Shape From Shading
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Shape From Shading
Photometric stereo is a technique in computer vision for estimating the surface normals of objects by observing that object under different lighting conditions (photometry). It is based on the fact that the amount of light reflected by a surface is dependent on the orientation of the surface in relation to the light source and the observer. By measuring the amount of light reflected into a camera, the space of possible surface orientations is limited. Given enough light sources from different angles, the surface orientation may be constrained to a single orientation or even overconstrained. The technique was originally introduced by Woodham in 1980.Woodham, R.J. 1980Photometric method for determining surface orientation from multiple images Optical Engineerings 19, I, 139-144. The special case where the data is a single image is known as shape from shading, and was analyzed by B. K. P. Horn in 1989.B. K. P. Horn, 1989. Obtaining shape from shading information. In B. K. P. Horn ...
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Bidirectional Reflectance Distribution Function
The bidirectional reflectance distribution function (BRDF), symbol f_(\omega_,\, \omega_), is a function of four real variables that defines how light from a source is reflected off an Opacity (optics), opaque surface. It is employed in the optics of real-world light, in computer graphics algorithms, and in computer vision algorithms. The function takes an incoming light direction, \omega_, and outgoing direction, \omega_ (taken in a coordinate system where the Normal (geometry), surface normal \mathbf n lies along the ''z''-axis), and returns the ratio of reflected radiance exiting along \omega_ to the irradiance incident on the surface from direction \omega_. Each direction \omega is itself Spherical coordinate system, parameterized by azimuth angle \phi and zenith angle \theta, therefore the BRDF as a whole is a function of 4 variables. The BRDF has units sr−1, with steradians (sr) being a unit of solid angle. Definition The BRDF was first defined by Fred Nicodemus around 19 ...
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Computer Graphics
Computer graphics deals with generating images and art with the aid of computers. Computer graphics is a core technology in digital photography, film, video games, digital art, cell phone and computer displays, and many specialized applications. A great deal of specialized hardware and software has been developed, with the displays of most devices being driven by graphics hardware, computer graphics hardware. It is a vast and recently developed area of computer science. The phrase was coined in 1960 by computer graphics researchers Verne Hudson and William Fetter of Boeing. It is often abbreviated as CG, or typically in the context of film as Computer-generated imagery, computer generated imagery (CGI). The non-artistic aspects of computer graphics are the subject of Computer graphics (computer science), computer science research. Some topics in computer graphics include user interface design, Sprite (computer graphics), sprite graphics, raster graphics, Rendering (computer graph ...
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3D Scanner
3D scanning is the process of analyzing a real-world object or environment to collect three dimensional data of its shape and possibly its appearance (e.g. color). The collected data can then be used to construct digital 3D models. A 3D scanner can be based on many different technologies, each with its own limitations, advantages and costs. Many limitations in the kind of objects that can be digitized are still present. For example, optical technology may encounter difficulties with dark, shiny, reflective or transparent objects while industrial computed tomography scanning, structured-light 3D scanners, LiDAR and Time Of Flight 3D Scanners can be used to construct digital 3D models, without destructive testing. Collected 3D data is useful for a wide variety of applications. These devices are used extensively by the entertainment industry in the production of movies and video games, including virtual reality. Other common applications of this technology include augmented rea ...
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Stereo Vision
Binocular vision is seeing with two eyes, which increases the size of the visual field. If the visual fields of the two eyes overlap, binocular depth can be seen. This allows objects to be recognized more quickly, camouflage to be detected, spatial relationships to be perceived more quickly and accurately(stereopsis) and perception to be less susceptible to optical illusions. In medical attention is paid to the occurrence, defects and sharpness of binocular vision. In biological the occurrence of binocular vision in animals is described. Geometric terms When the left eye (LE) and the right eye (RE) observe two objects X and Y, the following concepts are important: Egocentric distance The ''egocentric distance'' to object X is the distance from the observer to X. In the figure: Dx. Metric depth The ''metric depth'' between two objects X and Y is the difference of the egocentric distances to X and Y. In the figure: dXY. Direction in the left eye ''Direction αXY'' is the direc ...
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Photometry (optics)
Photometry is a branch of optics that deals with measuring light Light, visible light, or visible radiation is electromagnetic radiation that can be visual perception, perceived by the human eye. Visible light spans the visible spectrum and is usually defined as having wavelengths in the range of 400– ... in terms of its perceived brightness to the human eye. It is concerned with quantifying the amount of light that is emitted, transmitted, or received by an object or a system. In modern photometry, the radiant power at each wavelength is weighted by a luminosity function that models human brightness sensitivity. Typically, this weighting function is the photopic vision, photopic sensitivity function, although the scotopic vision, scotopic function or other functions may also be applied in the same way. The weightings are standardized by the International Commission on Illumination, CIE and International Organization for Standardization, ISO. Photometry is distinct ...
