Spatial Frequency Research Articles (Page 1)

Mouse superficial superior colliculus (sSC) has been found to have orientation selective maps, suggesting a fundamentally different selectivity than in primate SC. Moreover, orientation selectivity in mouse sSC appears to change with stimulus properties such as size, shape and spatial frequency, in contradistinction to the computational principle of invariance in primates. To reconcile mouse and primate mechanisms for orientation selectivity, we constructed a computational model of mouse sSC populations with circular-symmetric, center-surround (i.e., not intrinsically orientation selective), stimulus-invariant receptive fields (RFs), classically used to describe monkey lateral geniculate nucleus (LGN) neurons. This model produced population maps similar to those found in mouse sSC, which show strong radial orientation preferences at retinotopic locations along stimulus edges. We show how this selectivity depended critically on spatial frequency tuning of the model units. The model predicted a shift from radial to anti-radial orientation preferences from the same simulated units at high stimulus spatial frequencies, also consistent with measurements from mouse sSC. We found intrinsically oriented RFs were largely unnecessary to explain the imaging data, but could explain a possible small subpopulation of intrinsically orientation selective neurons. We conclude that to study orientation selectivity in mouse sSC and other systems, the problem is not the choice of stimulus. Rather than endless tweaks to find the perfect, unbiased stimulus, image-computable population modeling is the solution. Regardless of the stimulus presented, comparing how well models of intrinsically or non-intrinsically orientation selective units account for empirical data provides definitive evidence for underlying neural selectivity.Significance Statement Measurements of neural population activity from mouse superior colliculus (SC) show patterns of orientation selectivity differing markedly from those observed in primates. Do such measurements necessarily imply different neural mechanisms across species? We developed a modeling framework that explicitly predicts population activity using well-established mechanisms from classic primate single-unit neurophysiology. Notably, this framework was sufficient to explain a diverse array of population measurements in mouse SC. Our results reconcile seemingly contradictory neural phenomena across species and visual areas through a principled approach for making inferences across measurement scales (i.e., single neurons to neural populations), providing a unifying framework for determining shared computational mechanisms broadly throughout the brain.

The proliferation of deepfake technologies presents serious challenges for forensic speech authentication. We propose a deep learning framework combining Convolutional Neural Networks (CNNs) and Long Short-Term Memory (LSTM) networks to improve detection of manipulated audio. Leveraging the spectral feature extraction of CNNs and the temporal modeling of LSTMs, the model demonstrates superior accuracy and generalization across the ASVspoof2019 LA and WaveFake datasets. Linear Frequency Cepstral Coefficients (LFCCs) were employed as acoustic features and outperformed MFCC and GFCC representations. To enhance transparency and trustworthiness, explainable artificial intelligence (XAI) techniques, including Grad-CAM and SHAP, were applied, revealing that the model focuses on high-frequency artifacts and temporal inconsistencies. These interpretable analyses validate both the models design and the forensic relevance of LFCC features. The proposed approach thus provides a robust, interpretable, and XAI-driven solution for forensic authentic detection.

To prospectively evaluate bilateral visual function in Japanese patients implanted with nondiffractive extended depth-of-focus (EDoF) intraocular lenses (IOLs). Multisite prospective observational study. This study included 48 eyes of 24 Japanese patients with cataracts (mean age: 68.7 ± 9.2years) who underwent bilateral implantation of nondiffractive EDoF IOLs CNAET0 (Clareon Vivity, Alcon), made of high-water-content hydrophobic acrylic material. Three months postoperatively, binocular uncorrected and distance-corrected visual acuities (BUCVA and BDCVA) were assessed at far, 66cm, and 40cm. Binocular photopic contrast sensitivity (CSV-1000), binocular defocus curves, spectacle independence, and photic phenomena (glare, halo, starburst, and waxy vision) were also assessed. The mean logMAR BUCVA/BDCVA was -0.11/-0.15 at far, 0.05/0.08 at 66cm, and 0.18/0.22 at 40cm. Binocular contrast sensitivity was within the normal range for individuals aged 60-69years across all spatial frequencies. The mean defocus curve demonstrated 0.1 logMAR or better between -2.0 and +1.0 D addition, with better performance of 0.0 logMAR or better between -1.5 and +0.5 D addition. All patients were spectacle-independent for distance and intermediate vision, whereas nine of the 24 patients (37.5%) required spectacles for near vision. None of the patients reported severe photic phenomena; 17 patients (70.8%) did not experience glare or starburst, and 20 patients (83.3%) did not report halo or waxy vision. Bilateral implantation of nondiffractive EDoF IOLs provided good binocular functional vision from far to near, although some patients may require spectacles for near vision. The photic phenomenon was minimal.

