DOCSLIB.ORG

Chapter 9 Shading

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Chapter 9 Shading Chapter 9 Shading This chapter covers the physics of how light reflects from surfaces and de- scribes a method called photometric stereo for estimating the shape of sur- faces using the reflectance properties. Before covering PAhotometricstereo and shape from shading, we must explain the physics of image formation. Imaging is the process that maps light intensities from points in a scene onto an image plane. The presentation followsthe pioneering work of Horn [109]. 9.1 Image Irradiance The projections explained in Section 1.4 determine the location on the image plane of a scene point, but do not determine the image intensity of the point. Image intensity is determined by the physics of imaging, covered in this section. The proper term for image intensity is image irradiance, but terms such as intensity, brightness, or gray value are so common that they have been used as synonyms for image irradiance throughout this text. The image irradiance of a point in the image plane is defined to be the power per unit area of radiant energy falling on the image plane. Radiance is outgoing energy; irradiance is incoming energy. The irradiance at a point in the image plane E(x', y') is determined by the amount of energy radiated by the corresponding point in the scene L(x, y, z) in the direction of the image point: E(x', y') = L(x, y, z). (9.1) The scene point (x, y, z) lies on the ray from the center of projection through 257 258 CHAPTER 9. SHADING image point (x', y'). To find the source of image irradiance, we have to trace the ray back to the surface patch from which the ray was emitted and understand how the light from scene illumination is reflected by a surface patch. Two factors determine the radiance reflected by a patch of scene surface: . The illumination falling on the patch of scene surface . The fraction of the incident illumination that is reflected by the surface patch. The amount of illumination falling on a particular surface patch is deter- mined by the position of the surface patch relative to the distribution of the light sources in the scene. The fraction of the incident illumination that is reflected by the surface patch in a particular direction depends on the optical properties of the surface material. Consider an infinitesimal patch of surface in a scene that is illuminated with a single point light source. Establish a coordinate system on the surface patch as shown in Figure 9.1. The coordinate system represents the hemi- sphere of possible directions from which energy can arrive or depart from the surface. Let ((}i,(Pi)denote the direction, in polar coordinates relative to the surface patch, of the point source of scene illumination and let ((}e,<Pe)denote the direction in which energy from the surface patch is emitted. The energy arriving at the surface patch from a particular direction is E((}i, <Pi)and the energy radiated in a particular direction from the surface patch is L((}e,<Pe). The ratio of the amount of energy radiated from the surface patch in some direction to the amount of energy arriving at the surface patch from some direction is the bidirectional reflectance distribution function. The radiance is determined from the irradiance by (9.2) where f( (}i, <Pi,(}e,<Pe) is the bidirectional reflectance distribution function, called the BRDF for short. The BRDF depends on the optical properties of the surface material. This is the general formulation and can be very complicated, but in most cases of interest in machine vision, the effects are fairly simple. For most materials, the BRDF depends only on the difference between the incident and emitted angles: (9.3) 9.1. IMAGE IRRADIANCE 259 n Figure 9.1: A polar coordinate system is established on an infinitesimal patch of surface to describe the directions of illumination and radiance in the hemi- sphere of directions visible from the surface patch. 9.1.1 Illumination The radiance emitted from a surface patch can be calculated given the bidi- rectional reflectance distribution function (BRDF) for the surface material and the distribution of light sources. Two types of illumination will be cov- ered: . Point light source . Uniform light source First, the general formula for computing the total irradiance on a surface patch from a general distribution of light sources will be presented. The co- ordinate system is the polar coordinate system for the hemisphere of possible directions as diagrammed in Figure 9.1. The total irradiance on a surface patch is the sum of the contributions arriving at the surface patch from all of the directions in the hemisphere. Each small contribution of irradiance