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J. Imaging, Volume 4, Issue 12 (December 2018) – 14 articles

Cover Story (view full-size image): The aim of this study is to investigate a multimodal imaging system for monitoring retinal neovascularization using photoacoustic microscopy (PAM), optical coherence tomography (OCT), fluorescein angiography (FA), and color fundus photography. Retinal neovascularization was generated using intravitreal injection of the vascular endothelial growth factor (VEGF). PAM and OCT demonstrated changes in the retinal morphology and the spatial extent of retinal neovascularization. The multimodal-imaging platform performs imaging with a high lateral spatial resolution of 4.1 µm for PAM and 3.8 µm for OCT, with a high depth of penetration at a safe energy level. This allows for the visualization of retinal neovascularization and microvasculature morphologic changes after VEGF injection. Acquired PAM and OCT imaging provide 3D volumetric images of the vascular network that improve the characterization of the [...] Read more.
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18 pages, 5410 KiB  
Article
In Vivo 3D Imaging of Retinal Neovascularization Using Multimodal Photoacoustic Microscopy and Optical Coherence Tomography Imaging
by Van Phuc Nguyen, Yanxiu Li, Michael Aaberg, Wei Zhang, Xueding Wang and Yannis M. Paulus
J. Imaging 2018, 4(12), 150; https://doi.org/10.3390/jimaging4120150 - 12 Dec 2018
Cited by 23 | Viewed by 7201
Abstract
The pathological process of neovascularization of the retina plays a critical role in causing vision loss in several diseases, including diabetes, retinal vein occlusion, and sickle cell disease. Retinal neovascularization can lead to vitreous hemorrhage and retinal detachment, yet the pathological process of [...] Read more.
The pathological process of neovascularization of the retina plays a critical role in causing vision loss in several diseases, including diabetes, retinal vein occlusion, and sickle cell disease. Retinal neovascularization can lead to vitreous hemorrhage and retinal detachment, yet the pathological process of neovascularization is a complex phenomenon under active investigation. Understanding and monitoring retinal neovascularization is critically important in clinical ophthalmology. This study describes a novel multimodal ocular imaging system which combines photoacoustic microscopy (PAM) and a spectral domain optical coherence tomography (SD-OCT) to improve the visualization of retinal neovascularization (RNV), their depth, and the surrounding anatomy in living rabbits. RNV was induced in New Zealand rabbits by intravitreal injection of vascular endothelial growth factor (VEGF). The retinal vasculature before and after injection at various times was monitored and evaluated using multimodal imaging including color fundus photography, fluorescein angiography (FA), OCT, and PAM. In vivo experiments demonstrate that PAM imaging distinctly characterized the location as well as the morphology of individual RNV with high contrast at a safe laser energy of 80 nJ. SD-OCT was used to identify a cross-sectional structure of RNV. In addition, dynamic changes in the retinal morphology and retinal neovascularization were observed at day 4, 5, 6, 7, 9, 11, 14, 28, and day 35 after VEGF injection. PAM demonstrated high-resolution optical absorption of hemoglobin and vascular imaging of the retina and choroid with increased depth of penetration. With the current multimodal imaging system, RNV can be easily visualized in both 2D and 3D angiography. This multimodal ocular imaging system provides improved characterization of the microvasculature in a safe manner in larger rabbit eyes. Full article
(This article belongs to the Special Issue Biomedical Photoacoustic Imaging: Technologies and Methods)
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24 pages, 67496 KiB  
Review
Photoacoustic Ophthalmoscopy: Principle, Application, and Future Directions
by Van Phuc Nguyen and Yannis M. Paulus
J. Imaging 2018, 4(12), 149; https://doi.org/10.3390/jimaging4120149 - 12 Dec 2018
Cited by 25 | Viewed by 8300
Abstract
Photoacoustic ophthalmoscopy (PAOM) is a novel, hybrid, non-ionizing, and non-invasive imaging technology that has been used to assess the retina. PAOM can provide both anatomic and functional retinal characterizations with high resolution, high sensitivity, high contrast, and a high depth of penetration. Thus, [...] Read more.