Electroencephalograph (EEG) emotion recognition is a key task in the brain-computer interface(BCI) field. A mounting quantity of studies have shown that deep learning methods for emotion recognition exhibit superior performance compared to traditional techniques. However, it is still challenging to fuse the EEG's Spatial, Frequency and Temporal information, as well as how to make full use of discriminative local patterns among the features for different emotions. To address these issues, a novel hybrid model called Spatial-Frequency-Temporal Hybrid Network(SFT-HN) is proposed. This model includes three Spatial Frequency Residual Modules (SFRM) and an attention-based Bidirectional Long Short-Term Memory (ATBI-LSTM). The former module extracts spatial-frequency features, while the latter learns temporal contexts. SFT-HN is trained to seize the complementarity among the spatial-frequency-temporal information and adaptively explore discriminative local patterns. Specifically, 4D representations are created from raw EEG signals to preserve spatial, frequency, and temporal information. The SFRM module then adopts split-convert-merge techniques, residual and attention mechanisms to enhance its spatial-frequency feature extraction ability for each input 4D representation tensor time slice. Moreover, an attention-enhanced mechanism is incorporated into a bidirectional LSTM module to capture the crucial temporal dependencies among the extracted features, thereby enhancing the discriminative power of the EEG features. The proposed method attains average accuracies of 97.61% and 97.57% for arousal-based and valence-based classification on the DEAP dataset, respectively. On SEED dataset, the method achieves average accuracy of 97.44%. Furthermore, we validate the robust generalization of our proposed model on a novel dataset, FACED, achieving an average accuracy of 96.24%. The model code is available at: https://github.com/AllGGI/SFT-HN-model.

Motion detection is a primary task required for robotic systems to perceive and navigate in their environment. Proposed in the literature bioinspired neuromorphic Time-Difference Encoder (TDE-2) combines event-based sensors and processors with spiking neural networks to provide real-time and energy-efficient motion detection through extracting temporal correlations between two points in space. However, on the algorithmic level, this design leads to a loss of direction-selectivity of individual TDEs in textured environments. In the present work, we propose an augmented 3-point TDE (TDE-3) with additional inhibitory input that makes TDE-3 direction-selectivity robust in textured environments. We developed a procedure to train the new TDE-3 using backpropagation through time and surrogate gradients to linearly map input velocities into an output spike count or an Inter-Spike Interval (ISI). Using synthetic data, we compared training and inference with spike count and ISI with respect to changes in stimuli dynamic range, spatial frequency, and level of noise. ISI turns out to be more robust toward variation in spatial frequency, whereas the spike count is a more reliable training signal in the presence of noise. We conducted an in-depth quantitative investigation of optical flow coding with TDE and compared TDE-2 vs. TDE-3 in terms of energy efficiency and coding precision. The results show that at the network level, both detectors show similar precision (20° angular error, 88% correlation with the truth of the ground). However, due to the more robust direction selectivity of individual TDEs, the TDE-3 based network spikes less and is hence more energy efficient. Reported precision is on par with model-based methods but the spike-based processing of the TDEs provides allows more energy-efficient inference with neuromorphic hardware. Additionally, we also employed TDE-2 and TDE-3 to estimate ego-motion and showed results competitive with those achieved by neural networks with 1.5 × 10 5 parameters.