pass- ing through a patch of the unit hemisphere must be counted in such a way that the total area of the hemisphere is used. A given section of the hemi- sphere with angular increments Deiand 8(h covers an area of the hemisphere 8w called the solid angle: (9.4) 260 CHAPTER 9. SHADING The sin fJiterm accounts for the effect that the area of the portion of the hemisphere 8fJi84>iis smaller near the top of the hemisphere. The area of a sphere of radius r is 471"r2,so the area of a hemisphere with unit radius is 271". The area S of the hemisphere can be obtained by adding up the solid angles that comprise the hemisphere: (9.5) S = 120 dw (9.6) - 1/2120 0 sin fJdfJd4> - 271"1/20 sin fJdfJ (9.7) - 271"[- cosfJ]/2 (9.8) - 271". (9.9) Without the sin fJfactor in Equation 9.4, the individual infinitesimal pieces of hemisphere would not add up to the correct total area. The total radiance passing through the sphere is the sum of the infinitesimal patches of sphere weighted by the amount of radiance per unit solid angle passing through each patch. Let I(fJi, 4>i)be the radiance per unit solid anglepassing through the hemisphere from the direction (fJi,4>i)' The total irradiance of the surface patch is r2~ r/2 10= 10 10 I(fJi,4>i)sinfJicosfJidfJid4>i, (9.10) where the additional cosfJiterm is needed because the surface patch appears smaller from the direction of illumination due to foreshortening. The amount of radiance reflected from the surface patch is (9.11) With the assumption that scene radiance is equal to image irradiance, the image irradiance at position (x', y') in the image plane is equal to the radiance from the corresponding surface patch in the scene: E(x', y') = L(x, y,z) (9.12) - L(fJe,4>e), (9.13) 9.1. IMAGE IRRADIANCE 261 where the angles of emittance of the scene radiance are determined from the geometry of the scene surfaces. Note that for each image position (x', y/), the corresponding scene position (x, y, z) can be calculated, as well as the surface normal f1for the surface patch and the angle (Oe,<Pe)of the ray from the surface patch to the point (x', y/) in the image plane, in polar coordinates relative to the surface normal or the surface patch. To determine the irradiance of the entire image from the geometry of surfaces in the scene and the arrangement of light sources, it is necessary to know the BRDF for the scene surfaces. This is the subject of the next section. 9.1.2 Reflectance Several different types of reflectance will be covered: . Lambertian reflectance (also called diffuse reflectance) . Specular reflectance . Combinations of Lambertian and specular reflectance . Reflectance in scanning electron microscopy Lambertian Reflectance A Lambertian surface appears equally bright from all viewing directions for a fixed distribution of illumination and a Lambertian surface does not ab- sorb any incident illumination. Lambertian reflectance is also called diffuse reflectance since a Lambertian surface takes the incident illumination, what- ever the distribution of illumination may be, and distributes all of the incident illumination in all surface directions such that the same amount of energy is seen from any direction. Note that this is not the same as saying that the surface emits energy equally in all directions, as will be explained in Sec- tion 9.3.2. Many matte surfaces are approximately Lambertian, and many surfaces, with the exceptions noted below, are qualitatively Lambertian. The BRDF for a Lambertian surface is a constant: (9.14) 262 CHAPTER 9. SHADING The radiance is independent of the emitted direction and is obtained by summing the effect of the BRDF on the incident illumination coming from the hemisphere of possible directions: (9.15) (9.16) (9.17) where 10 is the total incident illumination on the surface patch. What is the perceived brightness of a Lambertian surface that is illumi- nated by a distant point source? The illumination from a point surface in a direction (Os,<Ps)relative to the normalof a surface patch is describedby (9.18) where 10is the total illumination. Essentially, the D-functions merely restrict the directions from which illumination arrives at the surface patch to the single direction (Os,<Ps).Equation 9.18 has a sine term in the denominator so that when it is plugged into Equation 9.10, the total illumination comes out to be 10. Now plug the illumination function from Equation 9.18 and the BRDF from Equation 9.14 into Equation 9.11 for the radiance from the surface patch to get the equation for the perceived brightness: This is the Lambert cosine law, which says that the perceived brightness of a surface patch illuminated by a point source varies with the incident angle relative to the surface normal of the patch.