Photoacoustic ophthalmoscopy (PAOM) is a novel, hybrid, non-ionizing, and non-invasive imaging technology that has been used to assess the retina. PAOM can provide both anatomic and functional retinal characterizations with high resolution, high sensitivity, high contrast, and a high depth of penetration. Thus, ocular diseases can be precisely detected and visualized at earlier stages, resulting in an improved understanding of pathophysiology, improved management, and the improved monitoring of retinal treatment to prevent vision loss. To better visualize ocular components such as retinal vessels, choroidal vessels, choroidal neovascularization, retinal neovascularization, and the retinal pigment epithelium, an advanced multimodal ocular imaging platform has been developed by a combination of PAOM with other optical imaging techniques such as optical coherence tomography (OCT), scanning laser ophthalmoscopy (SLO), and fluorescence microscopy. The multimodal images can be acquired from a single imaging system and co-registered on the same image plane, enabling an improved evaluation of disease. In this review, the potential application of photoacoustic ophthalmoscopy in both research and clinical diagnosis are discussed as a medical screening technique for the visualization of various ocular diseases. The basic principle and requirements of photoacoustic ocular imaging are introduced. Then, various photoacoustic microscopy imaging systems of the retina in animals are presented. Finally, the future development of PAOM and multimodal imaging is discussed. Full article
(This article belongs to the Special Issue Biomedical Photoacoustic Imaging: Technologies and Methods)
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19 pages, 3735 KiB  
Article
Image Reconstruction with Reliability Assessment in Quantitative Photoacoustic Tomography
by Niko Hänninen, Aki Pulkkinen and Tanja Tarvainen
J. Imaging 2018, 4(12), 148; https://doi.org/10.3390/jimaging4120148 - 11 Dec 2018
Cited by 10 | Viewed by 5418
Abstract
Quantitative photoacoustic tomography is a novel imaging method which aims to reconstruct optical parameters of an imaged target based on initial pressure distribution, which can be obtained from ultrasound measurements. In this paper, a method for reconstructing the optical parameters in a Bayesian [...] Read more.
Quantitative photoacoustic tomography is a novel imaging method which aims to reconstruct optical parameters of an imaged target based on initial pressure distribution, which can be obtained from ultrasound measurements. In this paper, a method for reconstructing the optical parameters in a Bayesian framework is presented. In addition, evaluating the credibility of the estimates is studied. Furthermore, a Bayesian approximation error method is utilized to compensate the modeling errors caused by coarse discretization of the forward model. The reconstruction method and the reliability of the credibility estimates are investigated with two-dimensional numerical simulations. The results suggest that the Bayesian approach can be used to obtain accurate estimates of the optical parameters and the credibility estimates of these parameters. Furthermore, the Bayesian approximation error method can be used to compensate for the modeling errors caused by a coarse discretization, which can be used to reduce the computational costs of the reconstruction procedure. In addition, taking the modeling errors into account can increase the reliability of the credibility estimates. Full article
(This article belongs to the Special Issue Biomedical Photoacoustic Imaging: Technologies and Methods)
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15 pages, 1605 KiB  
Article
Confidence Estimation for Machine Learning-Based Quantitative Photoacoustics
by Janek Gröhl, Thomas Kirchner, Tim Adler and Lena Maier-Hein
J. Imaging 2018, 4(12), 147; https://doi.org/10.3390/jimaging4120147 - 10 Dec 2018
Cited by 26 | Viewed by 6607
Abstract
In medical applications, the accuracy and robustness of imaging methods are of crucial importance to ensure optimal patient care. While photoacoustic imaging (PAI) is an emerging modality with promising clinical applicability, state-of-the-art approaches to quantitative photoacoustic imaging (qPAI), which aim to solve the [...] Read more.
