Digital scrapbooking is the term for the creation of a new 2D artwork by re-combining various graphic elements. It is a form of scrapbooking that is done using a personal computer, digital or scanned photos and computer graphics software. It is a relatively new form of the traditional print scrapbooking. Recent advances in technology now enable the craft to be pursued on tablets and smart devices utilising imaging apps as well as hobby specific apps, some of which have been created specifically by brands for use with their own image products. Digital scrapbooking kits are available to purchase and download at many websites that specialize in the craft. Kits contain graphics and word-art and are usually themed and color-coordinated. They usually consist of a mix of background images and "cut out" [extracted] images containing alpha channels. Once a kit has been downloaded to the computer or device, it can then be used over and over again to make new scrapbook pages (scrapbook layouts) within the software program that one chooses to use, often in combination with the users's own family photographs, scanned keepsakes and other unique personal elements scanned on a flatbed scanner. Scanning is usually done at 300dpi, to make the resulting images suitable for print. == Licensing and Copyright == Kits are sometimes licensed differently from other forms of traditional royalty-free stock images that may be purchased per-item or in sets at online stock photography sites. Some kit packs will be wholly royalty-free, but some kit makers may restrict usage to non-commercial work only. Some may specifically forbid the use of their work in projects for commercial gain, for example greetings cards and gift tags that may be made with their kits. Licensing often varies from kit to kit, even from the same maker. Some kits include derivative works of public domain material. In contrast to stock, creators of digital scrapbooking kits often require a credit or byline to indicate that their image elements have been used in a new creation. == Uses == Some artistic individuals combine digital scrapbooking with traditional scrapbooking to create what's known as hybrid scrapbooking projects. Hybrid scrapbooking involves creating layouts on the computer using digital supplies that will then be printed and combined with traditional supplies such as buttons, ribbons and other elements. Conversely, a hybrid scrapbook project may also be created using traditional paper supplies and augmented with digital elements that have been printed and cut out specifically for use on the project. Journaling may be done within the software programs to accompany images and to create digital storybooks, or scrapbooks, which are then published in photo books via various popular print-on-demand services, printed and added to traditional scrapbooks, burned to CDs or posted on the Web. Digital Scrapbooking may also be done online by uploading photos to a specialist scrapbooking website and utilising their custom built platforms and decorative image elements to complete the projects for print to finished products, for example photo books and holiday greeting cards. == Market Size == The traditional scrapbooking market appeared to decline somewhat in the USA since 2010, probably due to the 2008 financial crisis, and the digital scrapbooking market (being potentially a much cheaper form of scrapbooking) may have increased accordingly. Both markets currently appear to have recovered lost ground and expanded since the beginning of the COVID-19 pandemic as many people sought to productively fill their time during lockdowns, quarantines and self-isolation / stay at home directions. == Digital scrapbooking software == The main software programs that are typically used are Adobe Photoshop, Adobe Photoshop Elements, paint.net (freeware), Filter Forge, Corel Paintshop Pro, and GIMP. Additionally Adobe offer the Photoshop iOS product using the same code base as the desktop version to drive the app version. == Digital scrapbooking supplies == Digital scrapbooking supplies are downloaded from the Internet and then stored on a computer or external hardrive, DVD or CD media, SD cards, or in the cloud, to be used as needed. Both paid and free digital scrapbooking supplies available from numerous designers on their blogs or in e-commerce stores either as solo designers or as part of a wide cohort of designers working cooperatively in large full service e-commerce websites. Usually designed at 300ppi image resolution, digital scrapbooking product offerings and supplies often include: Full coordinated kits containing digital background “papers”, decorative alphabets, and diverse embellishments generally containing a mixture of .JPG and .PNG files; "Quick pages", flattened files containing a completed page layout with transparent photo windows in .PNG file format; Digital templates, fully layered layouts i.e. pages that have had the composition pre-designed ready for use in an imaging program or app, fully customizable for color schemes, kit choices, photographs and other embellishments, generally supplied in either .PSD or .TIF file format; Hybrid “quick pages”, i.e. layouts that are both fully designed and fully layered for customization, generally supplied in either .PSD or .TIF file format; Adobe Photoshop actions, brushes, custom shapes, paths and styles, saved in their respective native Photoshop file formats; and Corel PaintShop Pro equivalent tools.
