Lambertian Model Research Articles

Robust Photometric Stereo via Dictionary Learning

Photometric stereo is a method that seeks to reconstruct the normal vectors of an object from a set of images of the object illuminated under different light sources. While effective in some situations, classical photometric stereo relies on a diffuse surface model that cannot handle objects with complex reflectance patterns, and it is sensitive to non-idealities in the images. In this paper, we propose a novel approach to photometric stereo that relies on dictionary learning to produce robust normal vector reconstructions. Specifically, we develop two formulations for applying dictionary learning to photometric stereo. We propose a model that applies dictionary learning to regularize and reconstruct the normal vectors from the images under the classic Lambertian reflectance model. We then generalize this model to explicitly model non-Lambertian objects. We investigate both approaches using extensive experimentation on synthetic and real benchmark datasets and observe state-of-the-art performance compared to the existing robust photometric stereo methods.

FRESCO-B: a fast cloud retrieval algorithm using oxygen B-band measurements from GOME-2

Abstract. The FRESCO (Fast Retrieval Scheme for Clouds from the Oxygen A band) algorithm is a simple, fast and robust algorithm used to retrieve cloud information in operational satellite data processing. It has been applied to GOME-1 (Global Ozone Monitoring Experiment), SCIAMACHY (Scanning Imaging Absorption Spectrometer for Atmospheric Chartography), GOME-2 and more recently to TROPOMI (Tropospheric Monitoring Instrument). FRESCO retrieves effective cloud fraction and cloud pressure from measurements in the oxygen A band around 761 nm. In this paper, we propose a new version of the algorithm, called FRESCO-B, which is based on measurements in the oxygen B band around 687 nm. Such a method is interesting for vegetated surfaces where the surface albedo is much lower in the B band than in the A band, which limits the ground contribution to the top-of-atmosphere reflectances. In this study we first perform retrieval simulations. These show that the retrieved cloud pressures from FRESCO-B and FRESCO differ only between −10 and +10 hPa, except for high, thin clouds over vegetation where the difference is larger (about +15 to +30 hPa), with FRESCO-B yielding higher pressure. Next, inter-comparison between FRESCO-B and FRESCO retrievals over 1 month of GOME-2B data reveals that the effective cloud fractions retrieved in the O2 A and B bands are very similar (mean difference of 0.003), while the cloud pressures show a mean difference of 11.5 hPa, with FRESCO-B retrieving higher pressures than FRESCO. This agrees with the simulations and is partly due to deeper photon penetrations of the O2 B band in clouds compared to the O2 A-band photons and partly due to the surface albedo bias in FRESCO. Finally, validation with ground-based measurements shows that the FRESCO-B cloud pressure represents an altitude within the cloud boundaries for clouds that are not too far from the Lambertian reflector model, which occurs in about 50 % of the cases.

Polarization-based exploration for clear underwater vision in natural illumination.

Underwater imaging provides human vision system friendly images; however, it often suffers from severe image degradation. This research developed an underwater polarization imaging model, which considers the water scattering effect, as well as absorption effect. It fully explored the polarization information of the target scene that backscattered light is partially polarized and target light is unpolarized. Then backscattered light is first estimated and removed. The target scene's distance information is derived based upon the polarization information, and then applied to develop a distance-based Lambertian model. This model enables estimation of the intensity loss caused by water absorption and accurate target radiance recovery. Furthermore, real-world experiments show that the developed model handled the underwater image degradation well. In particular, it enables effective color cast correction resulting from water absorption, which traditional imaging methods always ignore.

Visible Light Positioning via Floor Reflections

The last two decades have witnessed significant advances in the field of indoor positioning systems, which have led to technologies with high location precision. However, there still lacks robust meter-level indoor positioning approaches which only rely on in-building communication infrastructures and smartphones. We present STARLIT, a system that enables a single LED beacon to localize smartphones to within sub-meter. As the smartphone camera contains millions of pixels, we create a virtual sensor array with the camera to measure the received signal strength (RSS) of the LED beacon. Different from the existing camera-based approaches, which need to capture images of the LED within a short light-to-camera distance, we utilize the reflection light from the floor. By exploiting the rolling shutter mechanism in the smartphone cameras, we propose a solution to separate the signal layer from the image background and noise. Given the measured RSSs, we establish an equation set with the Lambertian model and the camera projection model to solve the location of the smartphone. We have implemented STARLIT and evaluated its performance in an office room. Our experiments demonstrate that the STARLIT can achieve a median error of 23cm and an 80-percentile error of 55cm.