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Photoclinometry
Photoclinometry, or shape-from-shading, is the process by which a 2-dimensional image of a surface is transformed into a surface map that represents different levels of elevation. It uses the shadows and light direction as reference points. It is used mostly to depict the surface of sculptures, to give an idea of how it would look in 3-dimensions. The techniques depend on very specific conditions, especially light direction. The process When light bounces off an object, it reflects with location-specific brightness that depends on the shape of the object and the position of the lighting source. This reflection map can be used to create a bump map of a surface, which uses grayscale levels to depict the height of a point on a surface. Knowing the direction and angle of the light source, one can calculate the approximate height that a point has. However, the light direction and angle is usually unknown, which leads to poor quality images, or having to create multiple bump maps, each ti ...
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Structured Light
upright=1.3, A structured light pattern projected onto a surface (left) Structured light is a method that measures the shape and depth of a three-dimensional object by projecting a pattern of light onto the object's surface. The pattern can be either stripes, grids, or dots. The resulting distortions of the projected pattern reveals the object's solid geometry through triangulation, enabling the creation of a 3D model of the object. The scanning process relies on coding techniques for accurately detailed measurement. The most widely used coding techniques are binary, Gray, and phase-shifting, each offering distinct advantages and drawbacks. Structured light technology is applied across diverse fields, including industrial quality control, where it is used for precision inspection and dimensional analysis, and cultural heritage preservation, where it assists in the documentation and restoration of archaeological artifacts. In medical imaging, it facilitates non-invasive dia ...
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Diffuse Reflection
Diffuse reflection is the reflection of light or other waves or particles from a surface such that a ray incident on the surface is scattered at many angles rather than at just one angle as in the case of specular reflection. An ''ideal'' diffuse reflecting surface is said to exhibit Lambertian reflection, meaning that there is equal luminance when viewed from all directions lying in the half-space adjacent to the surface. A surface built from a non-absorbing powder such as plaster, or from fibers such as paper, or from a polycrystalline material such as white marble, reflects light diffusely with great efficiency. Many common materials exhibit a mixture of specular and diffuse reflection. The visibility of objects, excluding light-emitting ones, is primarily caused by diffuse reflection of light: it is diffusely-scattered light that forms the image of the object in an observer's eye over a wide range of angles of the observer with respect to the object. Mechanism Di ...
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Bidirectional Scattering Distribution Function
The definition of the BSDF (bidirectional scattering distribution function) is not well standardized. The term was probably introduced in 1980 by Bartell, Dereniak, and Wolfe. Most often it is used to name the general mathematical function which describes the way in which the light is scattered by a surface. However, in practice, this phenomenon is usually split into the reflected and transmitted components, which are then treated separately as BRDF (bidirectional reflectance distribution function) and BTDF (bidirectional transmittance distribution function). * BSDF is a superset and the generalization of the BRDF and BTDF. The concept behind all BxDF functions could be described as a black box with the inputs being any two angles, one for incoming (incident) ray and the second one for the outgoing (reflected or transmitted) ray at a given point of the surface. The output of this black box is the value defining the ratio between the incoming and the outgoing light energy for the ...
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Opacity (optics)
Opacity is the measure of impenetrability to electromagnetic or other kinds of radiation, especially visible light. In radiative transfer, it describes the absorption and scattering of radiation in a medium, such as a plasma, dielectric, shielding material, glass, etc. An opaque object is neither transparent (allowing all light to pass through) nor translucent (allowing some light to pass through). When light strikes an interface between two substances, in general, some may be reflected, some absorbed, some scattered, and the rest transmitted (also see refraction). Reflection can be diffuse, for example light reflecting off a white wall, or specular, for example light reflecting off a mirror. An opaque substance transmits no light, and therefore reflects, scatters, or absorbs all of it. Other categories of visual appearance, related to the perception of regular or diffuse reflection and transmission of light, have been organized under the concept of cesia in an order sys ...
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Inverse Function
In mathematics, the inverse function of a function (also called the inverse of ) is a function that undoes the operation of . The inverse of exists if and only if is bijective, and if it exists, is denoted by f^ . For a function f\colon X\to Y, its inverse f^\colon Y\to X admits an explicit description: it sends each element y\in Y to the unique element x\in X such that . As an example, consider the real-valued function of a real variable given by . One can think of as the function which multiplies its input by 5 then subtracts 7 from the result. To undo this, one adds 7 to the input, then divides the result by 5. Therefore, the inverse of is the function f^\colon \R\to\R defined by f^(y) = \frac . Definitions Let be a function whose domain is the set , and whose codomain is the set . Then is ''invertible'' if there exists a function from to such that g(f(x))=x for all x\in X and f(g(y))=y for all y\in Y. If is invertible, then there is exactly one functi ...
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