Supertoroid
In geometry and computer graphics, a supertoroid or supertorus is usually understood to be a family of doughnut-like surfaces (technically, a topological torus) whose shape is defined by mathematical formulas similar to those that define the superellipsoids. The plural of "supertorus" is either supertori or supertoruses. The family was described and named by Alan Barr in 1994. Barr's supertoroids have been fairly popular in computer graphics as a convenient model for many objects, such as smooth frames for rectangular things. One quarter of a supertoroid can provide a smooth and seamless 90-degree joint between two superquadric cylinders. However, they are not algebraic surfaces (except in special cases). == Formulas == Alan Barr's supertoroids are defined by parametric equations similar to the trigonometric equations of the torus, except that the sine and cosine terms are raised to arbitrary powers. Namely, the generic point P(u, v) of the surface is given by P ( u , v ) = ( X ( u , v ) Y ( u , v ) Z ( u , v ) ) = ( ( a + C u s ) C v t ( b + C u s ) S v t S u s ) {\displaystyle P(u,v)=\left({\begin{array}{c}X(u,v)\\Y(u,v)\\Z(u,v)\end{array}}\right)=\left({\begin{array}{c}(a+C_{u}^{s})C_{v}^{t}\\(b+C_{u}^{s})S_{v}^{t}\\S_{u}^{s}\end{array}}\right)} where C θ ε = sgn ( cos θ ) | cos θ | ε , S θ ε = sgn ( sin θ ) | sin θ | ε , {\displaystyle {\begin{aligned}C_{\theta }^{\varepsilon }&=\operatorname {sgn} (\cos \theta )\,\left|\,\cos \theta \,\right|^{\varepsilon },\\S_{\theta }^{\varepsilon }&=\operatorname {sgn} (\sin \theta )\ \left|\,\sin \theta \ \right|^{\varepsilon },\end{aligned}}} sgn is the sign function, and the parameters u, v range from 0 to 360 degrees (0 to 2π radians). In these formulas, the parameter s > 0 controls the "squareness" of the vertical sections, t > 0 controls the squareness of the horizontal sections, and a, b ≥ 1 are the major radii in the x and y directions. With s = t = 1 and a = b = R one obtains the ordinary torus with major radius R and minor radius 1, with the center at the origin and rotational symmetry about the z-axis. In general, the supertorus defined as above spans the intervals: − ( a + 1 ) ≤ x ≤ + ( a + 1 ) − ( b + 1 ) ≤ y ≤ + ( b + 1 ) − 1 ≤ z ≤ + 1 {\displaystyle {\begin{array}{rcccl}-(a+1)&\leq &x&\leq &+(a+1)\\[4pt]-(b+1)&\leq &y&\leq &+(b+1)\\[4pt]-1&\leq &z&\leq &+1\end{array}}} The whole shape is symmetric about the planes x = 0, y = 0, and z = 0. The hole runs in the z direction and spans the intervals − ( a − 1 ) ≤ x ≤ + ( a − 1 ) − ( b − 1 ) ≤ y ≤ + ( b − 1 ) − ∞ ≤ z ≤ + ∞ {\displaystyle {\begin{array}{rcccl}-(a-1)&\leq &x&\leq &+(a-1)\\[4pt]-(b-1)&\leq &y&\leq &+(b-1)\\[4pt]-\infty &\leq &z&\leq &+\infty \end{array}}} A curve of constant u on this surface is a horizontal Lamé curve with exponent 2 t , {\displaystyle {\tfrac {2}{t}},} scaled in x and y and displaced in z. A curve of constant v, projected on the plane x = 0 or y = 0, is a Lamé curve with exponent 2 s , {\displaystyle {\tfrac {2}{s}},} scaled and horizontally shifted. If v = 0, the curve is planar and spans the intervals: a − 1 ≤ x ≤ a + 1 − 1 ≤ z ≤ + 1 {\displaystyle {\begin{array}{rcccl}a-1&\leq &x&\leq &a+1\\[4pt]-1&\leq &z&\leq &+1\end{array}}} and similarly if v = 90°, 180°, 270°. The curve is also planar if a = b. In general, if a ≠ b and v is not a multiple of 90 degrees, the curve of constant v will not be planar; and, conversely, a vertical plane section of the supertorus will not be a Lamé curve. The basic supertoroid shape defined above is often modified by non-uniform scaling to yield supertoroids of specific width, length, and vertical thickness. == Plotting code == The following GNU Octave code generates plots of a supertorus:
Optical granulometry
Optical granulometry is the process of measuring the different grain sizes in a granular material, based on a photograph. Technology has been created to analyze a photograph and create statistics based on what the picture portrays. This information is vital in maintaining machinery in various trades worldwide. Mining companies can use optical granulometry to analyze inactive or moving rock to quantify the size of these fragments. Forestry companies can zero in on wood chip sizes without stopping the production process, and minimize sizing errors. With more photoanalysis technologies being produced, mining companies have shown an increased interest in these types of systems because of their ability to maintain efficiency throughout the mining process. Companies are saving millions of dollars annually because of this new technology, and are cutting back on maintenance costs on equipment. In order for optical granulometry