In medical applications, the accuracy and robustness of imaging methods are of crucial importance to ensure optimal patient care. While photoacoustic imaging (PAI) is an emerging modality with promising clinical applicability, state-of-the-art approaches to quantitative photoacoustic imaging (qPAI), which aim to solve the ill-posed inverse problem of recovering optical absorption from the measurements obtained, currently cannot comply with these high standards. This can be attributed to the fact that existing methods often rely on several simplifying a priori assumptions of the underlying physical tissue properties or cannot deal with realistic noise levels. In this manuscript, we address this issue with a new method for estimating an indicator of the uncertainty of an estimated optical property. Specifically, our method uses a deep learning model to compute error estimates for optical parameter estimations of a qPAI algorithm. Functional tissue parameters, such as blood oxygen saturation, are usually derived by averaging over entire signal intensity-based regions of interest (ROIs). Therefore, we propose to reduce the systematic error of the ROI samples by additionally discarding those pixels for which our method estimates a high error and thus a low confidence. In silico experiments show an improvement in the accuracy of optical absorption quantification when applying our method to refine the ROI, and it might thus become a valuable tool for increasing the robustness of qPAI methods. Full article
(This article belongs to the Special Issue Biomedical Photoacoustic Imaging: Technologies and Methods)
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13 pages, 4294 KiB  
Article
Exploiting Nonlinear Photoacoustic Signal Generation in Gold Nanospheres for Selective Detection in Serial 3D PA Tomography
by Susanne Schrof, Genny A. Pang, Jens Buchmann and Jan Laufer
J. Imaging 2018, 4(12), 146; https://doi.org/10.3390/jimaging4120146 - 08 Dec 2018
Cited by 11 | Viewed by 5614
Abstract
The photoacoustic (PA) signal amplitude measured in gold nanosphere suspensions has been shown to increase nonlinearly with the incident excitation fluence. In this work, this effect is exploited to recover the spatial distribution of gold nanoparticles in tomographic 3D photoacoustic (PA) images against [...] Read more.
The photoacoustic (PA) signal amplitude measured in gold nanosphere suspensions has been shown to increase nonlinearly with the incident excitation fluence. In this work, this effect is exploited to recover the spatial distribution of gold nanoparticles in tomographic 3D photoacoustic (PA) images against the background contrast provided by absorbers that exhibit a linear relationship between the PA signal amplitude and the fluence. Serial tomographic PA images of a tissue phantom containing gold nanospheres and a tissue-mimicking absorber were acquired. By assessing the linearity of the PA intensity voxel by voxel, the spatial distribution of the gold nanosphere suspension was recovered. The method is shown to enable the robust detection of gold nanoparticles. Full article
(This article belongs to the Special Issue Biomedical Photoacoustic Imaging: Technologies and Methods)
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11 pages, 1185 KiB  
Article
Receive Beam-Steering and Clutter Reduction for Imaging the Speed-of-Sound Inside the Carotid Artery
by Maju Kuriakose, Jan-Willem Muller, Patrick Stähli, Martin Frenz and Michael Jaeger
J. Imaging 2018, 4(12), 145; https://doi.org/10.3390/jimaging4120145 - 07 Dec 2018
Cited by 3 | Viewed by 4433
Abstract
Handheld imaging of the tissue’s speed-of-sound (SoS) is a promising multimodal addition to diagnostic ultrasonography for the examination of tissue composition. Computed ultrasound tomography in echo mode (CUTE) probes the spatial distribution of SoS, conventionally via scanning the tissue under a varying angle [...] Read more.
Handheld imaging of the tissue’s speed-of-sound (SoS) is a promising multimodal addition to diagnostic ultrasonography for the examination of tissue composition. Computed ultrasound tomography in echo mode (CUTE) probes the spatial distribution of SoS, conventionally via scanning the tissue under a varying angle of ultrasound transmission, and quantifying—in a spatially resolved way—phase variations of the beamformed echoes. So far, this technique is not applicable to imaging the lumen of vessels, where blood flow and tissue clutter inhibit phase tracking of the blood echoes. With the goal to enable the assessment of atherosclerotic plaque composition inside the carotid artery, we propose two modifications to CUTE: (a) use receive (Rx) beam-steering as opposed to transmit (Tx) beam-steering to increase acquisition speed and to reduce flow-related phase decorrelation, and (b) conduct pairwise subtraction of data obtained from repetitions of the scan sequence, to highlight blood echoes relative to static echo clutter and thus enable the phase tracking of blood echoes. These modifications were tested in a phantom study, where the echogenicity of the vessel lumen was chosen to be similar to the one of the background medium, which allows a direct comparison of SoS images obtained with the different techniques. Our results demonstrate that the combination of Rx-steering with the subtraction technique results in an SoS image of the same quality as obtained with conventional Tx-steering. Together with the improved acquisition speed, this makes the proposed technique a key step towards successful imaging of the SoS inside the carotid artery. Full article
(This article belongs to the Special Issue Biomedical Photoacoustic Imaging: Technologies and Methods)
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11 pages, 1695 KiB  
Article
Investigation of the Performance of Hyperspectral Imaging by Principal Component Analysis in the Prediction of Healing of Diabetic Foot Ulcers
by Qian Yang, Shen Sun, William J. Jeffcoate, Daniel J. Clark, Alison Musgove, Fran L. Game and Stephen P. Morgan
J. Imaging 2018, 4(12), 144; https://doi.org/10.3390/jimaging4120144 - 07 Dec 2018
Cited by 28 | Viewed by 5891
Abstract
Diabetic foot ulcers are a major complication of diabetes and present a considerable burden for both patients and health care providers. As healing often takes many months, a method of determining which ulcers would be most likely to heal would be of great [...] Read more.
