2D Gaussian Filter Research Articles

Gaussian Kernel Approximations Require Only Bit-Shifts

An approach to approximate the 2D Gaussian filter for all possible kernel sizes based on the binary optimization technique is introduced. The approximate filter coefficients are designed as negative powers of two, allowing hardware implementation with remarkable savings in the chip area. The proposed approximate filters were evaluated and compared with competing methods using both similarity analysis and edge detection applications. The proposed method and the competing works for masks of size 3×3, 5×5, and 7×7 were implemented in a Xilinx Artix-7 FPGA. The proposed method showed up to a 60.0% reduction in DSP usage and a 75.0% increase in the maximum operating frequency when compared with state-of-art methods for the 7×7 kernel size case and a 48.8% reduction in the dynamic power normalized by the maximum operating frequency.

Anti-scattering medium computational ghost imaging with modified Hadamard patterns

Illumination patterns of computational ghost imaging (CGI) systems suffer from reduced contrast when passing through a scattering medium, which causes the effective information in the reconstruction result to be drowned out by noise. A two-dimensional (2D) Gaussian filter performs linear smoothing operation on the whole image for image denoising. It can be combined with linear reconstruction algorithms of CGI to obtain the noise-reduced results directly, without post-processing. However, it results in blurred image edges while performing denoising and, in addition, a suitable standard deviation is difficult to choose in advance, especially in an unknown scattering environment. In this work, we subtly exploit the characteristics of CGI to solve these two problems very well. A kind of modified Hadamard pattern based on the 2D Gaussian filter and the differential operation features of Hadamard-based CGI is developed. We analyze and demonstrate experimentally that using Hadamard patterns for illumination but using our developed modified Hadamard patterns for reconstruction (MHCGI) can enhance the robustness of CGI against turbid scattering medium. Our method not only helps directly obtain noise-reduced results without blurred edges but also requires only an approximate standard deviation, i.e., it can be set in advance. The experimental results on transmitted and reflected targets demonstrate the feasibility of our method. Our method helps to promote the practical application of CGI in the scattering environment.

3-D Structure-Oriented Adaptive Gaussian Pyramid for Seismic Multiscale Fracture Detection

Gaussian pyramid (GP) has the property of decomposing the 2D data into multiple scales. It has been successfully applied in image processing, but rarely used in seismic data processing and interpretation. Specifically, seismic data is not just a 2D image in one time slice or horizon. Moreover, the pattern of geological body varies rapidly in 3D spaces. Hence, the classical GP method exists a limitation in processing 3D seismic data. Especially in fracture detection, the 2D isotropic Gaussian kernel used in GP tends to blur the fracture details. In this letter, to match the high dimensional seismic data, we propose a structure-oriented adaptive Gaussian pyramid (SOA-GP) algorithm, which expand the 2D GP method to 3D situation. In this case, to eliminate the influence of transverse change of wave impedance and consider stratigraphic characteristics, the 2D Gaussian filter is also substituted by the 3D structure adaptive anisotropic Gaussian kernel, which is constructed by instantaneous phase-based gradient structure tensor (GST) method. Meanwhile, seismic attributes are applied to the multi-resolution seismic data decomposed by SOA-GP method to realize multi-scale fracture detection. Finally, we apply this new 3D SOA-GP method to a field data. It demonstrates that the multi-scale decomposition of the new method could produce more details of fracture and less disturbs from noise.

Bedload transport analysis using image processing techniques

Bedload transport is an important factor to describe the hydromorphological processes of fluvial systems. However, conventional bedload sampling methods have large uncertainty, making it harder to understand this notoriously complex phenomenon. In this study, a novel, image-based approach, the Video-based Bedload Tracker (VBT), is implemented to quantify gravel bedload transport by combining two different techniques: Statistical Background Model and Large-Scale Particle Image Velocimetry. For testing purposes, we use underwater videos, captured in a laboratory flume, with future field adaptation as an overall goal. VBT offers a full statistics of the individual velocity and grainsize data for the moving particles. The paper introduces the testing of the method which requires minimal preprocessing (a simple and quick 2D Gaussian filter) to retrieve and calculate bedload transport rate. A detailed sensitivity analysis is also carried out to introduce the parameters of the method, during which it was found that by simply relying on literature and the visual evaluation of the resulting segmented videos, it is simple to set them to the correct values. Practical aspects of the applicability of VBT in the field are also discussed and a statistical filter, accounting for the suspended sediment and air bubbles, is provided.