to be completely successful, an accurate photo must be taken – under sufficient lighting, and using proper technology – to obtain quantified results. If these requirements are met, an image analysis system can be implemented. == The process == Software uses four basic steps in determining the average size of material: See the Wikipedia article on Photoanalysis to see how mining, forestry and agricultural companies are using this technology to improve quality control techniques. == Smartphone-based, segmentation-free estimation of grain size distribution == Recently, a methodology has emerged by which soil grain size distribution can be inferred from optical images acquired with commodity smartphones by training convolutional neural networks to predict parameters of the distribution curve directly from the image, without explicit image segmentation . In this approach, a standardized image of a soil surface is captured under controlled conditions, preprocessed to reduce device-specific variability, and passed to a regression model that outputs the parameters of a cumulative distribution function e.g., a two-parameter Weibull curve. The resulting distribution can be used to derive geotechnical descriptors and class boundaries.
Pixel shift
Pixel shift is a method in digital cameras for producing a super-resolution image. The method works by taking several images, after each such capture moving ("shifting") the sensor to a new position. In digital colour cameras that employ pixel shift, this avoids a major limitation inherent in using Bayer pattern for obtaining colour, and instead produces an image with increased colour resolution and, assuming a static subject or additional computational steps, an image free of colour moiré. Taking this idea further, sub-pixel shifting may increase the resolution of the final image beyond that suggested by the specified resolution of the image sensor. Additionally, assuming that the various individual captures are taken at the same sensitivity, the final combined image will have less image noise than a single capture. This can be thought of as an averaging effect (for instance, in a pixel shift image composed of four individual frames with a classic Bayer pattern, every pixel in the final colour image is based on two measurements of the green channel). == List of cameras implementing pixel shift == All of the following cameras are fabricated with one imaging sensor, thus any kind of pixel shift requires a movement of the whole sensor. === Canon === Canon R5: Contains a 45 Mpixel sensor. The High-Resolution Mode shifts the sensor by one pixel to obtain a sequence of nine images that are merged into a 400 Mpixel image. === Fujifilm === Fujifilm GFX50S II: contains a 51 Mpixel sensor. The Pixel Shift Multi-Shot mode shifts the imaging sensor by 0.5-pixel movements to obtain a sequence of 16 images that are subsequently merged into a 200 Mpixel image. Fujifilm GFX100, Fujifilm GFX100 II: contains a 102 Mpixel sensor. A sequence of 16 pixel shifted images are merged into a 400 Mpixel image. Fujifilm GFX100S, Fujifilm GFX100S II: contains a 102 Mpixel sensor. A sequence of 16 pixel shifted images are merged into a 400 Mpixel image Fujifilm GFX100IR: contains a 102 Mpixel sensor. A sequence of 16 pixel shifted images are merged into a 400 Mpixel image Fujifilm X-H2: contains a 40 Mpixel sensor. A sequence of 20 shifted images are merged into a 160 Mpixel image. Fujifilm X-T5: contains a 40 Mpixel sensor. A sequence of 20 shifted images are merged into a 160 Mpixel image. === Nikon === Nikon Z8: contains a 47.5 Mpixel sensor. The High Res shot mode shifts the imaging sensor by 0.5-pixel movements to obtain a sequence of up to 32 images that can be merged in Nikon's NX studio software. Nikon Zf: contains a 24 Mpixel sensor. The High Res shot mode shifts the imaging sensor by 0.5-pixel movements to obtain a sequence of up to 32 images that can be merged in Nikon's NX studio software. === Olympus === Olympus OM-D E-M1 Mark II: contains a 20.4 Mpixel sensor. The High Res shot mode produces a 50 Mpixel image. Olympus OM-D E-M5 Mark II: contains a 16 Mpixel sensor. The High Res shot mode shifts the imaging sensor by 0.5-pixel movements to obtain a sequence of 8 images that are subsequently merged into a 40 Mpixel image. Olympus OM-D E-M5 Mark III: contains a 20.4 Mpixel sensor. The High Res shot mode shifts the imaging sensor by 0.5-pixel movements to obtain a sequence of 8 images that are subsequently merged into a 50 Mpixel image. Olympus OM-D E-M1X: contains a 20.4 Mpixel sensor. The camera sports two pixel shift mode: (a) the 80Mp Tripod mode produces an 80 Mpixel