Underwater Image Enhancement Based on Removing Light Source Color and Dehazing

Typical underwater images exhibit poor visibility because of light scattering and absorption in turbid water. To resolve the ill-posed problem, a novel underwater image enhancement method based on Removing Light Source Color and Dehazing(RLSCD) is proposed. Scene depth, which is assumed strongly correlated with attenuations, is often ignored in most of the previous methods. A new scene depth estimation, which takes the attenuations of the different light conditions into account, is first presented. Additionally, the background light is estimated based on gray open operation and scene depth to avoid that the pixels in the white objects and artificial lighting regions may be wrongly estimated as the background light. With the estimated background light and transmission map, the dehazed image is achievable. Moreover, the theoretical analysis of the Lambertian Model indicates that the disturbance of the light source color in dehazed image can be estimated, this phenomenon enables us to correct color distortion and light overcompensation by removing the disturbance. Experimental results demonstrate the RLSCD method outperforms state-of-the-art methods in terms of relatively genuine color, increased contrast, and brightness.

Performance comparison and analysis on different optimization models for high-precision three-dimensional visible light positioning

With the development of visible light communication, indoor visible light positioning (VLP) becomes popular for researchers in the communication industry. However, most existing VLP algorithms only provide solutions for positioning on a two-dimensional plane, and those focusing on three-dimensional (3-D) positioning usually contain various sensors or hybrid algorithms. To solve these problems, first we transform the 3-D location model in VLP into an optimization model and adopt distance based optimization model (DBOM) for positioning based on the measured distances from the positioning terminal to multiple LEDs base stations. Second, we further come up with an area-based optimization model (ABOM) for localization by the intersection of three circles based on the received signal strength trilateration algorithm. The proposed ABOM converts the 3-D optimization problem into a one-dimensional searching problem, thereby ensuring the real-time positioning performance. Third, an effective 3-D optimization algorithm is adopted to judge the positioning performances of two proposed models. Last but not least, we also set up an extended simulation, analyzing the nonlinearity of the Lambert model and the positioning unit size’s effect on the maximum positioning height, which has never been considered by existing works. Our simulation shows that the average positioning error is 0.96 cm for ABOM and 3.21 cm for DBOM. Besides, the experimental results of the actual scene also confirm that the mentioned system can achieve an average 3-D positioning error of 4.34 cm.

Outage and error analysis of three hop hybrid VLC/FSO/VLC–based relayed optical wireless communication system

AbstractIn this paper, we consider a three hop hybrid visible light communication/free space optical/visible light communication (VLC/FSO/VLC) system in which the information is transmitted from a room inside the building on a VLC link toward the decode and forward (DF) relay attached to that building. The relay maps the incoming signal on the FSO link and forwards it to the other DF relay attached to the second building, which further passes it down to the user inside the room onto the VLC downlink. The VLC and FSO links follow the Lambertian emission model and Gamma‐Gamma fading statistics, respectively, under the impact of atmospheric turbulence, pointing errors, semiangle, and field of view of the detector. The performance of the three hop hybrid system is derived in terms of the closed‐form expression for the outage probability. The error performance is analyzed in terms of average symbol error probability of the considered hybrid system. Furthermore, an expression for asymptotic outage probability of the system is derived to investigate the behavior of the system at high signal‐to‐noise ratio (SNR) regimes. The impact of variation in the parameters on the hybrid VLC/FSO//VLC communication system performance is illustrated by the numerical plots.

Application of the Beer–Lambert Model to Attenuation of Photosynthetically Active Radiation in a Shallow, Eutrophic Lake

AbstractModels of primary production in aquatic systems must include a means to estimate subsurface light. Such models often use the Beer–Lambert law, assuming exponential attenuation of light with depth. It is further assumed that the diffuse attenuation coefficient may be estimated as a summation of scattering/absorbing constituent concentrations multiplied by their respective specific attenuation coefficients. While theoretical deviations from these assumptions have been documented, it is useful to consider the empirical performance of this common approach. Photosynthetically active radiation (PAR) levels and water quality conditions were recorded weekly from six to eight monitoring stations in western Lake Erie between 2012 and 2016. Exponential PAR extinction models yielded a mean attenuation coefficient of 1.55 m (interquartile range = 0.74–1.90 m). While more complex light attenuation models are available, analysis of residuals indicated that the simple Beer–Lambert model is adequate for shallow, eutrophic waters similar to western Lake Erie (R2 > 0.9 for 96% of samples). Three groups of water quality variables were predictive of PAR attenuation: total and nonvolatile suspended particles, dissolved organic substances (dissolved organic carbon and chromophoric dissolved organic matter), and organic solids (volatile suspended solids and chlorophyll). Multiple regression models using these variables predicted 3–90% of the variability in PAR attenuation, with a median adjusted R2 = 0.86. Explanatory variables within these groups may substitute for each other while maintaining similar model performance, indicating that various combinations of water quality variables may be useful to predict PAR attenuation, depending on availability within a model framework or monitoring program.