Accuracy-Configurable 2-D Gaussian Filter Architecture for Energy-Efficient Image Processing

Most compute-intensive applications demand approaches to optimize energy efficiency in CMOS design. Configurable architectures and approximate computing are alternatives to meet the quality and energy requirements in multimedia processing during the runtime. This work proposes a 2D Gaussian filter design to provide multiple quality-power-performance points of operation. The main goal is to design an accuracy-configurable 2D Gaussian filter accelerator at the runtime with a low overhead cost when a new configuration is dynamically selected. The power consumption results show reductions ranging from 9.87% to 58.96%, with an up to 14.8% increase in the hardware area.

Automated foveal location detection on spectral-domain optical coherence tomography in geographic atrophy patients

PurposeTo develop a fully automated algorithm for accurate detection of fovea location in atrophic age-related macular degeneration (AMD), based on spectral-domain optical coherence tomography (SD-OCT) scans.MethodsImage processing was conducted on a cohort of patients affected by geographic atrophy (GA). SD-OCT images (cube volume) from 55 eyes (51 patients) were extracted and processed with a layer segmentation algorithm to segment Ganglion Cell Layer (GCL) and Inner Plexiform Layer (IPL). Their en face thickness projection was convolved with a 2D Gaussian filter to find the global maximum, which corresponded to the detected fovea. The detection accuracy was evaluated by computing the distance between manual annotation and predicted location.ResultsThe mean total location error was 0.101±0.145mm; the mean error in horizontal and vertical en face axes was 0.064±0.140mm and 0.063±0.060mm, respectively. The mean error for foveal and extrafoveal retinal pigment epithelium and outer retinal atrophy (RORA) was 0.096±0.070mm and 0.107±0.212mm, respectively. Our method obtained a significantly smaller error than the fovea localization algorithm inbuilt in the OCT device (0.313±0.283mm, p <.001) or a method based on the thinnest central retinal thickness (0.843±1.221, p <.001). Significant outliers are depicted with the reliability score of the method.ConclusionDespite retinal anatomical alterations related to GA, the presented algorithm was able to detect the foveal location on SD-OCT cubes with high reliability. Such an algorithm could be useful for studying structural-functional correlations in atrophic AMD and could have further applications in different retinal pathologies.

Canny Edge Detector Algorithm Optimization Using 2D Spatial Separable Convolution

Abstract In the case of real-time image processing, it is necessary to determine the computational complexity of the mathematical operations used. Reduction of computational complexity of 2D discrete convolution can be achieved by using a separable convolution. In this article, we focus on the application of a canny edge detector for different types of images. The main goal was to speed up the process of applying the kernel matrix to a given image using a separable convolution. By applying a separable convolution, we compared the duration of the Gaussian filter application, edges detection and the Hysteresis threshold level. Applying a separable convolution should speed up the duration of the 2D Gaussian filter as well as the edge detection. The main variable that interested us was time, but an important factor in the application of the filter and edge detection is the number of operating cycles. The use of a separable convolution should significantly reduce the number of computational cycles and reduces the duration of filter application and detection.