Load more

Recommended publications
  • Spectral Reflectance and Emissivity of Man-Made Surfaces Contaminated with Environmental Effects
    Optical Engineering 47͑10͒, 106201 ͑October 2008͒ Spectral reflectance and emissivity of man-made surfaces contaminated with environmental effects John P. Kerekes, MEMBER SPIE Abstract. Spectral remote sensing has evolved considerably from the Rochester Institute of Technology early days of airborne scanners of the 1960’s and the first Landsat mul- Chester F. Carlson Center for Imaging Science tispectral satellite sensors of the 1970’s. Today, airborne and satellite 54 Lomb Memorial Drive hyperspectral sensors provide images in hundreds of contiguous narrow Rochester, New York 14623 spectral channels at spatial resolutions down to meter scale and span- E-mail: [email protected] ning the optical spectral range of 0.4 to 14 ␮m. Spectral reflectance and emissivity databases find use not only in interpreting these images but also during simulation and modeling efforts. However, nearly all existing Kristin-Elke Strackerjan databases have measurements of materials under pristine conditions. Aerospace Engineering Test Establishment The work presented extends these measurements to nonpristine condi- P.O. Box 6550 Station Forces tions, including materials contaminated with sand and rain water. In par- Cold Lake, Alberta ticular, high resolution spectral reflectance and emissivity curves are pre- T9M 2C6 Canada sented for several man-made surfaces ͑asphalt, concrete, roofing shingles, and vehicles͒ under varying amounts of sand and water. The relationship between reflectance and area coverage of the contaminant Carl Salvaggio, MEMBER SPIE is reported and found to be linear or nonlinear, depending on the mate- Rochester Institute of Technology rials and spectral region. In addition, new measurement techniques are Chester F. Carlson Center for Imaging Science presented that overcome limitations of existing instrumentation and labo- 54 Lomb Memorial Drive ratory settings.
    [Show full text]
  • Black Body Radiation and Radiometric Parameters
    Black Body Radiation and Radiometric Parameters: All materials absorb and emit radiation to some extent. A blackbody is an idealization of how materials emit and absorb radiation. It can be used as a reference for real source properties. An ideal blackbody absorbs all incident radiation and does not reflect. This is true at all wavelengths and angles of incidence. Thermodynamic principals dictates that the BB must also radiate at all ’s and angles. The basic properties of a BB can be summarized as: 1. Perfect absorber/emitter at all ’s and angles of emission/incidence. Cavity BB 2. The total radiant energy emitted is only a function of the BB temperature. 3. Emits the maximum possible radiant energy from a body at a given temperature. 4. The BB radiation field does not depend on the shape of the cavity. The radiation field must be homogeneous and isotropic. T If the radiation going from a BB of one shape to another (both at the same T) were different it would cause a cooling or heating of one or the other cavity. This would violate the 1st Law of Thermodynamics. T T A B Radiometric Parameters: 1. Solid Angle dA d r 2 where dA is the surface area of a segment of a sphere surrounding a point. r d A r is the distance from the point on the source to the sphere. The solid angle looks like a cone with a spherical cap. z r d r r sind y r sin x An element of area of a sphere 2 dA rsin d d Therefore dd sin d The full solid angle surrounding a point source is: 2 dd sind 00 2cos 0 4 Or integrating to other angles < : 21cos The unit of solid angle is steradian.