Revisiting Outlier Rejection Approach for Non-Lambertian Photometric Stereo.

Photometric stereo offers a single camera based approach to recover 3D information and has attracted wide range of applications in computer vision. Presence of non-Lambertian reflections in almost all the real-world objects limits the usage of the Lambertian model for surface normal vector estimation. Previous methods proposed to address such non-Lambertian phenomena employ an outlier rejection approach while more recent methods introduce BRDF models which can generate more accurate results. However, results with comparable accuracy can also be achieved by simply filtering the observed intensity values. This paper presents two novel outlier rejection techniques which attempt to identify the data which are more reliable and likely to be Lambertian. In the first technique, observed intensity values with less reliability are automatically eliminated. This reliability is determined by the responses from a newly introduced inter-relationship function. In the second technique, those photometric ratio equations which are less likely to be Lambertian are identified by observing the residue of the equations. By eliminating the data which is unreliable and likely to be non-Lambertian, surface normal vectors are more accurately estimated. Our comparative and reproducible experimental results using both real and synthetic datasets illustrate superior performance over the state-of-the-art methods, which validates our theoretical arguments presented in this paper.

Indoor visible light communications: performance evaluation and optimization

For indoor visible light communication (VLC), much work has been done when the noise is independent of the input signal. However, less effort is made when the VLC system suffers from the input-dependent noise. Considering the input-dependent noise, this paper focuses on the performance analysis and optimization for indoor VLC system. The Lambertian emission-based channel model and on-off keying modulation are employed. According to the system model, the bit error rate (BER) with a closed-form expression is derived. To enhance the system performance, an optimization problem that minimizes the BER by tilting the receiver plane is formulated. By solving the problem, the optimal tilting angle of the receiver is obtained. Simulation results verify the derived expression of BER. It is also shown that the BER is strongly affected by the input-dependent noise. Moreover, the optimal tilting angles for the receiver at any position are obtained, which can provide some insights for practical system design.

A Novel Approach to Droplet's 3D Shape Recovery Based on Mask R-CNN and Improved Lambert⁻Phong Model.

Aiming at the demand for extracting the three-dimensional shapes of droplets in microelectronic packaging, life science, and some related fields, as well as the problems of complex calculation and slow running speed of conventional shape from shading (SFS) illumination reflection models, this paper proposes a Lambert–Phong hybrid model algorithm to recover the 3D shapes of micro-droplets based on the mask regions with convolutional neural network features (R-CNN) method to extract the highlight region of the droplet surface. This method fully integrates the advantages of the Lambertian model’s fast running speed and the Phong model’s high accuracy for reconstruction of the highlight region. First, the Mask R-CNN network is used to realize the segmentation of the highlight region of the droplet and obtain its coordinate information. Then, different reflection models are constructed for the different reflection regions of the droplet, and the Taylor expansion and Newton iteration method are used for the reflection model to get the final height of all positions. Finally, a three-dimensional reconstruction experimental platform is built to analyze the accuracy and speed of the algorithm on the synthesized hemisphere image and the actual droplet image. The experimental results show that the proposed algorithm based on mask R-CNN had better precision and shorter running time. Hence, this paper provides a new approach for real-time measurement of 3D droplet shape in the dispensing state.

Normalization of face illumination using basic knowledge and information extracted from a single image

This paper presents a method for face image normalization that can be applied to the extraction of illumination invariant facial features or used to remove bad lighting effects and produce high-quality, photorealistic results. Most of the existing approaches concentrate on separating the constant albedo from the variable light intensity; that concept, however, is based on the Lambertian model, which fails in the presence of specularities and cast shadows. Therefore, to tackle this problem, various methods use bootstrap sets to learn the reflectance model of a given person or a face in general. Unfortunately, algorithms of this type are usually not practical for real applications. The proposed approach does not require any training procedure, as the normalization is performed only on the basis of information that is contained in the image that is being processed. Still, external knowledge that is represented by the deformable shape model is employed to execute the localization of the important points, such as eye centers. Additionally, an assumption regarding the symmetry of the face is utilized. The rest of the normalization algorithm relies mostly on simple image processing techniques. Experiments on the CMU-PIE and Extended Yale B databases show that the new method not only provides satisfactory recognition results but is also able to generate natural-looking images.

