Hessian-based Method Research Articles

A Hessian-Based Technique for Specular Reflection Detection and Inpainting in Colonoscopy Images.

In the field of Computer-Aided Detection (CADx), the use of AI-based algorithms for disease detection in endoscopy images, especially colonoscopy images, is on the rise. However, these algorithms often encounter performance issues due to obstructions like specular reflection, resulting in false positives. This paper presents a novel algorithm specifically designed to tackle the challenges posed by high specular reflection regions in colonoscopy images. The proposed algorithm identifies these regions and applies precise inpainting for restoration. The process entails converting the input image from RGB to HSV color space and focusing on the Saturation (S) component in convex regions detected using a Hessian-based method. This step creates a binary mask that pinpoints areas of specular reflection. The inpainting function then uses this mask to guide the restoration of these identified regions and their borders. To ensure a seamless blend of the restored regions with the background and adjacent pixels, a feathering process is applied to the repaired regions. This enhances both the accuracy and aesthetic coherence of the inpainted images. The performance of our algorithm was rigorously tested on five unique colonoscopy datasets and various endoscopy images from the Kvasir dataset, using an extensive set of evaluation metrics and a comparative analysis with existing methods consistently highlighted the superior performance of our algorithm.

Filamentary Dust Polarization and the Morphology of Neutral Hydrogen Structures

Filamentary structures in neutral hydrogen (H i) emission are well aligned with the interstellar magnetic field, so H i emission morphology can be used to construct templates that strongly correlate with measurements of polarized thermal dust emission. We explore how the quantification of filament morphology affects this correlation. We introduce a new implementation of the Rolling Hough Transform (RHT) using spherical harmonic convolutions, which enables efficient quantification of filamentary structure on the sphere. We use this Spherical RHT algorithm along with a Hessian-based method to construct H i-based polarization templates. We discuss improvements to each algorithm relative to similar implementations in the literature and compare their outputs. By exploring the parameter space of filament morphologies with the Spherical RHT, we find that the most informative H i structures for modeling the magnetic field structure are the thinnest resolved filaments. For this reason, we find a ∼10% enhancement in the B-mode correlation with polarized dust emission with higher-resolution H i observations. We demonstrate that certain interstellar morphologies can produce parity-violating signatures, i.e., nonzero TB and EB, even under the assumption that filaments are locally aligned with the magnetic field. Finally, we demonstrate that B modes from interstellar dust filaments are mostly affected by the topology of the filaments with respect to one another and their relative polarized intensities, whereas E modes are mostly sensitive to the shapes of individual filaments.

Hydraulic fracturing distributed acoustic sensing monitoring data source mechanism inversion: A Hessian-based method

Distributed acoustic sensing (DAS) microseismic monitoring during hydraulic fracturing provides microseismic data with high spatial samplings for fracturing zones. However, sources located perpendicular to the single horizontal well of the DAS acquisition system have limited source-receiver geometries with extremely poor azimuthal coverage, resulting in high uncertainty in source mechanism inversion. To address this problem, we introduce the Hessian matrix, which governs the blurring effect caused by the source-receiver geometry, into the DAS microseismic source mechanism inversion. Our Hessian-based source mechanism inversion method consists of three main steps: (1) construct the Hessian matrix of the source mechanism based on the source-receiver geometry, (2) obtain an initial source mechanism using a conventional source mechanism inversion method, and (3) update the initial source mechanism using a Hessian-based [Formula: see text]-regularized least-squares algorithm. We assess the robustness of our method using synthetic DAS microseismic data with the consideration of noise, source location error, and different regularization parameters, and we compare the results with those of the conventional method. The results demonstrate that the Hessian-based method has a remarkable ability to mitigate the blurring effect of the Hessian matrix caused by limited DAS source-receiver geometry with poor azimuthal coverage, thereby reducing the uncertainty of the inverted source mechanism even in the presence of real noise and/or source location error. Finally, we use our method to invert the source mechanism of a real DAS microseismic event acquired during hydraulic fracturing. Our Hessian-based method provides low uncertainty in the source mechanism inversion of the real DAS microseismic data.

A framework for pulmonary fissure segmentation in 3D CT images using a directional derivative of plate filter

Imaging pulmonary fissures by CT provides useful information on diagnosis of pulmonary diseases. Automatic segmentation of fissures is a challenging task due to the variable appearance of fissures, such as inhomogeneous intensities, pathological deformation and imaging noise. To overcome these challenges, we propose an anisotropic differential operator called directional derivative of plate (DDoP) filter to probe the presence of fissure objects in 3D space by modeling the profile of a fissure patch with three parallel plates. To reduce the huge computation burden of dense matching with rotated DDoP kernels, a family of spherical harmonics are particularly utilized for acceleration. Additionally, a two-stage post-processing scheme is introduced to segment fissures. The performance of our method was verified in experiments using 55 scans from the publicly available LOLA11 dataset and 50 low-dose CT scans of lung cancer patients from the VIA-ELCAP database. Our method showed superior performance compared to the derivative of sticks (DoS) method and the Hessian-based method in terms of median and mean F1−score. The median F1−score for DDoP, DoS-based and Hessian-based methods on the LOLA11 dataset was 0.899, 0.848 and 0.843, respectively, and the mean F1−score was 0.858 ± 0.103, 0.781 ± 0.165 and 0.747 ± 0.239, respectively.

