Spherical harmonics vs. Haar wavelets: basis for recovering illumination from cast shadows

Separating specular reflection components from diffuse reflection components is an important subject in computer vision. Hence, the author's group has developed a method to separate a diffuse image from a high-speed-video image with specular reflection components. The method uses an estimation technique based on luminance variation owing to flicker of a strobe. However, an issue with the method is that the strobe produces a new specular reflection component. In this study, we get around this limitation by introducing a method for combining two images produced based on flickering information. Experimental results show the validity of the proposed method.

Reflectance Analysis for 3D Computer Graphics Model Generation

The diffuse and specular components of leaf reflection are both important to determine the leaf optical properties as well as to describe the leaf bidirectional reflectance distribution function (BRDF). However, the specular component is usually ignored in practice in numerous canopy reflectance models that describe the interaction between solar light and vegetated scene components. To evaluate the impact of leaf-specular reflection on canopy bidirectional reflectance factor (BRF) characteristics, we introduce a leaf BRDF model into the radiosity-graphics combined model (RGM; a 3-D scene model) to calculate canopy BRFs with nondiffuse leaves. The modified RGM is validated by comparing simulated BRFs against in situ measured BRFs over real maize canopies. The results show that ignorance of leaf-specular reflection can result in up to 50% of relative error in the blue band (435.8 nm). A series of maize canopies with different leaf angle distributions (LADs) is reconstructed to investigate the effect of five major biophysical/geometrical parameters such as leaf area index, LAD, leaf surface property, view direction, and solar zenith angle on leaf-specular reflection contributions to the canopy BRF. It is demonstrated that increasing the incident solar zenith angle and decreasing the mean leaf angle impact the angular distribution of the canopy BRF more significantly than other factors. The cumulative hemispherical relative and absolute errors of canopy BRF caused by the leaf-specular reflection are often too large to be ignored, even for canopies with rough surface leaves. Moreover, the relative error of BRF in visible waveband shows that, in general, leaf-specular reflection has a large impact than that in near-infrared waveband. However, such impact can be sufficiently accounted for by even just consideration of the first-order leaf-specular reflection in canopy reflectance calculation, leading to a substantial improvement in simulation accuracy for most vegetation canopies.

A numerical investigation of radiative heat transfer constructed by curved surfaces with specular and diffuse reflection components is carried out. The ray tracing method is adopted for the calculation of view factors, in which a new ray emission model is proposed. The second-degree radiation ring elements are introduced, which are of engineering importance and numerical efficiency. The accuracy of the method is analyzed and verified using a simple configuration. The present computation using the proposed ray emission model is in good agreement with the analytical solution. As a numerical example and engineering application, the effects of the specular reflection and the meniscus of the melt surface in Czochralski (CZ) crystal growth are investigated. A marked temperature decrease in the melt surface is found by introducing specular reflection and the meniscus. The combined effects of the specular reflection and the meniscus should be considered in precision heat transfer control of a CZ apparatus.

Deep-learning-based polarization 3D imaging techniques, which train networks in a data-driven manner, are capable of estimating a target’s surface normal distribution under passive lighting conditions. However, existing methods have limitations in restoring target texture details and accurately estimating surface normals. Information loss can occur in the fine-textured areas of the target during the reconstruction process, which can result in inaccurate normal estimation and reduce the overall reconstruction accuracy. The proposed method enables extraction of more comprehensive information, mitigates the loss of texture information during object reconstruction, enhances the accuracy of surface normal estimation, and facilitates more comprehensive and precise reconstruction of objects. The proposed networks optimize the polarization representation input by utilizing the Stokes-vector-based parameter, in addition to separated specular and diffuse reflection components. This approach reduces the impact of background noise, extracts more relevant polarization features of the target, and provides more accurate cues for restoration of surface normals. Experiments are performed using both the DeepSfP dataset and newly collected data. The results show that the proposed model can provide more accurate surface normal estimates. Compared to the UNet architecture-based method, the mean angular error is reduced by 19%, calculation time is reduced by 62%, and the model size is reduced by 11%.

Combined heat transfer in floating zone growth of large silicon crystals with radiation on diffuse and specular surfaces

A method is proposed for estimating spectral radiances of the surrounding scene from a reflected image on the corneal surface. A digital color camera and the human eyeball are used to develop a simple imaging system without any specific device. The corneal image consists of a mixture of specular and diffuse reflections from the cornea and the iris. The desired scene radiances are only recovered from the specular reflection component after removing the diffuse reflection component. Experiments are executed in several different conditions.

In this paper we present the first practical method for importance sampling functions represented as spherical harmonics (SH). Given a spherical probability density function (PDF) represented as a vector of SH coefficients, our method warps an input point set to match the target PDF using hierarchical sample warping. Our approach is efficient and produces high quality sample distributions. As a by‐product of the sampling procedure we produce a multi‐resolution representation of the density function as either a spherical mip‐map or Haar wavelet. By exploiting this implicit conversion we can extend the method to distribute samples according to the product of an SH function with a spherical mip‐map or Haar wavelet. This generalization has immediate applicability in rendering, e.g., importance sampling the product of a BRDF and an environment map where the lighting is stored as a single high‐resolution wavelet and the BRDF is represented in spherical harmonics. Since spherical harmonics can be efficiently rotated, this product can be computed on‐the‐fly even if the BRDF is stored in local‐space. Our sampling approach generates over 6 million samples per second while significantly reducing precomputation time and storage requirements compared to previous techniques.