A New Oren–Nayar Shape-from-Shading Approach for 3D Reconstruction Using High-Order Godunov-Based Scheme

3D shape reconstruction from images has been an important topic in the field of robot vision. Shape-From-Shading (SFS) is a classical method for determining the shape of a 3D surface from a one intensity image. The Lambertian reflectance is a fundamental assumption in conventional SFS approaches. Unfortunately, when applied to characterize the reflection attribute of the diffuse reflection, the Lambertian model is tested to be inexact. In this paper, we present a new SFS approach for 3D reconstruction of diffuse surfaces whose reflection attribute is approximated by the Oren–Nayar reflection model. The partial differential Image Irradiance Equation (IIR) is set up with this model under a single distant point light source and an orthographic camera projection whose direction coincides with the light source. Then, the IIR is converted into an eikonal equation by solving a quadratic equation that includes the 3D surface shape. The viscosity solution of the resulting eikonal equation is approximated by using the high-order Godunov-based scheme that is accelerated by means of an alternating sweeping strategy. We conduct the experiments on synthetic and real-world images, and the experimental results illustrate the effectiveness of the presented approach.

Directional gradients integration image for illumination insensitive face representation

The illumination problem is one of the main bottlenecks in a practical face recognition system. Illumination preprocessing is an effective way to handle lighting variations for robust face recognition. In this paper, we present a novel illumination insensitive image, namely directional gradients integration image (DGII), for illumination insensitive face recognition. Unlike the existing model-based methods, the DGII is generated directly from the decomposed gradient components of a logarithmic image, without involving any training procedure. Based on the Lambertian reflectance model, we first calculate the horizontal and vertical gradients in the logarithmic domain to eliminate the illumination component. Secondly, to utilize the gradient orientation information, the two gradients are further decomposed into four components along four directions. Then, the four directional gradients are integrated to reconstruct an illumination insensitive image using anisotropic diffusion. Finally, the reconstructed image is fused with the gradient magnitude image through weighted summing. For performance evaluation, we simply use principal component analysis for feature extraction, Euclidean distance as similarity measure and nearest-neighbor classifier for face recognition. Experiments on the Yale B, the extended Yale B and the CMU PIE (The Carnegie Mellon University pose, illumination and expression database) face databases show that the proposed method provides better results than some state-of-the-art methods, showing its effectiveness for illumination normalization.

Tensors, Differential Geometry and Statistical Shading Analysis

We develop a linear algebraic framework for the shape-from-shading problem, because tensors arise when scalar (e.g., image) and vector (e.g., surface normal) fields are differentiated multiple times. Using this framework, we first investigate when image derivatives exhibit invariance to changing illumination by calculating the statistics of image derivatives under general distributions on the light source. Second, we apply that framework to develop Taylor-like expansions and build a boot-strapping algorithm to find the polynomial surface solutions (under any light source) consistent with a given patch to arbitrary order. A generic constraint on the light source restricts these solutions to a 2-D subspace, plus an unknown rotation matrix. It is this unknown matrix that encapsulates the ambiguity in the problem. Finally, we use the framework to computationally validate the hypothesis that image orientations (derivatives) provide increased invariance to illumination by showing (for a Lambertian model) that a shape-from-shading algorithm matching gradients instead of intensities provides more accurate reconstructions when illumination is incorrectly estimated under a flatness prior.

Radiative transfer models for retrieval of cloud parameters from EPIC/DSCOVR measurements

In this paper we analyze the accuracy and efficiency of several radiative transfer models for inferring cloud parameters from radiances measured by the Earth Polychromatic Imaging Camera (EPIC) on board the Deep Space Climate Observatory (DSCOVR). The radiative transfer models are the exact discrete ordinate and matrix operator methods with matrix exponential, and the approximate asymptotic and equivalent Lambertian cloud models. To deal with the computationally expensive radiative transfer calculations, several acceleration techniques such as, for example, the telescoping technique, the method of false discrete ordinate, the correlated k-distribution method and the principal component analysis (PCA) are used. We found that, for the EPIC oxygen A-band absorption channel at 764 nm, the exact models using the correlated k-distribution in conjunction with PCA yield an accuracy better than 1.5% and a computation time of 18 s for radiance calculations at 5 viewing zenith angles.