This study reports the first successful design and fabrication of a thermal imaging sight for tank artillery in Vietnam, utilizing an uncooled detector operating in the long-wave infrared (LWIR) spectrum. The objective lens, consisting of only three spherical elements with a focal length of 100 mm, was evaluated using the modulation transfer function (MTF). The system achieved MTF values approximately 0.5 at a spatial frequency of 30 cycles per millimeter (cycles/mm), approaching the diffraction limit. Measurements of the minimum resolvable temperature difference (MRTD) demonstrate that the sighting system is capable of detecting tank-sized targets at ranges exceeding 2 kilometers.

Digital image correlation (DIC) technology is widely employed in speckle-based measurement techniques, including X-ray speckle tracking. By enhancing DIC’s measurement capability to the subpixel scale through subpixel registration technology, the accuracy of such tracking methods is significantly improved. Consequently, selecting an appropriate subpixel registration algorithm becomes crucial for advancing the precision of both DIC and its application in tracking methods. Nevertheless, current evaluation approaches for these algorithms overlook spatial resolution—an essential metric not only for X-ray speckle tracking but also for other comparable methodologies. Inspired by the modulation transfer function, this study proposes a novel evaluation method that uses the root mean square error of displacement measurement at different spatial frequencies to assess spatial resolution. Two widely used subpixel registration algorithms—the peak-finding algorithm and the iterative spatial domain cross-correlation algorithm—are evaluated and compared. The result strongly contrasts with traditional evaluations based on ideal translational conditions, and underscores the necessity of incorporating spatial resolution and speckle size into algorithm selection criteria for practical applications.

High spatial frequency information, including fine details like textures, significantly contributes to the accuracy of semantic segmentation. However, according to the Nyquist-Shannon Sampling Theorem, high-frequency components are vulnerable to aliasing or distortion when propagating through downsampling layers such as strided-convolution. Here, we propose a novel Spatial Frequency Modulation (SFM) that modulates high-frequency features to a lower frequency before downsampling and then demodulates them back during upsampling. Specifically, we implement modulation through adaptive resampling (ARS) and design a lightweight add-on that can densely sample the high-frequency areas to scale up the signal, thereby lowering its frequency in accordance with the Frequency Scaling Property. We also propose Multi-Scale Adaptive Upsampling (MSAU) to demodulate the modulated feature and recover high-frequency information through non-uniform upsampling This module further improves segmentation by explicitly exploiting information interaction between densely and sparsely resampled areas at multiple scales. Both modules can seamlessly integrate with various architectures, extending from convolutional neural networks to transformers. Feature visualization and analysis demonstrate that our method effectively alleviates aliasing while successfully retaining details after demodulation. As a result, the proposed approach considerably enhances existing state-of-the-art segmentation models (e.g., Mask2Former-Swin-T +1.5 mIoU, InternImage-T +1.4 mIoU on ADE20 K). Furthermore, ARS also enhances the performance of powerful Deformable Convolution (+0.8 mIoU on Cityscapes) by maintaining relative positional order during non-uniform sampling. Finally, we validate the broad applicability and effectiveness of SFM by extending it to image classification, adversarial robustness, instance segmentation, and panoptic segmentation tasks.

The contribution of magnocellular selective adaptation to spatial distance compression.

In this study, we present a novel single-shot polarization-resolved digital holographic microscope (PDHM) that integrates both double field-of-view (DFoV) and polarization imaging for real-time, live-cell imaging. This innovative system overcomes the limitations of conventional techniques by simultaneously capturing two distinct regions of the sample, each with polarization information. Using a carefully configured Sagnac setup, the reference beam is split into orthogonally polarized components, each modulated with a distinct spatial carrier frequency. This allows the independent reconstruction of polarization-resolved complex fields. At the same time, a beam splitter placed in the object path spatially folds two separate regions of the sample onto the same sensor area, thereby achieving angular multiplexing without the need for additional optics. This configuration allows both spatially and polarization-resolved information in a single acquisition. The system is experimentally validated on live MCF-7 breast cancer cells, where it successfully reconstructs phase anisotropy and internal cellular features in real time. Its ability to capture wide-field, label-free, and polarization-sensitive information in a compact format makes it a promising tool for biomedical imaging and dynamic cell analysis.