    [Show full text]
  • Reflectometers for Absolute and Relative Reflectance
    sensors Communication Reflectometers for Absolute and Relative Reflectance Measurements in the Mid-IR Region at Vacuum Jinhwa Gene 1 , Min Yong Jeon 1,2 and Sun Do Lim 3,* 1 Institute of Quantum Systems (IQS), Chungnam National University, Daejeon 34134, Korea; [email protected] (J.G.); [email protected] (M.Y.J.) 2 Department of Physics, College of Natural Sciences, Chungnam National University, Daejeon 34134, Korea 3 Division of Physical Metrology, Korea Research Institute of Standards and Science, Daejeon 34113, Korea * Correspondence: [email protected] Abstract: We demonstrated spectral reflectometers for two types of reflectances, absolute and relative, of diffusely reflecting surfaces in directional-hemispherical geometry. Both are built based on the integrating sphere method with a Fourier-transform infrared spectrometer operating in a vacuum. The third Taylor method is dedicated to the reflectometer for absolute reflectance, by which absolute spectral diffuse reflectance scales of homemade reference plates are realized. With the reflectometer for relative reflectance, we achieved spectral diffuse reflectance scales of various samples including concrete, polystyrene, and salt plates by comparing against the reference standards. We conducted ray-tracing simulations to quantify systematic uncertainties and evaluated the overall standard uncertainty to be 2.18% (k = 1) and 2.99% (k = 1) for the absolute and relative reflectance measurements, respectively. Keywords: mid-infrared; total reflectance; metrology; primary standard; 3rd Taylor method Citation: Gene, J.; Jeon, M.Y.; Lim, S.D. Reflectometers for Absolute and 1. Introduction Relative Reflectance Measurements in Spectral diffuse reflectance in the mid-infrared (MIR) region is now of great interest the Mid-IR Region at Vacuum.
    [Show full text]
  • Analyzing Reflectance Data for Various Black Paints and Coatings
    Analyzing Reflectance Data for Various Black Paints and Coatings Mimi Huynh US Army NVESD UNITED STATES OF AMERICA [email protected] ABSTRACT The US Army NVESD has previously measured the reflectance of a number of different levels of black paints and coatings using various laboratory and field instruments including the SOC-100 hemispherical directional reflectometer (2.0 – 25 µm) and the Perkin Elmer Lambda 1050 (0.39 – 2.5 µm). The measurements include off-the-shelf paint to custom paints and coatings. In this talk, a number of black paints and coatings will be presented along with their reflectivity data, cost per weight analysis, and potential applications. 1.0 OVERVIEW Black paints and coatings find an important role in hyperspectral imaging from the sensor side to the applications side. Black surfaces can enhance sensor performance and calibration performance. On the sensor side, black paints and coatings can be found in the optical coatings, mechanical and enclosure coating. Black paints and coating can be used inside the sensor to block or absorb stray light, preventing it from getting to the detector and affecting the imagery. Stray light can affect the signal-to-noise ratio (SNR) as well introduce unwanted photons at certain wavelengths. Black paints or coatings can also be applied to a baffle or area around the sensor in laboratory calibration with a known light source. This is to ensure that no stray light enter the measurement and calculations. In application, black paints and coatings can be applied to calibration targets from the reflectance bands (VIS- SWIR) and also in the thermal bands (MWIR-LWIR).
    [Show full text]
  • Reflectance IR Spectroscopy, Khoshhesab
    11 Reflectance IR Spectroscopy Zahra Monsef Khoshhesab Payame Noor University Department of Chemistry Iran 1. Introduction Infrared spectroscopy is study of the interaction of radiation with molecular vibrations which can be used for a wide range of sample types either in bulk or in microscopic amounts over a wide range of temperatures and physical states. As was discussed in the previous chapters, an infrared spectrum is commonly obtained by passing infrared radiation through a sample and determining what fraction of the incident radiation is absorbed at a particular energy (the energy at which any peak in an absorption spectrum appears corresponds to the frequency of a vibration of a part of a sample molecule). Aside from the conventional IR spectroscopy of measuring light transmitted from the sample, the reflection IR spectroscopy was developed using combination of IR spectroscopy with reflection theories. In the reflection spectroscopy techniques, the absorption properties of a sample can be extracted from the reflected light. Reflectance techniques may be used for samples that are difficult to analyze by the conventional transmittance method. In all, reflectance techniques can be divided into two categories: internal reflection and external reflection. In internal reflection method, interaction of the electromagnetic radiation on the interface between the sample and a medium with a higher refraction index is studied, while external reflectance techniques arise from the radiation reflected from the sample surface. External reflection covers two different types of reflection: specular (regular) reflection and diffuse reflection. The former usually associated with reflection from smooth, polished surfaces like mirror, and the latter associated with the reflection from rough surfaces.