Parameter recovery, bias and standard errors in the linear ballistic accumulator model.

The linear ballistic accumulator (LBA) model (Brown & Heathcote, , Cogn. Psychol., 57, 153) is increasingly popular in modelling response times from experimental data. An R package, glba, has been developed to fit the LBA model using maximum likelihood estimation which is validated by means of a parameter recovery study. At sufficient sample sizes parameter recovery is good, whereas at smaller sample sizes there can be large bias in parameters. In a second simulation study, two methods for computing parameter standard errors are compared. The Hessian-based method is found to be adequate and is (much) faster than the alternative bootstrap method. The use of parameter standard errors in model selection and inference is illustrated in an example using data from an implicit learning experiment (Visser etal., , Mem. Cogn., 35, 1502). It is shown that typical implicit learning effects are captured by different parameters of the LBA model.

Reconstruction of vasculature in optical resolution photoacoustic microscopy using wavelet and Hessian based method

Photoacoustic microscopy is a high-resolution and high- contrast function modality where optical absorption is detected by ultrasonic transducer. The noise generated by the detector due to its size, sensitivity make the photoacoustic images difficult to visualize. Denoising and reconstruction of vascular structures is crucial for the early diagnosis and therapy in many medical applications. Therefore, the accurate detection of blood vessels has a great significance to assist the users including radiologists and clinicians by making them visualization of the vascular information in the images. In the proposed method, use of wavelet filtering to enhance the effect of smaller and bigger vessels in Optical Resolution Photoacoustic Microscopy (OR-PAM) is analyzed. The proposed method uses the wavelet to enhance the vasculature and then Hessian based method is applied to classify the vessel-like structures. For the evaluation, the algorithm is tested on photoacoustic images acquired non-invasively from living m...

Low-dose 2D X-ray angiography enhancement using 2-axis PCA for the preservation of blood-vessel region and noise minimization

Enhancing 2D angiography while maintaining a low radiation dose has become an important research topic. However, it is difficult to enhance images while preserving vessel-structure details because X-ray noise and contrast blood vessels in 2D angiography have similar intensity distributions, which can lead to ambiguous images of vessel structures. In this paper, we propose a novel and fast vessel-enhancement method for 2D angiography. We apply filtering in the principal component analysis domain for vessel regions and background regions separately, using assumptions based on energy compaction. First, we identify an approximate vessel region using a Hessian-based method. Vessel and non-vessel regions are then represented sparsely by calculating their optimal bases separately. This is achieved by identifying periodic motion in the vessel region caused by the flow of the contrast medium through the blood vessels when viewed on the time axis. Finally, we obtain noise-free images by removing noise in the new coordinate domain for the optimal bases. Our method was validated for an X-ray system, using 10 low-dose sets for training and 20 low-dose sets for testing. The results were compared with those for a high-dose dataset with respect to noise-free images. The average enhancement rate was 93.11±0.71%. The average processing time for enhancing video comprising 50–70 frames was 0.80±0.35s, which is much faster than the previously proposed technique. Our method is applicable to 2D angiography procedures such as catheterization, which requires rapid and natural vessel enhancement.

Accelerated Optical Projection Tomography Applied to In Vivo Imaging of Zebrafish.

Optical projection tomography (OPT) provides a non-invasive 3-D imaging modality that can be applied to longitudinal studies of live disease models, including in zebrafish. Current limitations include the requirement of a minimum number of angular projections for reconstruction of reasonable OPT images using filtered back projection (FBP), which is typically several hundred, leading to acquisition times of several minutes. It is highly desirable to decrease the number of required angular projections to decrease both the total acquisition time and the light dose to the sample. This is particularly important to enable longitudinal studies, which involve measurements of the same fish at different time points. In this work, we demonstrate that the use of an iterative algorithm to reconstruct sparsely sampled OPT data sets can provide useful 3-D images with 50 or fewer projections, thereby significantly decreasing the minimum acquisition time and light dose while maintaining image quality. A transgenic zebrafish embryo with fluorescent labelling of the vasculature was imaged to acquire densely sampled (800 projections) and under-sampled data sets of transmitted and fluorescence projection images. The under-sampled OPT data sets were reconstructed using an iterative total variation-based image reconstruction algorithm and compared against FBP reconstructions of the densely sampled data sets. To illustrate the potential for quantitative analysis following rapid OPT data acquisition, a Hessian-based method was applied to automatically segment the reconstructed images to select the vasculature network. Results showed that 3-D images of the zebrafish embryo and its vasculature of sufficient visual quality for quantitative analysis can be reconstructed using the iterative algorithm from only 32 projections—achieving up to 28 times improvement in imaging speed and leading to total acquisition times of a few seconds.