image, (b) the Handheld High Res shot mode produces a 50 Mpixel image. Olympus PEN-F: contains a 20.4 Mpixel sensor. The High Res Shot mode takes multiple images, continually shifting the position of the sensor in sub-pixel increments. Combining these images results in either a 50MP JPEG or an 80MP Raw file. ==== OM System ==== OM System OM-1: contains a 20MPix sensor. The High Res Shot mode takes multiple images, and it can be used handheld or on a tripod. Handheld it will internally produce 50 Mpix files and 80 Mpix when mounted on a tripod. OM System OM-5: contains a 20MPix sensor. The High Res Shot mode takes multiple images, and it can be used handheld or on a tripod. Handheld it will internally produce 50 Mpix files and 80 Mpix when mounted on a tripod. === Panasonic === Panasonic Lumix DC-G9: contains a 20.3 Mpixel sensor. The High Resolution Mode takes a sequence of 8 shots in quick succession between which the sensor is shifted by 0.5 pixel for each image. These are subsequently merged into an 80 Mpixel image. Panasonic Lumix DC-S1: contains a 24.2 Mpixel sensor. The High Resolution Mode takes a sequence of shots in quick succession between which the sensor is shifted by a small amount. These are subsequently merged into a 96 Mpixel image. Panasonic Lumix DC-S1R: contains a 47.3 Mpixel sensor. The High Resolution Mode shifts the imaging sensor by a small increments to obtain a sequence of 8 images that are subsequently merged into a 187 Mpixel image. Panasonic Lumix DC-S1H Panasonic Lumix DC-S5 === Pentax === Pentax K-70: contains a 24.3 Mpixel sensor. The pixel shift mode takes a sequence of 4 shots between which the sensor is shifted by 1 pixel. These are subsequently merged into an image sporting 'all color data in each pixel to deliver super-high-resolution images'. Pentax KP: contains a 24.3 Mpixel sensor. The pixel shift mode takes a sequence of 4 shots between which the sensor is shifted by 1 pixel. These are subsequently merged into an image sporting 'high-resolution images with more accurate colours and much finer details'. Pentax K-3 II: contains a 24.3 Mpixel sensor. The pixel shift mode takes a sequence of 4 shots between which the sensor is shifted by 1 pixel. These are subsequently merged into an image sporting 'super-high-resolution images with far more truthful color reproduction and much finer details'. Pentax K-3 III: contains a 25.7 Mpixel sensor. The pixel shift mode takes a sequence of 4 shots between which the sensor is shifted by 1 pixel. These are subsequently merged into an image sporting 'a cancelling out of the Bayer pattern and removal of the need for sharpness-sapping demosaicing'. Pentax K-1: contains a 36.4 Mpixel sensor. The pixel shift mode takes a sequence of 4 shots between which the sensor is shifted by 1 pixel. These are subsequently merged into an image sporting 'improved detail and colour resolution'. Pentax K-1 II: contains a 36.4 Mpixel sensor. The camera sports two pixel shift mode: (a) a series of 4 tripod-stabilised images shifted by 1 pixel each are subsequently combined into a 47.3 Mpixel image, (b) a series of images taken in handheld mode are combined into a 47.3 Mpixel image that is, within limits, able to cope even with moving subjects. === Sony === Sony a6600: contains a 24.3 Mpixel sensor. The pixel shift mode takes a sequence of 4 shots between which the sensor is shifted by 1 pixel. These are subsequently merged into an image sporting 'all color data in each pixel to deliver super-high-resolution images'. Sony α7R III: contains a 42.4 Mpixel sensor. The pixel shift mode takes a sequence of 4 shots between which the sensor is shifted by 1 pixel. These are subsequently merged into a 42.4 Mpixel image with improved tonal resolution. Sony α7R IV: contains a 61 Mpixel sensor. The camera has two pixel shift modes, (a) the first takes a sequence of 4 shots between which the sensor is shifted by 1 pixel. These are subsequently merged into a 61 Mpixel image with improved tonal resolution, (b) the other takes a sequence of 16 shots between which the sensor is shifted by 0.5 pixel. These are subsequently merged into a 240 Mpixel image with both enhanced detail and improved tonal resolution. Sony α1: contains a 50 Mpixel sensor. The camera has two pixel shift modes, (a) the first takes a sequence of 4 shots between which the sensor is shifted by 1 pixel. These are subsequently merged into a 50 Mpixel image with improved tonal resolution, (b) the other takes a sequence of 16 shots between which the sensor is shifted by 0.5 pixel. These are subsequently merged into a 200 Mpixel image with both enhanced detail and improved tonal resolution. === Hasselblad === Hasselblad H3DII: the model H3DII-39 sports a 39 Mpixel sensor, the model H3DII-50 a 50 Mpixel sensor. Both enable a pixel shift mode which takes a sequence of 4 shots between which the sensor is shifted by 1 pixel. These are subsequently merged into a single image. Hasselblad H4D series: the model H4D-200MS contains a 50 Mpixel sensor. The sensor sports 3 different pixel shift modes which take (a) a sequence of 6 shots taken at slight offsets, (b) a sequence of 4 shots between which the sensor is shifted by 1 pixel, (c) a sequence of 4 shots between which the sensor is shifted by 0.5 pixels. Images obtained by all three modes are subsequently merged into 200 Mpixel images. Hasselblad H5D series: both models H5D-50c MS and H5D-200c MS contain a 50 Mpixel sensor. This sensor sports 2 different pixel shift modes which take (a) a sequence of 6 shots with full and half pixel moveme
PhotoWorks (ray tracing software)
PhotoWorks is a raytrace rendering program created by Dassault Systèmes SolidWorks Corporation, formerly supplied as a photorealistic rendering add-in for SolidWorks. The program is based on the Mental Ray rendering engine. It has a library of scenes and materials that can be used with user-created SolidWorks files to create still frame images within the SolidWorks GUI. Since the 2011 release of SolidWorks, PhotoWorks has been replaced by the PhotoView 360 rendering utility. A 2010 review comparing PhotoWorks with three other rendering programs for SolidWorks (including PhotoView 360) gave the program high marks for render speed and built-in materials, but low marks for realism and user interface. Appearance File Type: .p2m
DUAL table
The DUAL table is a special one-row, one-column table present by default in Oracle and other database installations. In Oracle, the table has a single VARCHAR2(1) column called DUMMY that has a value of 'X'. It is suitable for use in selecting a pseudo column such as SYSDATE or USER. == Example use == Oracle's SQL syntax requires the FROM clause but some queries don't require any tables - DUAL can be used in these cases. == History == Charles Weiss explains why he created DUAL: I created the DUAL table as an underlying object in the Oracle Data Dictionary. It was never meant to be seen itself, but instead used inside a view that was expected to be queried. The idea was that you could do a JOIN to the DUAL table and create two rows in the result for every one row in your table. Then, by using GROUP BY, the resulting join could be summarized to show the amount of storage for the DATA extent and for the INDEX extent(s). The name, DUAL, seemed apt for the process of creating a pair of rows from just one. == Optimization == Beginning with 10g Release 1, Oracle no longer performs physical or logical I/O on the DUAL table, though the table still exists. DUAL is readily available for all authorized users in a SQL database. == In other database systems == Several other databases (including Microsoft SQL Server, MySQL, PostgreSQL, SQLite, and Teradata) enable one to omit the FROM clause entirely if no table is needed. This avoids the need for any dummy table. ClickHouse has a one-row system table system.one with a single column named "dummy" of type UInt8 and value 0. This table is implicitly used when no table is specified in the SELECT query. Firebird has a one-row system table RDB$DATABASE that is used in the same way as Oracle's DUAL, although it also has a meaning of its own. IBM Db2 has a view that resolves DUAL when using Oracle Compatibility. It also has a table called sysibm.sysdummy1 that has similar properties to the Oracle DUAL one. Informix: Informix version 11.50 and later has a table named sysmaster:"informix".sysdual with the same functionality but a more verbose name. You can use CREATE PUBLIC SYNONYM dual FOR sysmaster:"informix".sysdual to create a name dual in the current database with the same functionality. Microsoft Access: A table named DUAL may be created and the single-row constraint enforced via ADO (Table-less UNION query in MS Access) Microsoft SQL Server: SQL Server does not require a dummy table. Queries like 'select 1 + 1' can be run without a "from" clause/table name. MySQL allows DUAL to be specified as a table in queries that do not need data from any tables. It is suitable for use in selecting a result function such as SYSDATE() or USER(), although it is not essential. PostgreSQL: A DUAL-view can be added to ease porting from Oracle. Snowflake: DUAL is supported, but not explicitly documented. It appears in sample SQL for other operations in the documentation. SQLite: A VIEW named "dual" that works the same as the Oracle "dual" table can be created as follows: CREATE VIEW dual AS SELECT 'x' AS dummy; SAP HANA has a table called DUMMY that works the same as the Oracle "dual" table. Teradata database does not require a dummy table. Queries like 'select 1 + 1' can be run without a "from" clause/table name. Vertica has support for a DUAL table in their official documentation.