Geometrically linear and nonlinear frequency analyses of piezoelectric three-phase nanocomposite sandwich beams in thermal environment

This paper investigates the dual-functional broadband properties of an asymmetric piezoelectric metamaterial beam for simultaneous vibration reduction and energy harvesting. Firstly, a grading method is proposed, and an asymmetric piezoelectric metamaterial beam structure model with the gradient mode is established. The effects of various gradient modes on the grading parameters of each segment are examined. Subsequently, the band structure and group velocity of each segment are examined to elucidate the propagation and energy harvesting mechanisms for the bending-dominated wave. Furthermore, the evaluation criteria for dual-functional properties in the gradient mode are introduced, revealing the broadening law of the dual-functional band under various gradient modes. Finally, the theoretical results are analyzed and compared with the finite element method (FEM). The results show that in gradient mode, the bending-dominated wave in the asymmetric piezoelectric metamaterial beam generates the spatial frequency division and enhances wave field energy. Compared with the uniform mode, the gradient modes can simultaneously achieve dual-functional effects in both the low-frequency and broadband ranges, significantly improving performance. Parameters such as gradient modes and grading variation ranges significantly impact the dual-functional performance. By reasonably selecting the grading parameters, enhanced dual-functional performance can be achieved.

Biophotonic imaging technology offers a non-invasive solution for objectively and quantitatively staging diabetic retinopathy (DR) and detecting pre-DR before structural damage occurs. Integrating this technology into clinical practice enables more accurate staging, early risk management, and prediction of treatment outcomes, ultimately reducing DR-related structural damage. The platform featured a novel physics-based retinal oximetry algorithm, built on Saccadic-Phase Spatial Frequency Domain Imaging (SP-SFDI). This technology measured an oxygen saturation analogue (αSO2) in tissue with high resolution, detecting oxygenation changes <3% using two snapshots capturing phase shifts in spatially modulated light. Its first application, BioxyDR™, focused on measuring αSO2 in the superficial retinal vasculature for accurate DR staging and early detection. For clinical validation, the study included 63 DR patients, 60 diabetes mellitus (DM) patients without DR (DM no DR), and 18 controls (no DM, no known ocular diseases). Retinal venous αSO2 significantly differed (p = 0.007) between controls and patient groups, including proliferative (PDR) and non-proliferative DR (NPDR). 100% of controls and DR patients were correctly classified per standard-of-care (SOC) criteria. Among DM no DR patients, 8 were classified as pre-DR, and 7 (87%) developed DR within 18 months. Notably, all patients classified as not pre-DR (100%) remained DR-free. Initial studies across various ocular diseases showed distinct classifications based on venous and arterial αSO2. Taken together, these findings suggest that venous αSO2 measured with SP-SFDI may serve as a biomarker for DR progression, with higher αSO2 levels indicating greater disease severity. αSO2 also shows promise as a metric for staging pre-DR.

This randomised clinical trial investigated whether a high spatial frequency enhancing classroom presenting outdoor scenes (outdoor scene classroom, OSC) can arrest myopia development in children. This is a two-arm, parallel, non-blinding, cluster randomised trial. The trial was single centre, school-based and conducted in Lijiang Shiyan School, Lijiang, Yunnan. China. Grade 3 primary school students were recruited. The intervention was the OSC, designed to resemble the natural outdoor environment by adorning the walls with wallpaper featuring natural images with high spatial frequency content. The primary outcome was 1-year myopia incidence. Secondary outcomes were 1-year change of spherical equivalent refraction (SER) and 1-year change in axial length (AL). The primary outcome, myopia incidence, was not significantly different between the OSC group and the traditional classroom (TC) group, (14.1% vs 16.9%, p = 0.42). The secondary outcomes showed a protective effect of OSC. The mean ± SE of the 1-year change in SER was -0.47 ± 0.04 and -0.67 ± 0.04 D in the OSC and TC groups, respectively (p < 0.001). The mean ± SE 1-year change in AL was 0.25 ± 0.01 and 0.31 ± 0.02 mm in the OSC and TC groups, respectively (p = 0.02). In multivariable analysis, the TC group had a 0.21 D (95% CI -0.30, -0.11) more myopic shift than the OSC group, after controlling for age, gender and baseline refractive error. OSC was protective in slowing myopic shift. Large implementation of OSC provides an alternative strategy to increased time outdoors in myopia prevention and provides an approach that involves less disruption to school routines.