High Spatial Resolution Investigation of OFDR Based on Image Denoising Methods

Measurement accuracy of the optical frequency domain reflectometry (OFDR) will be deteriorated severely when the spatial resolution is improved due to the influence of the random noise, especially in long range distributed fiber optical sensing system. In order to eliminate the random noise, we have experimentally compared and analyzed the performance of OFDR system with and without the image processing methods in term of spatial resolution. The data arrays of the cross-correlation results are obtained after processing the collected distributed Rayleigh scattering signals along the sensing fiber, which can be used to construct a two-dimension (2D) image with the spectrum shift information induced by the strain. Thus, the image denoising methods can be applied to remove the random noise and improve the measurement accuracy. Based on this principle, two image denoising methods including the total variation method and the 2D Gaussian filter arithmetic are introduced to realize distributed sensing with high spatial resolution in long distance OFDR system. Experimental results show that the random noise can be suppressed and the outliers can be removed by the proposed methods. The strain gradients with high spatial resolution are identified effectively when the image denoising methods are used. Furthermore, spatial resolution with 1.3mm is achieved by the proposed methods with a wavelength sweeping rate of 20nm/s in 52m sensing fiber. The proposed methods provide a potential solution for OFDR system in long distance sensing with high spatial resolution, which is a significant step toward a high-performance OFDR system for practical applications.

An Efficient Implementation of Low-Latency Two-Dimensional Gaussian Smoothing Filter using Approximate Carry-Save Adder

The two-dimensional Gaussian smoothing filter (2D-GSF) is one of the most useful techniques in image processing. Since the 2D-GSF requires high computational resources, its efficient design and implementation are critical in real-time processing purposes. Approximate computing is a new method that can be used to increase the performance of 2D Gaussian filter design with low computing overhead on field-programmable gate arrays (FPGAs). This study aims to provide a low-latency Gaussian filter architecture on FPGA such that it can be used in real-time processing applications. In this regard, accurate and approximate carry-save adders (CSAs) have been used in adder tree-based Gaussian filters. In our proposed method, we use two approximation steps: in the first step, we use an approximation structure named Speed–Power–Area–Accuracy for Gaussian filter design and in the second stage, we use approximate CSAs to convert adder-tree structures that are used in Gaussian filter, and as a result, we have significantly reduced the delay. The results of simulation and implementation show that the latency has reduced in a 3[Formula: see text] 3 2D-GSF architecture up to 22% using proposed accurate CSAs and 45% using proposed approximate CSAs, compared to existing Gaussian filters with an adder tree structure.

On the 2D Post-Processing of Brillouin Optical Time-Domain Analysis

The benefits and limitations inherent to the 2D postprocessing of measurements from Brillouin optical time-domain analyzers are investigated from a fundamental point of view. In a preliminary step, the impact of curve fitting on the precision of the estimated Brillouin frequency shift is analyzed, enabling a fair comparison between the representative noise-reduction algorithms studied in this article. The performances in terms of signal-to-noise ratio, experimental uncertainty σ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</sub> on the Brillouin frequency shift and spatial resolution delivered by advanced image processing methods-such as wavelet transform and non-local means algorithms-are then compared with the impact of a 2D Gaussian filter. The major discrepancies observed when comparing the gain in signal-to-noise ratio to the σ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</sub> reduction are then determined by exploiting the separability of the Gaussian filter, which reveals that noise reduction is only effective along 1-D of the 2D array of measurements and originates from a digital reduction of the system analog bandwidth. The signal-to-noise ratio improvement obtained from filtering in the spectral dimension is only illusory, since its action is redundant with the curve fitting procedure to estimate the Brillouin frequency shift. Finally, the maximum σ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</sub> reduction achievable by digital post-processing is theoretically given, hence setting a fundamental limit to the improvement brought by data processing.