Super-resolution imaging
Super-resolution imaging (SR) is a class of techniques that improve the resolution of an imaging system. In optical SR the diffraction limit of systems is transcended, while in geometrical SR the resolution of digital imaging sensors is enhanced. In some radar and sonar imaging applications (e.g. magnetic resonance imaging (MRI), high-resolution computed tomography), subspace decomposition-based methods (e.g. MUSIC) and compressed sensing-based algorithms (e.g., SAMV) are employed to achieve SR over standard periodogram algorithm. Super-resolution imaging techniques are used in general image processing and in super-resolution microscopy. == Super-resolution principles == Several concepts are fundamental to super-resolution imaging: Diffraction limit: the capacity of an optical instrument to reproduce the details of an object in an image has limits that are imposed by laws of physics: the diffraction equations in the wave theory of light, or the uncertainty principle for photons in quantum mechanics. Information transfer can never be increased beyond this boundary, but packets outside the limits can be cleverly swapped for (or multiplexed with) some inside it. Super-resolution microscopy does not so much “break” as “circumvent” the diffraction limit. New procedures probing electro-magnetic disturbances at the molecular level (in the so-called near field) remain fully consistent with Maxwell's equations. Spatial frequency domain: A succinct expression of the diffraction limit is given in the spatial frequency domain. In Fourier optics light distributions are expressed as superpositions of a series of grating light patterns in a range of fringe widths - these widths represent the spatial frequencies. It is generally taught that diffraction theory stipulates an upper limit, the cut-off spatial-frequency, beyond which pattern elements fail to be transferred into the optical image, i.e., are not resolved. But in fact what is set by diffraction theory is the width of the passband, not a fixed upper limit. No laws of physics are broken when a spatial frequency band beyond the cut-off spatial frequency is swapped for one inside it: this has long been implemented in dark-field microscopy. Nor are information-theoretical rules broken when superimposing several bands, disentangling them in the received image needs assumptions of object invariance during multiple exposures, i.e., the substitution of one kind of uncertainty for another. Information: When the term super-resolution is used in techniques based on the inference of object details using a statistical treatment of the image within standard resolution limits (for example, averaging multiple exposures), it involves an exchange of one kind of information (extracting signal from noise) for another (the assumption that the target has remained invariant). Recent breakthroughs incorporate quantum-transformer hybrids into super-resolution, such as QUIET‑SR, a 2025 model that employs shifted quantum window attention within a transformer to enhance image detail while respecting diffraction and information-theory limits Similarly, frequency-integrated transformers (e.g., FIT) enrich super-resolution by explicitly combining spatial and frequency-domain information via FFT-based attention, improving reconstruction across scales Resolution and localization: True resolution involves the distinction of whether a target, e.g. a star or a spectral line, is single or double, ordinarily requiring separable peaks in the image. When a target is known to be single, its location can be determined with higher precision than the image width by finding the centroid (center of gravity) of its image light distribution. The word ultra-resolution had been proposed for this process but it did not catch on, and the high-precision localization procedure is typically referred to as super-resolution. == Techniques == === Optical or diffractive super-resolution === Substituting spatial-frequency bands: Though the bandwidth allowable by diffraction is fixed, it can be positioned anywhere in the spatial-frequency spectrum. Dark-field illumination in microscopy is an example. See also aperture synthesis. ==== Multiplexing spatial-frequency bands ==== An image is formed using the normal passband of the optical device. Then, some