Photometric stereo for strong specular highlights

Photometric stereo is a fundamental technique in computer vision known to produce 3D shape with high accuracy. It uses several input images of a static scene taken from one and the same camera position but under varying illumination. The vast majority of studies in this 3D reconstruction method assume orthographic projection for the camera model. In addition, they mainly use the Lambertian reflectance model as the way that light scatters at surfaces. Thus, providing reliable photometric stereo results from real world objects still remains a challenging task. We address 3D reconstruction by use of a more realistic set of assumptions, combining for the first time the complete Blinn–Phong reflectance model and perspective projection. Furthermore, we compare two different methods of incorporating the perspective projection into our model. Experiments are performed on both synthetic and real world images; the latter do not benefit from laboratory conditions. The results show the high potential of our method even for complex real world applications such as medical endoscopy images which may include many specular highlights.

Self-Normalized Photoacoustic Technique for the Quantitative Analysis of Paper Pigments

A self-normalized photoacoustic technique was applied for quantitative analysis of pigments embedded in solids. Paper samples (filter paper, Whatman No. 1), attached with the pigment: Direct Fast Turquoise Blue GL, were used for this study. This pigment is a blue dye commonly used in industry to dye paper and other fabrics. The optical absorption coefficient, at a wavelength of 660 nm, was measured for this pigment at various concentrations in the paper substrate. It was shown that Beer–Lambert model for light absorption applies well for pigments in solid substrates and optical absorption coefficients as large as \(220\,\hbox {cm}^{-1}\) can be measured with this photoacoustic technique.

Simulation of SAR images of urban areas by using the ray tracing method with measured values of backscatter coefficients

ABSTRACTThis study uses the ray tracing method to simulate synthetic aperture radar (SAR) images of urban areas. The images are constructed for polarisations: horizontal-horizontal (HH) and vertical-vertical (VV), and different types of buildings, vegetation, and streets. Simulated images of a given area are compared with real SAR images of the same area acquired by the TerraSAR-X satellite. The simulations use the measured backscatter coefficient for HH and VV polarisations and for five different classes of terrain: houses, trees, shrubs, grass, and ground. For multiple reflections, we apply the generalized bistatic Lambertian model. The results show that, despite the limits of the ray tracing method and the approximations involved in modelling three-dimensional objects in the simulated scene, the simulated SAR images correspond well with the actual scene. All features present in the real image are reproduced in the simulated image; in particular, the double reflections of buildings and the surrounding ground appear clearly. However, discrepancies exist, and these are also discussed.

Passive underwater polarization imaging detection method in neritic area

Underwater imaging is widely applied to mariculture, archaeology, and hydrocarbon exploration, because it can provide the information about visualized target. Among various underwater imaging techniques, polarization imaging is of particular interest to us, due to its simple system structure and low cost. It images the waterbody through using the polarization characteristics of light, specifically, the background light and target light. Active polarization imaging method illuminates a target scene with an artificial polarized light source to provide polarization information for imaging. But in neritic area, active imaging leads to complex light scattering conditions when artificial light and natural light are superimposed together, which further leads to poor image quality. Passive underwater polarization imaging attempts to recover a clear image by utilizing the polarization characteristics of background light and target light. However, serious color cast always appears in the final image, resulting from light absorbed by water, which may further result in target distortion. In this manuscript, we present a passive underwater polarization imaging method for detecting a target in neritic area. A depth-information-based underwater Lambertian reflection model is established by incorporating the depth information into the traditional Lambertian reflection model. First, we attribute the light changes in color and brightness of a Lambertian surface to the spatial variation of the light. According to Lambertian reflection model, the appearance of a target on a detector depends on the light source, the surface reflectance, and the camera sensitivity function. But in underwater imaging, light attenuation at different wavelengths also varies with depth. By analyzing the transmission characteristics of background light in water, we build a physical relationship between the depth information of the scene and the background light. After that, we take the depth information as the weight of light intensity distribution. Then we calculate the product of the light intensity and the camera sensitivity function in the underwater scene according to gray world algorithm, and the real color information of the target can be obtained. Finally, the clear image of an underwater target scene can be obtained, where color cast is calibrated and background light is removed. Underwater experiments are conducted to demonstrate the validity of the proposed method. Besides, the quantitative analyses also verify the improvement of the quality in final target image. Compared with conventional passive underwater polarization imaging methods, the proposed method is capable of detecting targets in various conditions, with the color cast problem solved. It can provide underwater images with better quality and valid detailed information. Furthermore, the proposed method is easy to conduct with no need to change the conventional polarization imaging system and is promising in various practical applications.