    [Show full text]
  • Relation of Emittance to Other Optical Properties *
    JOURNAL OF RESEARCH of the National Bureau of Standards-C. Engineering and Instrumentation Vol. 67C, No. 3, July- September 1963 Relation of Emittance to Other Optical Properties * J. C. Richmond (March 4, 19G3) An equation was derived relating t he normal spcctral e mittance of a n optically in homo­ geneous, partially transmitting coating appli ed over an opaque substrate t o t he t hi ckncs and optical properties of t he coating a nd the reflectance of thc substrate at thc coaLin g­ SLI bstrate interface. I. Introduction The 45 0 to 0 0 luminous daylight r efl ectance of a composite specimen com prising a parLiall:\' transparent, spectrally nonselective, ligh t-scattering coating applied to a completely opaque (nontransmitting) substrate, can be computed from the refl ecta.nce of the substrate, the thi ck­ ness of the coaLin g and the refl ectivity and coefficien t of scatter of the coating material. The equaLions derived [01' these condi tions have been found by experience [1 , 2)1 to be of considerable praeLical usefulness, even though sever al factors ar e known to exist in real m aterials that wer e no t consid ered in the derivation . For instance, porcelain enamels an d glossy paints have significant specular refl ectance at lhe coating-air interface, and no r ea'! coating is truly spectrally nonselective. The optical properties of a material vary with wavelength , but in the derivation of Lh e equations refened to above, they ar e consid ered to be independent of wavelength over the rather narrow wavelength band encompassin g visible ligh t.
    [Show full text]
  • Radiometry and Photometry
    Radiometry and Photometry Wei-Chih Wang Department of Power Mechanical Engineering National TsingHua University W. Wang Materials Covered • Radiometry - Radiant Flux - Radiant Intensity - Irradiance - Radiance • Photometry - luminous Flux - luminous Intensity - Illuminance - luminance Conversion from radiometric and photometric W. Wang Radiometry Radiometry is the detection and measurement of light waves in the optical portion of the electromagnetic spectrum which is further divided into ultraviolet, visible, and infrared light. Example of a typical radiometer 3 W. Wang Photometry All light measurement is considered radiometry with photometry being a special subset of radiometry weighted for a typical human eye response. Example of a typical photometer 4 W. Wang Human Eyes Figure shows a schematic illustration of the human eye (Encyclopedia Britannica, 1994). The inside of the eyeball is clad by the retina, which is the light-sensitive part of the eye. The illustration also shows the fovea, a cone-rich central region of the retina which affords the high acuteness of central vision. Figure also shows the cell structure of the retina including the light-sensitive rod cells and cone cells. Also shown are the ganglion cells and nerve fibers that transmit the visual information to the brain. Rod cells are more abundant and more light sensitive than cone cells. Rods are 5 sensitive over the entire visible spectrum. W. Wang There are three types of cone cells, namely cone cells sensitive in the red, green, and blue spectral range. The approximate spectral sensitivity functions of the rods and three types or cones are shown in the figure above 6 W. Wang Eye sensitivity function The conversion between radiometric and photometric units is provided by the luminous efficiency function or eye sensitivity function, V(λ).