To investigate and compare the effects of bifocal soft contact lenses, single-focus soft contact lenses, and orthokeratology lenses (OK lenses) on patients with small-angle intermittent exotropia (IXT) accompanied by myopia, providing a basis for reducing secondary surgeries in clinical practice. A prospective, randomized, controlled study was conducted on 142 patients with small-angle IXT who had undergone IXT surgery and had concomitant myopia. Patients were randomly assigned to three groups using a computer-generated random number sequence with allocation concealment: the bifocal soft contact lens group (group A), the single-focus soft contact lens group (group B), and the OK lens group (group C). During the one-year treatment period, multiple visual function parameters were measured, including best-corrected visual acuity (BCVA), contrast sensitivity, accommodative function, eye position control ability, strabismus angle, and axial length (AL). There were no significant differences in BCVA among the three groups, indicating similar basic visual acuity correction effects. Compared with the other two lens types, defocus soft contact lenses led to reduced contrast sensitivity at high spatial frequencies. Orthokeratology lenses resulted in decreased accommodative amplitude, increased accommodative lag, and reduced accommodative facility compared with the other lenses. The strabismus angle decreased in all patients, with improved positive fusional convergence. Groups A and B showed better improvements in eye position control and strabismus angle reduction than group C. Defocus soft contact lenses and OK lenses were comparable in controlling AL growth. The strabismus angle positively correlated with near stereopsis acuity and eye position control scores and negatively correlated with near horizontal positive fusional convergence. After the initial IXT surgery, patients wearing defocus soft contact lenses with a concentric bifocal design can effectively control AL growth, enhance eye position control ability, improve visual function, and achieve good subjective visual outcomes.

PurposeCentral vision loss in macular diseases severely affects visual perception and cognition, particularly scene recognition. A key question is whether observed impairments result solely from reduced input or reflect functional changes in spatial frequency processing. This study investigated how macular diseases affects this processing at both behavioral and brain levels.MethodsWe compared patients with macular diseases with age-matched controls using an artificial scotoma simulating each patient's central vision loss. Participants performed a scene categorization task with images filtered in high spatial frequencies (HSFs; fine details) or low spatial frequencies (LSFs; global shape). Patients fixated using their preferred retinal locus (PRL), whereas controls fixated on the location corresponding to the patient's fovea, within the artificial scotoma. Behavioral performance and functional magnetic resonance imaging (fMRI) responses were analyzed.ResultsPatients performed worse than the healthy controls for both HSF and LSF scenes, with a more pronounced deficit for HSFs. These deficits were associated with reduced activation in occipital cortex and in the parahippocampal place area (PPA), particularly for HSF scenes. In contrast, LSF processing was relatively preserved and accompanied by increased recruitment of higher-level cognitive and oculomotor areas in patients.ConclusionsThese findings demonstrate that macular diseases leads to altered spatial frequency processing within residual vision itself, particularly affecting fine-detail analysis. This perceptual degradation is accompanied by functional brain reorganization supporting partial compensation. The results highlight the importance of considering both degraded input and adaptive mechanisms when designing rehabilitation strategies based on residual peripheral vision.