Diabetic foot ulcers are a major complication of diabetes and present a considerable burden for both patients and health care providers. As healing often takes many months, a method of determining which ulcers would be most likely to heal would be of great value in identifying patients who require further intervention at an early stage. Hyperspectral imaging (HSI) is a tool that has the potential to meet this clinical need. Due to the different absorption spectra of oxy- and deoxyhemoglobin, in biomedical HSI the majority of research has utilized reflectance spectra to estimate oxygen saturation (SpO2) values from peripheral tissue. In an earlier study, HSI of 43 patients with diabetic foot ulcers at the time of presentation revealed that ulcer healing by 12 weeks could be predicted by the assessment of SpO2 calculated from these images. Principal component analysis (PCA) is an alternative approach to analyzing HSI data. Although frequently applied in other fields, mapping of SpO2 is more common in biomedical HSI. It is therefore valuable to compare the performance of PCA with SpO2 measurement in the prediction of wound healing. Data from the same study group have now been used to examine the relationship between ulcer healing by 12 weeks when the results of the original HSI are analyzed using PCA. At the optimum thresholds, the sensitivity of prediction of healing by 12 weeks using PCA (87.5%) was greater than that of SpO2 (50.0%), with both approaches showing equal specificity (88.2%). The positive predictive value of PCA and oxygen saturation analysis was 0.91 and 0.86, respectively, and a comparison by receiver operating characteristic curve analysis revealed an area under the curve of 0.88 for PCA compared with 0.66 using SpO2 analysis. It is concluded that HSI may be a better predictor of healing when analyzed by PCA than by SpO2. Full article
(This article belongs to the Special Issue The Future of Hyperspectral Imaging)
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13 pages, 9653 KiB  
Article
Spatial Referencing of Hyperspectral Images for Tracing of Plant Disease Symptoms
by Jan Behmann, David Bohnenkamp, Stefan Paulus and Anne-Katrin Mahlein
J. Imaging 2018, 4(12), 143; https://doi.org/10.3390/jimaging4120143 - 04 Dec 2018
Cited by 18 | Viewed by 6538
Abstract
The characterization of plant disease symptoms by hyperspectral imaging is often limited by the missing ability to investigate early, still invisible states. Automatically tracing the symptom position on the leaf back in time could be a promising approach to overcome this limitation. Therefore [...] Read more.
The characterization of plant disease symptoms by hyperspectral imaging is often limited by the missing ability to investigate early, still invisible states. Automatically tracing the symptom position on the leaf back in time could be a promising approach to overcome this limitation. Therefore we present a method to spatially reference time series of close range hyperspectral images. Based on reference points, a robust method is presented to derive a suitable transformation model for each observation within a time series experiment. A non-linear 2D polynomial transformation model has been selected to cope with the specific structure and growth processes of wheat leaves. The potential of the method is outlined by an improved labeling procedure for very early symptoms and by extracting spectral characteristics of single symptoms represented by Vegetation Indices over time. The characteristics are extracted for brown rust and septoria tritici blotch on wheat, based on time series observations using a VISNIR (400–1000 nm) hyperspectral camera. Full article
(This article belongs to the Special Issue The Future of Hyperspectral Imaging)
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15 pages, 6045 KiB  
Article
Efficient Lossless Compression of Multitemporal Hyperspectral Image Data
by Hongda Shen, Zhuocheng Jiang and W. David Pan
J. Imaging 2018, 4(12), 142; https://doi.org/10.3390/jimaging4120142 - 02 Dec 2018
Cited by 13 | Viewed by 5295
Abstract
Hyperspectral imaging (HSI) technology has been used for various remote sensing applications due to its excellent capability of monitoring regions-of-interest over a period of time. However, the large data volume of four-dimensional multitemporal hyperspectral imagery demands massive data compression techniques. While conventional 3D [...] Read more.