known light structure (for example, a set of light fringes) is superimposed on the target. The image now contains components resulting from the combination of the target and the superimposed light structure, e.g. moiré fringes, and carries information about target detail which simple unstructured illumination does not. The “superresolved” components, however, need disentangling to be revealed. For an example, see structured illumination (figure to left). ==== Multiple parameter use within traditional diffraction limit ==== If a target has no special polarization or wavelength properties, two polarization states or non-overlapping wavelength regions can be used to encode target details, one in a spatial-frequency band inside the cut-off limit the other beyond it. Both would use normal passband transmission but are then separately decoded to reconstitute target structure with extended resolution. ==== Probing near-field electromagnetic disturbance ==== Super-resolution microscopy is generally discussed within the realm of conventional optical imagery. However, modern technology allows the probing of electromagnetic disturbance within molecular distances of the source, which has superior resolution properties. See also evanescent waves and the development of the new super lens. === Geometrical or image-processing super-resolution === ==== Multi-exposure image noise reduction ==== When an image is degraded by noise, the resolution may be improved by averaging multiple exposures. See example on the right. ==== Single-frame deblurring ==== Known defects in a given imaging situation, such as defocus or aberrations, can sometimes be mitigated in whole or in part by suitable spatial-frequency filtering of even a single image. Such procedures all stay within the diffraction-mandated passband, and do not extend it. ==== Sub-pixel image localization ==== The location of a single source can be determined by computing the "center of gravity" (centroid) of the light distribution extending over several adjacent pixels (see figure on the left). Provided that there is enough light, this can be achieved with arbitrary precision, very much better than pixel width of the detecting apparatus and the resolution limit for the decision of whether the source is single or double. This technique, which requires the presupposition that all the light comes from a single source, is at the basis of what has become known as super-resolution microscopy, e.g. stochastic optical reconstruction microscopy (STORM), where fluorescent probes attached to molecules give nanoscale distance information. It is also the mechanism underlying visual hyperacuity. ==== Bayesian induction beyond traditional diffraction limit ==== Some object features, though beyond the diffraction limit, may be known to be associated with other object features that are within the limits and hence contained in the image. Then conclusions can be drawn, using statistical methods, from the available image data about the presence of the full object. The classical example is Toraldo di Francia's proposition of judging whether an image is that of a single or double star by determining whether its width exceeds the spread from a single star. This can be achieved at separations well below the classical resolution bounds, and requires the prior limitation to the choice "single or double?" The approach can take the form of extrapolating the image in the frequency domain, by assuming that the object is an analytic function, and that we can exactly know the function values in some interval. This method is severely limited by the ever-present noise in digital imaging systems, but it can work for radar, astronomy, microscopy or magnetic resonance imaging. More recently, a fast single image super-resolution algorithm based on a closed-form solution to ℓ 2 − ℓ 2 {\displaystyle \ell _{2}-\ell _{2}} problems has been proposed and demonstrated to accelerate most of the existing Bayesian super-resolution methods significantly. == Aliasing == Geometrical SR reconstruction algorithms are possible if and only if the input low resolution images have been under-sampled and therefore contain aliasing. Because of this aliasing, the high-frequency content of the desired reconstruction image is embedded in the low-frequency content of each of the observed images. Given a sufficient number of observation images, and if the set of observations vary in their phase (i.e. if the images of the scene are shifted by a sub-pixel amount), then the phase information can be used to separate the aliased high-frequency content from the true low-frequency content, and the full-resolution image can be accurate