This study looks into the design of Helmholtz resonators along with lateral closed resonators for sensing applications, mainly for gas sample detection. A periodic parallel arrangement of both Helmholtz resonator and closed resonators was studied, while one resonator was defected to study the performance of the system. A relevant study was carried out in terms of numerical simulations with available data in the finite element method that give insight into the acoustic wave transmission and resonant frequencies of the system with or without defect. The study presented that due to the defect, highly localized modes deriving at lower spatial frequencies are induced within the system, making it highly sensitive to fine shifts of frequency. This sensitivity enables it to detect a wide variety of gas samples. Further, increasing the number of periods to 9 resulted in optimal performance, with significant improvements in sensitivity, quality factor, and detection limit. The study discusses the impact of geometric parameters and gas properties on system sensitivity, quality factor, and detection limit, indicating high potential for precision in sensing use for environmental monitoring and biosensing. The proposed sensor demonstrates exceptional selectivity in gas mixtures and maintains robust stability across a wide range of operating temperatures.Supplementary InformationThe online version contains supplementary material available at 10.1038/s41598-025-22935-x.

Primary visual cortex (V1) has long served as a model system for understanding cortical organization. Although its structural and functional properties vary markedly across its surface, patterns of covariation suggest possible underlying constancies. Such constancies would imply that V1 is composed of multiple identical units whose visual properties differ only due to differences in their inputs. To test this, we used fMRI to investigate how V1 cortical magnification and preferred spatial frequency covary with eccentricity and polar angle, measured in 40 observers. V1 cortical magnification and preferred spatial frequency were strongly correlated across eccentricity and around polar angle, however their relation differed between these dimensions: they were proportional across eccentricity but not polar angle. The constant ratio of cortical magnification to preferred spatial frequency when measured as a function of eccentricity suggests a shared underlying cause of variation in the two properties, e.g., the gradient of retinal ganglion cell density across eccentricity. In contrast, the deviation from proportionality around polar angle implies that cortical variation differs from that in retina along this dimension. Thus, a constancy hypothesis is supported for one of the two spatial dimensions of V1, highlighting the importance of examining the full 2D-map to understand how V1 is organized.

Primary visual cortex (V1) has long served as a model system for understanding cortical organization. Although its structural and functional properties vary markedly across its surface, patterns of covariation suggest possible underlying constancies. Such constancies would imply that V1 is composed of multiple identical units whose visual properties differ only due to differences in their inputs. To test this, we used fMRI to investigate how V1 cortical magnification and preferred spatial frequency covary with eccentricity and polar angle, measured in 40 observers. V1 cortical magnification and preferred spatial frequency were strongly correlated across eccentricity and around polar angle, however their relation differed between these dimensions: they were proportional across eccentricity but not polar angle. The constant ratio of cortical magnification to preferred spatial frequency when measured as a function of eccentricity suggests a shared underlying cause of variation in the two properties, e.g., the gradient of retinal ganglion cell density across eccentricity. In contrast, the deviation from proportionality around polar angle implies that cortical variation differs from that in retina along this dimension. Thus, a constancy hypothesis is supported for one of the two spatial dimensions of V1, highlighting the importance of examining the full 2D-map to understand how V1 is organized.

Cylindrical surfaces with complex parameters (CSCP), including off-axis, aspheric, and other properties, constitute fundamental components within complex optical systems. Two-dimensional pseudo lateral shearing interferometry (2DPLSI) is a non-null and generalized method for CSCP. It can eliminate wavefront error of components within systematic and retrace error, thereby achieving high-precision measurement. However, the accuracy of measurement is influenced by factors such as the parameters of the measurement system, rendering the analysis of measurement precision of 2DPLSI to be important. The sources of error in 2DPLSI are discussed in this paper; their effects are simulated using the Monte Carlo (MC) method. Furthermore, a wavefront construction method based on power spectral density (PSD) is proposed, which simulates actual wavefronts more effectively. In addition, experiments are conducted to validate the optimized measurement system parameters derived from the simulation results. Experimental results show that the optimized measurement system parameters effectively improve measurement accuracy, retain low-mid spatial frequency information of wavefront, and eliminate the influence of gridding artifacts.