One of the origins of error in the angle of arrival estimation of a signal is the response of the ground to the reflected waves from the target. In low-height target situations, this phenomenon can be so harrowing that it may result in much more error than thermal noise. In this article, two methods of fixed beam and double null are used as preliminary techniques to overcome the problem of low-altitude target angle estimation, and the optimum weights for beam-forming array radar are proposed. These beam-forming methods enable the radar to estimate the target angle precisely without the exact knowledge of the surface slope, whereas they are robust against diffuse and specular ground reflection components.

BackgroundHumans readily perceive whole shapes as intact when some portions of these shapes are occluded by another object. This type of amodal completion has also been widely reported among nonhuman animals and is related to pictorial depth perception. However, the effect of a cast shadow, a critical pictorial-depth cue for amodal completion has been investigated only rarely from the comparative-cognitive perspective. In the present study, we examined this effect in chimpanzees and humans.ResultsChimpanzees were slower in responding to a Pacman target with an occluding square than to the control condition, suggesting that participants perceptually completed the whole circle. When a cast shadow was added to the square, amodal completion occurred in both species. On the other hand, however, critical differences between the species emerged when the cast shadow was added to the Pacman figure, implying that Pacman was in the sky casting a shadow on the square. The cast shadow prevented, to a significant extent, compulsory amodal completion in humans, but had no effect on chimpanzees.ConclusionThese results suggest that cast shadows played a critical role in enabling humans to infer the spatial relationship between Pacman and the square. For chimpanzees, however, a cast shadow may be perceived as another "object". A limited role for cast shadows in the perception of pictorial depth has also been reported with respect to human cognitive development. Further studies on nonhuman primates using a comparative-developmental perspective will clarify the evolutionary origin of the role of cast shadows in visual perception.

Having an accurate model of the lights in a scene is important for many applications. Augmented reality requires light information for seamlessly composing computer generated objects into a real scene. Similarly, computer vision algorithms such as photometric stereo and shape from shading require accurate lighting. Inverse lighting allows such algorithms to be used in real world environments, instead of strictly controlled laboratory setups. While algorithms that recover light as individual point light sources work for simple illumination environments, it has been shown that a basis representation achieves better results for complex illumination. We propose a light model that uses Daubechies wavelets and a method for recovering light from cast shadows and specular highlights in images. Experimentally, we tested our method for difficult cases of both uniform and textured objects and under complex geometry and light conditions. We evaluate the stability of estimation and quality of the relight scene using our smooth wavelet representation compared to a non-smooth Haar basis and two other popular light representations (a discrete set of infinite light sources and a global spherical harmonics basis). We show good results using the proposed Daubechies basis on both synthetic and real datasets.

This paper shows that significant errors occur if a formulation of reflectance is employed that does not utilize both diffuse and specular components. It then discusses how these components can be measured, and describes in detail the construction of a suitable goniophotometer. It also shows how a series of measurements with various source sizes can be employed to calculate the specular and diffuse components of reflectance from the experimental data.

A method is described for reducing the large error that often occurs in the measurement of three-dimensional (3D) objects using the photometric stereo method when there is a specular component in te reflection characteristics of the object’s surface. First, the change in the luminance distribution caused by the component is estimated based on the correlation between the modeled distribution and a gray-level image of the object, created by numerical experiment. Next, the shape measurement of the hemisphere object was carried out. Nurmerical experiment of three dimensional measurement of a hemispherical object showed that the mean error of normal vector can be reduced by as much as 90%. This method is applicable to machine vision, automatic manufacturing, and other industrial processes.

Separation of the diffuse and specular components of observed reflectance has been an active area of research in computer graphics and vision, with major applications in reflectance modeling and scene analysis. Traditionally, researchers have investigated diffusespecular separation under point or directional illumination conditions while employing polarization and, in the case of dielectric materials, color space analysis techniques. Recently, Ma et al. [2007] introduced a technique for estimating high quality diffuse and specular normals and albedo maps (see Fig. 1, (a) & (d)) of a specular object using polarized spherical gradient illumination. However, the employed polarization technique imposes view-point restriction, and results in insufficient light levels for performance capture with high speed acquisition. Hence, in this work, we look into an alternate diffuse-specular separation technique for spherical gradients based on a data-driven reflectance model. Traditional separation techniques based on color space analysis focus on removing specular reflections from the observation for scene analysis [Mallick et al. 2005]. In contrast, we focus on obtaining high quality estimates of both the diffuse and the specular reflectance components.

The powerful methodology of “Wavelet analysis in frequency domain” for analyzing time-series data is studied. As an illustration, Indian monsoon rainfall time-series data from 1879–2006 is considered. The entire data analysis is carried out using SPLUS WAVELET TOOLKIT software package. The discrete wavelet transform (DWT) and multiresolution analysis (MRA) of the data are computed to analyze the behaviour of trend present in the time-series data in terms of different times and scales. By using bootstrap method, size and power of the test for testing significance of trend in the data is computed. It is found that the size of the test for Daubechies wavelet is more than that for Haar wavelet. In respect of both Daubechies and Haar wavelet filters, it is found that the test for presence of trend is unbiased. Also, power of the test for both Daubechies (D4) and Haar wavelets, at level 5 is less than the one at level 6. Further, Haar wavelet at level 6 has generally performed better than Daubechies (D4) wavelet at level 6 in terms of power of the test. Using the former wavelet, a declining trend in the data under consideration is revealed.