and expands via thresholded (top-k) boundary activation. We prove that the local update is exact: the degree-preconditioned projected subgradient step restricted to the active region and its boundary coincides with the unrestricted global update. We establish finite-time dual suboptimality for both exact and thresholded updates, treating the latter as inexact projected subgradient steps with explicit skipped-boundary error. We further derive an additive activated-volume bound controlled by realized local subgradient norms and the minimum boundary-push among newly activated vertices, and translate approximate dual optimality with localized support into a robust sweep-cut guarantee for early-stopped iterates. For general submodular cut-costs, each iteration is local in the scanned region and oracle-sensitive in the hyperedge primitive. Empirically, TL-HFD often matches or improves over HFD while activating less volume, with the largest gains on noisy instances where diffusion tends to absorb non-target vertices.

Low-rank projection has emerged as a promising approach for compressing the KV cache by exploiting hidden-dimension redundancy. However, prior methods rely on fixed or heuristic rank selection and struggle to achieve aggressive compression with minimal accuracy degradation. We propose STAR-KV, an adaptive low-rank KV cache compression framework with fine-grained rank control. STAR-KV encompasses 1) a differentiable thresholding mechanism that enables optimal rank selection at both attention-head and block levels, 2) a hybrid decomposition strategy that applies different low-rank factorizations according to the sensitivity of key and value projections, and 3) a low-rank-aware mixed precision quantization that leverages data statistics for near lossless low-bit quantization. Evaluated across multiple LLMs and benchmarks, STAR-KV achieves up to 75% KV cache compression and up to 20x overall KV cache reduction when combined with quantization. Enabled by custom Triton-based GPU kernels, STAR-KV delivers up to 6.9x speedup for the attention module and 3.1x end-to-end generation throughput. Our code is publicly available at: https://github.com/PriyanshBhatnagar/STAR-KV.

While LLM-based Automatic Speech Recognition (ASR) achieves high accuracy, its speed is limited by sequential autoregressive decoding. Diffusion Language Models (DLMs) offer a parallel alternative, yet their decoding strategies remain under-explored in ASR contexts. This paper analyzes three decoding schemes for DLM-based ASR: fixed-number, static confidence threshold, and dynamic confidence threshold. We introduce a round-wise analysis of decoding progress using Negative Log-Likelihood-based uncertainty as a proxy for prediction reliability. Our results show that both threshold-based strategies provide a better accuracy-speed trade-off than fixed-number schemes. This behavior is associated with the more concentrated confidence distribution observed in the evaluated ASR settings: many tokens reach high confidence early, enabling multiple tokens to be committed in early decoding rounds while lower-confidence tokens are deferred to later rounds. The static-threshold strategy achieves accuracy close to autoregressive decoding at lower decoding cost.

Multilevel Image thresholding is an important preprocessing algorithm in computer vision applications nowadays. Since most common thresholding methods take the desired count of thresholds as input by the user, thresholding methods that automatically determines a suitable count of thresholds from the input image itself are advantageous. In this article, a novel thresholding method based on a dynamic programming algorithm and a modification of Minimum Error Thresholding (MET) criterion is thoroughly presented. An empirical statistical study is performed to pinpoint why this proposed method is superior. Moreover, an extended comparison between this proposed method and other state-of-the-art methods is performed on a comprehensive set of natural, satellite and medical test images. The numerical results show that the proposed MET-DP method takes much less time than traditional dynamic programming thresholding methods when the number of thresholds is high. The proposed method can detect a suitable count of thresholds for most of tested images of different types. However, traditional methods that take the count of thresholds as input produce thresholded images of higher structural similarity index measure (SSIM) and peak signal-to-noise ratio (PSNR) values than MET-DP. Source code can be found on https://w3id.org/met-dp/article1-code

Multilevel image thresholding is widely used for segmentation in applications ranging from medical imaging to remote sensing. Classical objective functions, such as Otsu's between-class variance and Kapur's entropy, are often optimized using metaheuristic algorithms, with performance evaluated via metrics like Structural Similarity Index (SSIM) and Peak Signal-to-Noise Ratio (PSNR). These evaluations implicitly assume that SSIM and PSNR provide unbiased measures of segmentation quality. In this study, we examine this assumption by analyzing the correlation between thresholding objective functions and quality metrics across all possible thresholds for images in the BSDS500 dataset. Results show that Otsu's criterion consistently exhibits high correlation with both SSIM and PSNR, while Kapur's entropy demonstrates weaker and more variable correlation. Otsu outperforms Kapur in correlation with PSNR for all images and with SSIM for over 91%. Our findings reveal an inherent metric-objective-function bias. This work highlights the need for more neutral evaluation frameworks and motivates extending the analysis to additional thresholding criteria and domains. Source code of this paper can be found at https://w3id.org/met-dp/icpr26-95