Hyperspectral imaging (HSI) technology has been used for various remote sensing applications due to its excellent capability of monitoring regions-of-interest over a period of time. However, the large data volume of four-dimensional multitemporal hyperspectral imagery demands massive data compression techniques. While conventional 3D hyperspectral data compression methods exploit only spatial and spectral correlations, we propose a simple yet effective predictive lossless compression algorithm that can achieve significant gains on compression efficiency, by also taking into account temporal correlations inherent in the multitemporal data. We present an information theoretic analysis to estimate potential compression performance gain with varying configurations of context vectors. Extensive simulation results demonstrate the effectiveness of the proposed algorithm. We also provide in-depth discussions on how to construct the context vectors in the prediction model for both multitemporal HSI and conventional 3D HSI data. Full article
(This article belongs to the Special Issue The Future of Hyperspectral Imaging)
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11 pages, 3222 KiB  
Article
Age Determination of Blood-Stained Fingerprints Using Visible Wavelength Reflectance Hyperspectral Imaging
by Samuel Cadd, Bo Li, Peter Beveridge, William T. O'Hare and Meez Islam
J. Imaging 2018, 4(12), 141; https://doi.org/10.3390/jimaging4120141 - 29 Nov 2018
Cited by 22 | Viewed by 7853
Abstract
The ability to establish the exact time a crime was committed is one of the fundamental aims of forensic science. The analysis of recovered evidence can provide information to assist in age determination, such as blood, which is one of the most commonly [...] Read more.
The ability to establish the exact time a crime was committed is one of the fundamental aims of forensic science. The analysis of recovered evidence can provide information to assist in age determination, such as blood, which is one of the most commonly encountered types of biological evidence and the most common fingerprint contaminant. There are currently no accepted methods to establish the age of a blood-stained fingerprint, so progress in this area would be of considerable benefit for forensic investigations. A novel application of visible wavelength reflectance, hyperspectral imaging (HSI), is used for the detection and age determination of blood-stained fingerprints on white ceramic tiles. Both identification and age determination are based on the unique visible absorption spectrum of haemoglobin between 400 and 680 nm and the presence of the Soret peak at 415 nm. In this study, blood-stained fingerprints were aged over 30 days and analysed using HSI. False colour aging scales were produced from a 30-day scale and a 24 h scale, allowing for a clear visual method for age estimations for deposited blood-stained fingerprints. Nine blood-stained fingerprints of varying ages deposited on one white ceramic tile were easily distinguishable using the 30-day false colour scale. Full article
(This article belongs to the Special Issue The Future of Hyperspectral Imaging)
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12 pages, 5174 KiB  
Article
MRI Robot for Prostate Focal Laser Ablation: An Ex Vivo Study in Human Prostate
by Reza Seifabadi, Ming Li, Sheng Xu, Yue Chen, Alex Squires, Ayele H. Negussie, Ivane Bakhutashvili, Peter Choyke, Ismail B. Turkbey, Zion Tsz Ho Tse and Bradford J. Wood
J. Imaging 2018, 4(12), 140; https://doi.org/10.3390/jimaging4120140 - 29 Nov 2018
Cited by 8 | Viewed by 6035
Abstract
Purpose: A novel grid-template-mimicking MR-compatible robot was developed for in-gantry MRI-guided focal laser ablation of prostate cancer. Method: A substantially compact robot was designed and prototyped to meet in-gantry lithotomy ergonomics and allow for accommodation in the perineum. The controller software [...] Read more.