A hybrid method towards automated nipple detection in 3D breast ultrasound images.

In clinical work-up of breast cancer, nipple position is an important marker to locate lesions. Moreover, it serves as an effective landmark to register a 3D automated breast ultrasound (ABUS) images to other imaging modalities, e.g., X-ray mammography, tomosynthesis or magnetic resonance imaging (MRI). However, the presence of speckle noises caused by the interference waves and variant imaging directions poses challenges to automatically identify nipple positions. In this work, a hybrid fully automatic method to detect nipple positions in ABUS images is presented. The method extends the multi-scale Laplacian-based method that we proposed previously, by integrating a specially designed Hessian-based method to locate the shadow area beneath the nipple and areola. Subsequently, the likelihood maps of nipple positions generated by both methods are combined to build a joint-likelihood map, where the final nipple position is extracted. To validate the efficiency and robustness, the extended hybrid method was tested on 926 ABUS images, resulting in a distance error of 7.08±10.96 mm (mean±standard deviation).

A Hessian-Based Method for Uncertainty Quantification in Global Ocean State Estimation

Derivative-based methods are developed for uncertainty quantification (UQ) in large-scale ocean state estimation. The estimation system is based on the adjoint method for solving a least-squares op...

Automatic Detection of the Nipple in Screen-Film and Full-field Digital Mammograms Using a Novel Hessian-Based Method

Automatic detection of the nipple in mammograms is an important step in computerized systems that combine multiview information for accurate detection and diagnosis of breast cancer. Locating the nipple is a difficult task owing to variations in image quality, presence of noise, and distortion and displacement of the breast tissue due to compression. In this work, we propose a novel Hessian-based method to locate automatically the nipple in screen-film and full-field digital mammograms (FFDMs). The method includes detection of a plausible nipple/retroareolar area in a mammogram using geometrical constraints, analysis of the gradient vector field by mean and Gaussian curvature measurements, and local shape-based conditions. The proposed procedure was tested on 566 mammographic images consisting of 372 randomly selected scanned films from two public databases (mini-MIAS and DDSM), and 194 digital mammograms acquired with a GE Senographe 2000D FFDM system. A radiologist independently marked the centers of the nipples for evaluation of the results. The average error obtained was 6.7 mm (22 pixels) with reference to the center of the nipple as identified by the radiologist. Only two out of the 566 detected nipples (0.35 %) had an error larger than 50 mm. The method was also directly compared with two other techniques for the detection of the nipple. The results indicate that the proposed method outperforms other algorithms presented in the literature and can be used to identify accurately the nipple on various types of mammographic images.

A Hessian-based filter for vascular segmentation of noisy hepatic CT scans

Extraction and enhancement of tubular structures are important in image processing applications, especially in the analysis of liver CT scans where delineation of vascular structures is needed for surgical planning. Portal vein cross-sections have circular or elliptical shapes, so an algorithm must accommodate both. A vessel segmentation method based on medial-axis points was developed and tested on portal veins in CT images. A medial-axis enhancement filter was developed. Consider a line passing through a point inside a tube and intersecting the edges of the tube. If the point is located on the medial axis, the distance of the point in the direction of the line to the edges of the tube will be equal. This feature was employed in a multi-scale framework to identify liver vessels. Dynamic thresholding was used to reduce noise sensitivity. The isotropic coefficient introduced by Pock etal. was used to reduce the response of the filter for asymmetric cross-sections. Quantitative and qualitative evaluation of the proposed method were performed using both 2D/3D and synthetic/clinical datasets. Compared to other methods for medial-axis enhancement, our method produces better results in low-resolution CT images. Detection rate of the medial axis by the proposed method in a noisy image of standard deviation equal to 0.3 is 68% higher than prior methods. A new Hessian-based method for medial axis vessel segmentation was developed and tested. This method produced superior results compared to prior methods. This new method has the potential for many applications of medial-axis enhancement.

Normal mode analysis using the driven molecular dynamics method. II. An application to biological macromolecules.

The driven molecular-dynamics (DMD) method, recently proposed by Bowman, Zhang, and Brown [J. Chem. Phys. 119, 646 (2003)], has been implemented into the TINKER molecular modeling program package. The DMD method yields frequencies and normal modes without evaluation of the Hessian matrix. It employs an external harmonic driving term that can be used to scan the spectrum and determine resonant absorptions. The molecular motions, induced by driving at resonant frequencies, correspond to the normal-mode vibrations. In the current work we apply the method to a 20-residue protein, Trp-cage, that has been reported by Neidigh, Fesinmeyer, and Andersen [Nature Struct. Biol. 9, 425 (2002)]. The structural and dynamical properties of this molecule, such as B-factors, root-mean square fluctuations, anisotropies, vibrational entropy, and cross-correlations coefficients, are calculated using the DMD method. The results are in very good agreement with ones calculated using standard normal-mode analysis method. Thus, the DMD method provides a viable alternative to the standard Hessian-based method and has considerable potential for the study of large systems, where the Hessian-based method is not feasible.