Conditionally positive definite (CPD) kernels are defined with respect to a function class $\mathcal{F}$. It is well known that such a kernel $K$ is associated with its native space (defined analogously to an RKHS), which in turn gives rise to a learning method -- called conditional kernel ridge regression (conditional KRR) due to its analogy with KRR -- where the estimated regression function is penalized by the square of its native space norm. This method is of interest because it can be viewed as classical linear regression, with features specified by $\mathcal{F}$, followed by the application of standard KRR to the residual (unexplained) component of the target variable. Methods of this type have recently attracted increasing attention. We study the statistical properties of this method by reducing its behavior to that of KRR with another fixed kernel, called the residual kernel. Our main theoretical result shows that such a reduction is indeed possible, at the cost of an additional term in the expected test risk, bounded by $\mathcal{O}(1/\sqrt{N})$, where $N$ is the sample size and the hidden constant depends on the class $\mathcal{F}$ and the input distribution. This reduction enables us to analyze conditional KRR in the case where $K$ is positive definite and $\mathcal{F}$ is given by the first $k$ principal eigenfunctions in the Mercer decomposition of $K$. We also consider the setting where $\mathcal{F}$ consists of $k$ random features from a random feature representation of $K$. It turns out that these two settings are closely related. Both our theoretical analysis and experiments confirm that conditional KRR outperforms standard KRR in these cases whenever the $\mathcal{F}$-component of the regression function is more pronounced than the residual part.

With climate change and increasing human pressure on natural landscapes, inland water resources are becoming progressively scarcer, more vulnerable, and more difficult to manage sustainably. Reliable and automated methods for detecting, monitoring, and assessing surface water bodies are therefore of growing scientific and practical importance. In this paper, we investigate and compare three distinct machine learning architectures for water body identification and monitoring. Their performance is evaluated through quantitative metrics and real-world examples. Furthermore, a direct comparison with classical NDWI thresholding is conducted on a representative test image to highlight differences between data-driven and index-based approaches. This analysis allows us to identify the best-performing model in terms of accuracy, robustness, and practical applicability. Beyond detection, a major challenge for meaningful water quality assessment lies in the consistent and interpretable visualization of spectral water indices. Standard color mapping techniques are often inadequate or potentially misleading for environmental applications. To address this gap, we propose a suite of meaningful color schemes adapted for water quality indices, facilitating clearer interpretation, comparison, and decision-making for human users.

This work introduces a continuous soft near-orthogonality score and a resolution-aware saturated coverage objective for projection selection in region-of-interest focused cone-beam CT, grounded in Tuy's completeness theory. Replacing the binary hit-or-miss model of classical Tuy completeness with a graded, differentiable formulation preserves a direct link to achievable feature sizes while enabling both efficient approximate and exact optimisation. We establish that the underlying discrete decision problems are NP-complete via polynomial-time reductions from Set Cover, motivating a submodular greedy algorithm with proven $(1-1/\mathrm{e})$ approximation guarantees and a mixed-integer linear program (MILP) that provides certified optimality bounds. The MILP serves as a quality certificate for the greedy solution rather than a competing optimiser. The primary empirical finding confirms this relationship: across a systematic benchmark spanning six target regions, multiple projection budgets, and four controlled occlusion conditions, the pooled median greedy-to-MILP objective ratio was 0.998, with a substantial fraction of cases certified globally optimal. A binary formulation is included as a diagnostic baseline; it strengthens hard directional completeness but is weaker on the continuous coverage scale. We additionally introduce Effective Spatial Resolution (ESR), a physically interpretable trajectory-level diagnostic that maps directional sampling gaps to achievable feature sizes. ESR correlates reliably with matched reconstruction quality across projection budgets and occlusion levels, providing a practical bridge between the selection stage and the image domain without requiring reconstruction.