    [Show full text]
  • Principles of the Measurement of Solar Reflectance, Thermal Emittance, and Color
    Principles of the Measurement of Solar Reflectance, Thermal Emittance, and Color Contents Roof Heat Transfer Electromagnetic Radiation Radiative Properties of Surfaces Measuring Solar Radiation Measuring Solar Reflectance Measuring Thermal Emittance Measuring Color 1. Roof Heat Transfer 3 Roof surface is heated by solar absorption, cooled by thermal emission + convection Radiative Cooling Convective Solar Cooling Absorption Troof Insulatio n T Qin = U (Troof – inside Tinside) Most solar heat gain is dissipated by convective and radiative cooling… ...because the conduction heat transfer coefficient is much less than those for convection & radiation 2. Electromagnetic Radiation 7 The electromagnetic spectrum spans radio waves to gamma rays This includes sunlight (0.3 – 2.5 μm) and thermal IR radiation (4 – 80 μm) (0.4 – 0.7 All surfaces emit temperature-dependent electromagnetic radiation • Stefan-Boltzmann law • Blackbody cavity is a perfect absorber and emitter of radiation • Total blackbody radiation [W m-2] = σ T 4, where – σ = 5.67 10-8 W m-2 K-4 – T = absolute temperature [K] • At 300 K (near room temperature) σ T 4 = 460 W m-2 Higher surface temperatures → shorter wavelengths Solar radiation from sun's surface (5,800 K) peaks near 0.5 μm (green) Thermal radiation from ambient surfaces (300 K) peaks near 10 μm (infrared) Extraterrestrial sunlight is attenuated by absorption and scattering in atmosphere Global (hemispherical) solar radiation = direct (beam) sunlight + diffuse skylight Pyranometer measures global (a.k.a. Pyranometer hemi-spherical) sunlight on with horizontal surface sun-tracking shade Pyrheliometer measures measures direct (a.k.a. collimated, diffuse beam) light from sun skylight Let's compare rates of solar heating and radiative cooling Spectral heating rate of a black roof facing the sky on a 24-hour average basis, shown on a log scale.
    [Show full text]
  • Colorimetric and Spectral Matching
    Colorimetric and spectral matching Prague, Czech republic June 29, 2017 Marc Mahy Agfa Graphics Overview • Modeling color • Color matching • Process control • Profile based color transforms —Visual effects —Light interactions • Color matching —Colorimetric matching —Spectral matching —Metameric colors Modeling color • Object has the color of the “light” leaving its surface —Light source —Object —Human observer , ) Modeling color • Light source —Electro Magnetic Radiation (EMR) – Focus on wavelength range from 300 till 800 nm —Different standard illuminants – Illuminant E (equi-energy) – Illuminant A, D50 , D65 , F11 Spectral Power Distribution Modeling color • Object colors: Classes object types —Opaque objects – Diffuse reflection: Lambertian reflector – Specular reflection: mirror – Most objects: diffuse and specular reflection —Transparent objects – Absorption, no scattering: plexi, glass, … —Translucent objects – Absorption and scattering: backlit —Special effects – Fluorescence: substrates – Metallic surfaces: (in plane) BRDF Modeling color • Object colors: Characterizing object types —Opaque objects – Measurement geometry: 45°:0° or 0°:45° – Colorimetric or reflectance spectra —Transparent objects – Measurement geometry: d:0° or 0°:d – Colorimetric or transmission spectra —Translucent objects – In reflection or transmission mode – For reflection mode: White backing, black backing or self backing —Special effects – Fluorescent substrates: colorimetric data or bi-spectral reflectance – Metallic surfaces: BRDF based on colorimetric
    [Show full text]
  • 13. Fresnel's Equations for Reflection and Transmission
    13. Fresnel's Equations for Reflection and Transmission Incident, transmitted, and reflected beams Boundary conditions: tangential fields are continuous Reflection and transmission coefficients The "Fresnel Equations" Brewster's Angle Total internal reflection Power reflectance and transmittance Augustin Fresnel 1788-1827 Posing the problem What happens when light, propagating in a uniform medium, encounters a smooth interface which is the boundary of another medium (with a different refractive index)? k-vector of the incident light nincident boundary First we need to define some ntransmitted terminology. Definitions: Plane of Incidence and plane of the interface Plane of incidence (in this illustration, the yz plane) is the y plane that contains the incident x and reflected k-vectors. z Plane of the interface (y=0, the xz plane) is the plane that defines the interface between the two materials Definitions: “S” and “P” polarizations A key question: which way is the E-field pointing? There are two distinct possibilities. 1. “S” polarization is the perpendicular polarization, and it sticks up out of the plane of incidence I R y Here, the plane of incidence (z=0) is the x plane of the diagram. z The plane of the interface (y=0) T is perpendicular to this page. 2. “P” polarization is the parallel polarization, and it lies parallel to the plane of incidence. Definitions: “S” and “P” polarizations Note that this is a different use of the word “polarization” from the way we’ve used it earlier in this class. reflecting medium reflected light The amount of reflected (and transmitted) light is different for the two different incident polarizations.