Fast hardware architecture for fixed-point 2D Gaussian filter

This study presents the hardware architecture for 16-bit, 5 × 5 fixed-point 2D Gaussian kernel. Two filters are proposed, one using generalized kernel and other using separable kernel. The quality analysis of both the filters are obtained for different metrics and it is observed that the generalized filter achieves the best performance compared to all the existing methods. The proposed filters are evaluated on different images and its performance is similar to that of the original filter, evident from the difference in values of Peak Signal to Noise Ratio (PSNR) and Structural Similarity Index Metric (SSIM) of proposed filters to that of the original filter. Based on the principle of Distributed Arithmetic (DA), two hardware architectures, Generalized Filter Architecture (GFA) and Separable Filter Architecture (SFA) are proposed. SFA achieves an improvement in area, delay, power, Area Delay Product (ADP) and Area Power Product (APP) compared to GFA. GFA, on the other hand, achieves high performance compared to the SFA model. The performance of both the architectures are analyzed in terms of max speed and frames per second metric and it is shown that the proposed architectures achieve significantly better performance compared to all the existing techniques.

Retinal vascular segmentation combined with PCNN and morphological matching enhancement

Aiming at the problem of large workload and strong subjectivity for manual retinal vessels extraction, this paper proposes a retinal vessel segmentation method that combines regional growing strategy, pulse coupled neural network (PCNN), a Gaussian filter bank and a Gabor filter. First, 2D Gaussian filter bank and 2D Gabor filter are combined to enhance the shape retinal blood vessel region and strengthen the contrast between the blood vessel and the background. Then, PCNN with fast linking mechanism and region growing idea is implemented to achieve automatic retinal vessel segmentation in which the unprocessed pixel with highest intensity is set as the seed, and the adaptive linking weight and stop conditions are adopted. The experimental results on the DRIVE fundus database show that the average accuracy, sensitivity and specificity are 93.96%, 78.64%, 95.64%, respectively. The segmentation results have less vascular breakpoints and clear micro-vessels. This work has promising application value.

Study of PCA-Based Adaptive Denoising of CFA Images for Single-Sensor Digital Cameras

To study the Single-sensor digital color cameras use a process called color demosaicking to produce full color images from the data captured by a color filter array (CFA). The quality of demosaicked images is degraded due to the sensor noise introduced during the image acquisition process. The conventional solution to combating CFA sensor noise is demosaicking first, followed by a separate process. This strategy generates many noise-caused color artifacts in the demosaicking process, which are hard to remove in the process. Few schemes that work directly on the CFA images have been presented because of the difficulties arisen from the red, green and blue interlaced mosaic pattern, yet a well designed denoising first and demosaicking later scheme can have advantages such as less noise-caused color artifacts and cost-effective implementation. Already in the technique, first decomposed the noisy CFA image into two parts: the low-pass smooth image and high-pass smooth image by using 2D-Gaussian low-pass filter and denoised the high-pass image only and further combine with lowpass image. Not large but least noise component are present in the low-pass image, which can create more noise in the image when it process further (demosaicking). An adaptive algorithm can be used by using principle component analysis (PCA), which works directly on the high-pass as well as low-pass CFA data. Which can give the better result for the denoising.

A Gaussian filtering method to reduce directionality on high-density point clouds digitized by a conoscopic holography sensor

This work analyses the directional effect shown by the high-density point clouds digitized with a conoscopic holography (CH) sensor. The asymmetric shape of the laser spot for this sensor yields directionality to appear along the largest spot dimension and to occur repeatedly under different working conditions. To study this effect, several digitizing tests were performed under different conditions on a surface machined by EDM with a uniform and isotropic finish, so that the directional effect should not appear. Nevertheless, the use of the 2D Fourier transform (2DFT) confirmed the existence of directionality in the point clouds along the largest spot direction and that it appeared repetitively under different working conditions. Thus, this effect could be considered as a systematic error associated to the CH sensor and then, feasible to be reduced. The use of an anisotropic 2D Gaussian filter is suggested for this purpose. The results found before and after applying the filter were compared to those obtained by a confocal microscope, which was used as reference due to the absence of directionality in the captured images. Results show that the filtered point clouds suitably fit the actual surface topography.