Purpose: A novel grid-template-mimicking MR-compatible robot was developed for in-gantry MRI-guided focal laser ablation of prostate cancer. Method: A substantially compact robot was designed and prototyped to meet in-gantry lithotomy ergonomics and allow for accommodation in the perineum. The controller software was reconfigured and integrated with the custom-designed navigation and multi-focal ablation software. Three experiments were conducted: (1) free space accuracy test; (2) phantom study under computed tomography (CT) guidance for image-guided accuracy test and overall workflow; and (3) magnetic resonance imaging (MRI)-guided focal laser ablation of an ex vivo prostate. The free space accuracy study included five targets that were selected across the workspace. The robot was then commanded five times to each target. The phantom study used a gel phantom made with color changing thermos-chromic ink, and four spherical metal fiducials were deployed with the robot. Then, laser ablation was applied, and the phantom was sliced for gross observation. For an MR-guided ex vivo test, a prostate from a donor who died of prostate cancer was obtained and multi-focally ablated using the system within the MRI gantry. The tissue was sliced after ablation for validation. Results: free-space accuracy was 0.38 ± 0.27 mm. The overall system targeting accuracy under CT guidance (including robot, registration, and insertion error) was 2.17 ± 0.47 mm. The planned ablation zone was successfully covered in both acrylamide gel phantom and in human prostate tissue. Conclusions: The new robot can accurately facilitate fiber targeting for MR-guided focal laser ablation of targetable prostate cancer. Full article
(This article belongs to the Special Issue Image-Guided Medical Robotics)
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9 pages, 2539 KiB  
Article
A Tomograph Prototype for Quantitative Microwave Imaging: Preliminary Experimental Results
by Alessandro Fedeli, Manuela Maffongelli, Ricardo Monleone, Claudio Pagnamenta, Matteo Pastorino, Samuel Poretti, Andrea Randazzo and Andrea Salvadè
J. Imaging 2018, 4(12), 139; https://doi.org/10.3390/jimaging4120139 - 26 Nov 2018
Cited by 15 | Viewed by 5764
Abstract
A new prototype of a tomographic system for microwave imaging is presented in this paper. The target being tested is surrounded by an ad-hoc 3D-printed structure, which supports sixteen custom antenna elements. The transmission measurements between each pair of antennas are acquired through [...] Read more.
A new prototype of a tomographic system for microwave imaging is presented in this paper. The target being tested is surrounded by an ad-hoc 3D-printed structure, which supports sixteen custom antenna elements. The transmission measurements between each pair of antennas are acquired through a vector network analyzer connected to a modular switching matrix. The collected data are inverted by a hybrid nonlinear procedure combining qualitative and quantitative reconstruction algorithms. Preliminary experimental results, showing the capabilities of the developed system, are reported. Full article
(This article belongs to the Special Issue Microwave Imaging and Electromagnetic Inverse Scattering Problems)
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21 pages, 509 KiB  
Article
Border Handling for 2D Transpose Filter Structures on an FPGA
by Donald G. Bailey and Anoop S. Ambikumar
J. Imaging 2018, 4(12), 138; https://doi.org/10.3390/jimaging4120138 - 26 Nov 2018
Cited by 7 | Viewed by 6038
Abstract
It is sometimes desirable to implement filters using a transpose-form filter structure. However, managing image borders is generally considered more complex than it is with the more commonly used direct-form structure. This paper explores border handling for transpose-form filters, and proposes two novel [...] Read more.
It is sometimes desirable to implement filters using a transpose-form filter structure. However, managing image borders is generally considered more complex than it is with the more commonly used direct-form structure. This paper explores border handling for transpose-form filters, and proposes two novel mechanisms: transformation coalescing, and combination chain modification. For linear filters, coefficient coalescing can effectively exploit the digital signal processing blocks, resulting in the smallest resources requirements. Combination chain modification requires similar resources to direct-form border handling. It is demonstrated that the combination chain multiplexing can be split into two stages, consisting of a combination network followed by the transpose-form combination chain. The resulting transpose-form border handling networks are of similar complexity to the direct-form networks, enabling the transpose-form filter structure to be used where required. The transpose form is also significantly faster, being automatically pipelined by the filter structure. Of the border extension methods, zero-extension requires the least resources. Full article
(This article belongs to the Special Issue Image Processing Using FPGAs)
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18 pages, 2176 KiB  
Article
The Ascendency of Numerical Methods in Lens Design
by Donald C. Dilworth
J. Imaging 2018, 4(12), 137; https://doi.org/10.3390/jimaging4120137 - 24 Nov 2018
Cited by 3 | Viewed by 5138
Abstract
Advancement in physics often results from analyzing numerical data and then creating a theoretical model that can explain and predict those data. In the field of lens design, the reverse is true: longstanding theoretical understanding is being overtaken by more powerful numerical methods. [...] Read more.
Advancement in physics often results from analyzing numerical data and then creating a theoretical model that can explain and predict those data. In the field of lens design, the reverse is true: longstanding theoretical understanding is being overtaken by more powerful numerical methods. Full article
(This article belongs to the Special Issue Computation and Analysis of Imaging Aberrations)
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