Hard-thresholding is an important type of algorithm in machine learning that is used to solve $\ell_0$ constrained optimization problems. However, the true gradient of the objective function can be difficult to access in certain scenarios, which normally can be approximated by zeroth-order (ZO) methods. The SZOHT algorithm is the only algorithm tackling $\ell_0$ sparsity constraints with ZO gradients so far. Unfortunately, SZOHT has a notable limitation on the number of random directions % in ZO gradients due to the inherent conflict between the deviation of ZO gradients and the expansivity of the hard-thresholding operator. This paper approaches this problem by considering the role of variance and provides a new insight into variance reduction: mitigating the unique conflicts between ZO gradients and hard-thresholding. Under this perspective, we propose a generalized variance reduced ZO hard-thresholding algorithm as well as the generalized convergence analysis under standard assumptions. The theoretical results demonstrate the new algorithm eliminates the restrictions on the number of random directions, leading to improved convergence rates and broader applicability compared with SZOHT. Finally, we illustrate the utility of our method on a ridge regression problem as well as black-box adversarial attacks.

Calibrated probability outputs of trained classifiers are increasingly used as inputs to downstream regression estimands such as effects, prevalences, or disparities for a latent group observed only on a small labelled subset. A standard practice is to threshold the calibrated score at a confidence cutoff and treat the hard label as the truth. Building on a recent identification result for the underlying moment equation, we develop a calibration-aware diagnostic apparatus for pseudo-labelling pipelines. We derive a closed-form expression for the attenuation bias that confidence thresholding induces in the downstream regression coefficient, and show that the bias can be predicted, before any inference is run, from the residual score variance $V^{*}=\mathbb{E}[\operatorname{Var}(p\mid X)]$ on the unlabelled set after partialling out the downstream controls $X$. We further obtain a sharp sensitivity bound under bounded calibration drift, and identify the boundary $V^{*}=0$, which holds iff $p$ is a deterministic function of $X$; this motivates a structural separation between classifier features $W$ and downstream controls $X\subsetneq W$. Five controlled simulations and a UCI Adult illustration trace the predictions. The contribution is operational: a $(V^{*}, κ)$ decision rule that practitioners can compute from any classifier output to decide whether confidence thresholding is safe.

Event cameras have emerged as a high-bandwidth, low-latency sensing modality for safety-critical perception in automated driving systems (ADS), offering microsecond temporal resolution, 120-140 dB dynamic range, and intrinsic absence of motion blur. However, no task-agnostic quality metric currently operates directly on the asynchronous event stream: state-of-the-art proxies require a downstream task (e.g., detection accuracy, tracking error) to assess stream integrity, which is incompatible with the certification requirements of ISO 21448 (SOTIF) and ISO/PAS 8800:2024. The recent BiasBench benchmark (CVPR 2025) explicitly identifies this gap. This work proposes a unified algebraic framework that lifts the Pearson Correlation Coefficient (PCC), historically used in two prior works for redundancy filtering and ROI selection on frame-based images, to the three standard event representations: Time Surface, Event Frame, and Voxel Grid. The framework yields three metrics: (i) r-TS for stream integrity monitoring against an ego-motion-predicted Time Surface, (ii) r2-EF for adaptive ROI selection requiring only integer comparisons, and (iii) r-VG for temporal redundancy gating. A structural isomorphism is established between the contrast-threshold mechanism of the event camera (|Delta L| >= C) and the PCC-based change criterion, the three lifted metrics are formalized, and pipeline latency and information loss are analyzed symmetrically against the raw stream. Illustrative behavior of each metric is demonstrated on a procedural-synthetic event stream, generated by direct simulation of the emission model rather than drawn from any real or video-derived dataset, including a tunnel-dip integrity-anomaly scenario in which r_C drops from 0.93 (coherent flow) to below 0 (alarm). An explicit epistemic convention ([ESTABLISHED], [SOLID], [HYPOTH.], [OPEN]) delineates the status of every contribution.

Acute Myeloid Leukemia (AML) is one of the most life-threatening type of blood cancers, and its accurate classification is considered and remains a challenging task due to the visual similarity between various cell types. This study addresses the classification of the multiclasses of AML cells Utilizing YOLOv12 deep learning model. We applied two segmentation approaches based on cell and nucleus features, using Hue channel and Otsu thresholding techniques to preprocess the images prior to classification. Our experiments demonstrate that YOLOv12 with Otsu thresholding on cell-based segmentation achieved the highest level of validation and test accuracy, both reaching 99.3%.