Improvement of image performance in digital breast tomosynthesis (DBT) by incorporating a compressed-sensing (CS)-based deblurring scheme

In this work, we investigated a compressed-sensing (CS)-based deblurring scheme incorporated with the total-variation (TV) regularization penalty for image deblurring of high accuracy and adopted it into the image reconstruction in conventional digital breast tomosynthesis (DBT). We implemented the proposed algorithm and performed a systematic simulation to demonstrate its viability for improving the image performance in DBT as well as two-dimensional (2D) mammography. In the simulation, blurred noisy projection images of a 3D numerical breast phantom were generated by convolving their original (or exact) version by a designed 2D Gaussian filter kernel (standard deviation=2 in pixel unit, kernel size=11×11), followed by adding Gaussian noise (mean=0, variance=0.05), and deblurred by using the algorithm before performing the DBT reconstruction procedure. Here the projection images were taken with a half tomographic angle of θ=20° and an angle step of Δθ=2°. We investigated the image performance of the reconstructed DBT images quantitatively in terms of the modulation and the slice-sensitive profile (SSP).

FPGA implementation of filtered image using 2D Gaussian filter

Image filtering is one of the very useful techniques in image processing and computer vision. It is used to eliminate useless details and noise from an image. In this paper, a hardware implementation of image filtered using 2D Gaussian Filter will be present. The Gaussian filter architecture will be described using a different way to implement convolution module. Thus, multiplication is in the heart of convolution module, for this reason, three different ways to implement multiplication operations will be presented. The first way is done using the standard method. The second way uses Field Programmable Gate Array (FPGA) features Digital Signal Processor (DSP) to ensure and make fast the scalability of the effective FPGA resource and then to speed up calculation. The third way uses real multiplier for more precision and a the maximum uses of FPGA resources. In this paper, we compare the image quality of hardware (VHDL) and software (MATLAB) implementation using the Peak Signal-to-Noise Ratio (PSNR). Also, the FPGA resource usage for different sizes of Gaussian kernel will be presented in order to provide a comparison between fixed-point and floating point implementations.

Investigating the sources of phase contrast: iron oxide nanoparticle study to exclude deoxyhemoglobin as a major source for the gray/white matter phase contrast

Introduction Recently, the benefits of image phase for the study of brain anatomy at high field (> 7 T) have been demonstrated [1]. In some brain regions, the improved contrast to noise ratio (over the magnitude images) between and within grey and white matter structures has provided the opportunity to study the laminar structure of the cortex. Several sources such as iron [1,2], myelin [3], deoxy-hemoglobin [4], and macromolecular concentration [5] have been suggested to contribute to the phase contrast. However, the relative contribution of these sources is not well understood. Recently, Marques et al. [6] used an oxygen challenge in rat to demonstrate a relatively small contribution of deoxy-hemoglobin. However, quantitative interpretation of this result was compromised by the limited contrast modulation introduced by this challenge and potential confounds such as associated blood volume changes. Therefore, the result did not fully eliminate deoxy-hemoglobin as a substantial contributor to gray/white matter phase contrast. Here, we administered iron oxide nanoparticles that induce a relatively large increase in vascular susceptibility to further confirm that deoxy-hemoglobin is not a major source for the gray/white matter contrast. Methods All scans were performed at a 7 Tesla (Bruker BioSpin) animal system with a 4 channel surface coil. The scan sequence for phase images was a 2D multi-echo GRE sequence with FOV = 2.56 x 2.56 cm, resolution = 67 x 67 x 500 μm, flip angle = 60o, TR = 1 sec, TE = 8 / 20 / 32 msec, 4 average, and total scan time = 27 min. After coil-combining, phase images were unwrapped and filtered by a 2D Gaussian high-pass filter (FWHM = 26 voxels) to remove large scale phase variations. The frequency images were calculated from a linear fit to the phase change over the three echoes. T2 * values were also calculated from the multi-echo magnitude data. Scans were performed on an isoflurane anesthetized rat before and after various intravascular administrations of an iron oxide nanoparticle solution (Molday ION, BioPAL). Cumulative doses of 0.5, 0.8, and 3 mg/kg (adjusted for half life) were used. Images were acquired 5 min. after each injection.