    [Show full text]
  • ATMOS 5140 Lecture 6 – Chapter 5
    ATMOS 5140 Lecture 6 – Chapter 5 • Radiative Properties of Natural Surfaces • Absorptivity • Reflectivity • Greybody Approximation • AnGular Distribution of Reflected Radiances Natural Surfaces Idealized as Planar Boundaries Natural Surfaces Idealized as Planar Boundaries Incident radiation Reflected radiation Imaginary plane Absorptivity and Reflectivity Absorptivity and Reflectivity Absorptivity and Reflectivity Reflectivity as a function of wavelenGth ow Near Infrared 100 Violet Blue Green Yell Red 80 Fresh Snow Wet Snow (%) y 60 Light soil Grass 40 eflectivit R Alfalfa 20 Straw Dark Soil Lake 0 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 Wavelength (µm) Reflectivity as a function of wavelenGth ow Near Infrared 100 Violet Blue Green Yell Red 80 Fresh Snow Wet Snow (%) y 60 Light soil Grass 40 eflectivit R Alfalfa 20 Straw Dark Soil Lake 0 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 Wavelength (µm) Fresh Snow very reflective in the visible Reflectivity as a function of wavelenGth ow Near Infrared 100 Violet Blue Green Yell Red 80 Fresh Snow Wet Snow (%) y 60 Light soil Grass 40 eflectivit R Alfalfa 20 Straw Dark Soil Lake 0 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 Wavelength (µm) Dark Soil is very absorptive in the visible Reflectivity as a function of wavelenGth ow Near Infrared 100 Violet Blue Green Yell Red 80 Fresh Snow Wet Snow (%) y 60 Light soil Grass 40 eflectivit R Alfalfa 20 Straw Dark Soil Lake 0 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6
    [Show full text]
  • Radiometry, BRDF and Photometric Stereo
    EECS 432-Advanced Computer Vision Notes Series 3 Radiometry, BRDF and Photometric Stereo Ying Wu Electrical Engineering & Computer Science Northwestern University Evanston, IL 60208 [email protected] Contents 1 Radiometry 2 1.1 Solid Angle . 2 1.2 Radiance and Irradiance . 2 2 The Relationship between Image Intensity and Object Illuminance 5 3 Surfaces and BRDF 6 3.1 BRDF . 6 3.2 Lambertian Surface, Diffusion and Albedo . 6 3.3 Specular Surface . 7 4 Shading Model of Point Source 7 5 Photometric Stereo 8 5.1 The Problem . 8 5.2 Recover Surface Normals . 8 5.3 From Normals to Shape . 9 6 Illumination Cone (optional) 10 1 1 Radiometry 1.1 Solid Angle Solid angle is a very important concept. Solid angle is defined by the projected area of a surface patch onto a unit sphere of a point, meaning that a solid angle is subtended by a point and a surface patch, which is shown in Figure 1. n is the normal of the surface S0 unit sphere dA0 r n θ surface patch dA Figure 1: Solid angle subtended by S0 and surface patch dA patch dA, and S0 is the point centered at a unit sphere. The distance between S0 and dA is r, and the angle between surface normal n and the point direction is θ. dA0 is the projection of the surface patch on the unit sphere. So, dAcosθ d! = dA = (1) 0 r2 Where dAcosθ is the foreshortened area of dA on the direction of dA-S0. The unit of solid angle is steradians, or sr for short.
    [Show full text]