Gaussian prefiltering of 123I DAT SPECT images when using depth-independent resolution recovery

Previously we have investigated a depth-independent compensation for collimator detector response (CDR) included in the OSEM reconstruction, intended for SPECT images that have been corrected for scatter and septal penetration using convolution-based methods. In this work, the aim was to study how different filtering strategies affect contrast as a function of noise when using Gaussian smoothing filters in combination with the above-described CDR compensation. The evaluation was performed for 123I dopamine transporter (DAT) SPECT images. Prefiltering with 2D Gaussian filter kernels, where the deterioration in resolution is included in the depth-independent CDR compensation, was compared to conventional postfiltering with 3D Gaussian filter kernels. Images reconstructed without filtering are also included in the comparison. It was found that there is little benefit in noise reduction when using CDR compensation. However, this variant of prefiltering gives consistently higher contrasts as a function of noise compared with the postfiltering alternative, and that could be of interest when using other types of filters with contrast improving properties.

Combination of two novel LDA-based methods for face recognition

Linear discriminant analysis (LDA)-based methods have been very successful in face recognition, yet little investigation has been done on the fusion of different LDA methods. Combination of two LDA methods which performed LDA on distinctly different subspaces may be effective in further improving the recognition performance. In this paper we first present two novel LDA-based methods, post-processed Fisherfaces (pFisherfaces) and bi-directional PCA plus LDA ( BDPCA + LDA ). pFisherfaces uses 2D-Gaussian filter to smooth classical Fisherfaces, and BDPCA + LDA is a LDA performed in the BDPCA subspace. Then we propose a combination framework of these two LDA-based approaches. Two popular face databases, the ORL and the FERET, are used to evaluate the efficiency of the proposed combination framework. The results of our experiments indicate that the combination framework is superior to pFisherfaces, BDPCA + LDA , and other appearance-based methods in terms of recognition accuracy.

Development of a portable 3D ultrasound imaging system for musculoskeletal tissues

3D ultrasound is a promising imaging modality for clinical diagnosis and treatment monitoring. Its cost is relatively low in comparison with CT and MRI, no intensive training and radiation protection is required for its operation, and its hardware is movable and can potentially be portable. In this study, we developed a portable freehand 3D ultrasound imaging system for the assessment of musculoskeletal body parts. A portable ultrasound scanner was used to obtain real-time B-mode ultrasound images of musculoskeletal tissues and an electromagnetic spatial sensor was fixed on the ultrasound probe to acquire the position and orientation of the images. The images were digitized with a video digitization device and displayed with its orientation and position synchronized in real-time with the data obtained by the spatial sensor. A program was developed for volume reconstruction, visualization, segmentation and measurement using Visual C++ and Visualization toolkits (VTK) software. A 2D Gaussian filter and a Median filter were implemented to improve the quality of the B-scan images collected by the portable ultrasound scanner. An improved distance-weighted grid-mapping algorithm was proposed for volume reconstruction. Temporal calibrations were conducted to correct the delay between the collections of images and spatial data. Spatial calibrations were performed using a cross-wire phantom. The system accuracy was validated by one cylinder and two cuboid phantoms made of silicone. The average errors for distance measurement in three orthogonal directions in comparison with micrometer measurement were 0.06 ± 0.39, −0.27 ± 0.27, and 0.33 ± 0.39 mm, respectively. The average error for volume measurement was −0.18% ± 5.44% for the three phantoms. The system has been successfully used to obtain the volume images of a fetus phantom, the fingers and forearms of human subjects. For a typical volume with 126 × 103 × 109 voxels, the 3D image could be reconstructed from 258 B-scans (640 × 480 pixels) within one minute using a portable PC with Pentium IV 2.4 GHz CPU and 512 MB memories. It is believed that such a portable volume imaging system will have many applications in the assessment of musculoskeletal tissues because of its easy accessibility.