Inpainting

Inpainting is a conservation process where damaged, deteriorated, or missing parts of an artwork are filled in to present a complete image. This process is commonly used in image restoration. It can be applied to both physical and digital art mediums such as oil or acrylic paintings, chemical photographic prints, sculptures, or digital images and video. With its roots in physical artwork, such as painting and sculpture, traditional inpainting is performed by a trained art conservator who has carefully studied the artwork to determine the mediums and techniques used in the piece, potential risks of treatments, and ethical appropriateness of treatment. == History == The modern use of inpainting can be traced back to Pietro Edwards (1744–1821), Director of the Restoration of the Public Pictures in Venice, Italy. Using a scientific approach, Edwards focused his restoration efforts on the intentions of the artist. It was during the 1930 International Conference for the Study of Scientific Methods for the Examination and Preservation of Works of Art, that the modern approach to inpainting was established. Helmut Ruhemann (1891–1973), a German restorer and conservator, led the discussions on the use of inpainting in conservation. Helmut Ruhemann was a leading figure in modernizing restoration and conservation. His greatest contribution to the field of conservation "was his insistence on following the methods of the original painter exactly, and on understanding the painter's artistic intention". After his career of over 40 years as a conservator, Ruhemann published his treatise The Cleaning of Paintings: Problems & Potentialities in 1968. In describing his method, Ruhemann states that "The surface [of the fill] should be slightly lower than that of the surrounding paint to allow for the thickness of the inpainting...Inpainting medium should look and behave like the original medium, but must not darken with age." Cesare Brandi (1906–1988) developed the teoria del restauro, the inpainting approach combining aesthetics and psychology. However, this approach was used primarily by Italian restorers and conservators, with the terminology becoming widespread in the 1990s. Technological advancements led to new applications of inpainting. Widespread use of digital techniques range from entirely automatic computerized inpainting to tools used to simulate the process manually. Since the mid-1990s, the process of inpainting has evolved to include digital media. More commonly known as image or video interpolation, a form of estimation, digital inpainting includes the use of computer software that relies on sophisticated algorithms to replace lost or corrupted parts of the image data. == Ethics == In order to preserve the integrity of an original artwork, any inpainting technique or treatment applied to physical or digital work should be reversible or distinguishable from the original content of the artwork. Prior to any treatments, conservators proceed according to the American Institute of Conservation of Historical and Artistic Works. There are several ethic considerations before Inpainting can be justified. Various deliberation decisions over the ethical appropriateness of the amount and type of inpainting done, resides on many factors. As most conservation treatments, inpainting's ethical questions rest mainly with authenticity, reversibility and documentation.Any intervention to compensate for loss should be documented in treatment records and reports and should be detectable by common examination methods. Such compensation should be reversible and should not falsely modify the known aesthetic, conceptual, and physical characteristics of the cultural property, especially by removing or obscuring original material.New technologies and the aesthetic demand for perfect images without imperfections challenge conservators' ethical practices to protect the integrity of originals. == Methods == Inpainting methods and techniques depend on the desired goal and type of image being treated. Treatments to fill in the gaps are different between physical and digital art. In inpainting, detailed records of the initial state of the images can help with the treatment and replicate the original closer. === Physical inpainting === Inpainting is rooted in the conservation and restoration of paintings. Inpainting can aim to make a visual improvement to the artwork as a whole by repairing missing or damaged parts using methods and materials equivalent to the original artist's work. ==== Application techniques ==== By studying the painting methods of various artists and the composition of paints used historically, conservators are able to restore works very closely to their original visual appearance. The picture as a whole determines how to fill in the gap. Helmut Ruhemann's inpainting techniques by Jessell have procedures to "preserve" the quality of oil and tempera paintings. === Digital inpainting === Many programs are able to reconstruct missing or damaged areas of digital photographs and videos. Most widely known for use with digital images is Adobe Photoshop. Given the various abilities of the digital camera and the digitization of old photos, inpainting has become an automatic process that can be performed on digital images. The inpainting techniques can be applied to object removal, text removal, and other automatic modifications of images and videos. In video special effects, inpainting is usually performed after video matting. They can also be observed in applications like image compression and super-resolution. In photography and cinema, it is used for film restoration to reverse, repair, or mitigate deterioration (e.g., physical damage such as cracks in photographs, scratches and dust spots in film, or chemical damage resulting in image loss; performed infrared cleaning). It can also be used for removing red-eye, the stamped date from photographs, and objects for creative effect. This technique can be used to replace any lost blocks in the coding and transmission of images, for example, in a streaming video. It can also be used to remove logos or watermarks in videos. Deep learning neural network-based inpainting can be used for decensoring images. Deep image prior-based techniques can be used for digital image inpainting, where a trained deep learning model is either unavailable or infeasible. Deep models for visual content generation, like text-to-image or text-to-video, learn complex priors over the distribution of visual content, and can be used to inpaint missing parts. For example, videos can be separated into layers, using a technique called omnimatte, which either pretrain an omnimatte model or without any training using an omnimatte-zero model. Three main groups of 2D image-inpainting algorithms can be found in the literature. The first one to be noted is structural (or geometric) inpainting, the second one is texture inpainting, the last one is a combination of these two techniques. They use the information of the known or non-destroyed image areas in order to fill the gap, similar to how physical images are restored. ==== Structural ==== Structural or geometric inpainting is used for smooth images that have strong, defined borders. There are many different approaches to geometric inpainting, but they all come from the idea that geometry can be recovered from similar areas or domains. Bertalmio proposed a method of structural inpainting that mimics how conservators address painting restoration. Bertalmio proposed that by progressively transferring similar information from the borders of an inpainting domain inwards, the gap can be filled. ==== Textural ==== While structural/geometric inpainting works to repair smooth images, textural inpainting works best with images that are heavily textured. Texture has a repetitive pattern which means that a missing portion cannot be restored by continuing the level lines into the gap; level lines provide a complete, stable representation of an image. To repair texture in an image, one can combine frequency and spatial domain information to fill in a selected area with a desired texture. This method, while the most simple and very effective, works well when selecting a texture to be in-painted. For a texture that covers a wider area or a larger frame one would have to go through the image segmenting the areas to be in-painted and selecting the corresponding textures from throughout the image; there are programs that can help find the corresponding areas that work in a similar way as 'find and replace' works in a word processor. ==== Combined structural and textural ==== Combined structural and textural inpainting approaches simultaneously try to perform texture- and structure-filling in regions of missing image information. Most parts of an image consist of texture and structure and the boundaries between image regions contain a large amount of structural information. This is the result when blending differ

SimSimi

SimSimi is an artificial intelligence conversation program created in 2002 by ISMaker. It grows its artificial intelligence day by day assisted by a feature that allows users to teach it to respond correctly. SimSimi, pronounced as "shim-shimi", is from a Korean word simsim (심심) which means "bored". It has an application designed for Android, Windows Phone and iOS. The application was banned in Thailand in 2012 after users taught it to make responses containing profanity, and to criticise leading politicians. In April 2018, SimSimi was suspended in Brazil due to accusations of sending inappropriate messages, such as sexual language, bullying and even death threats, being labeled as "dangerous" mainly due to its popularity among children, and according to its developer, the suspension of the app in the country "was inevitable because the SimSimi app, at least in the last few days, had a significant negative social impact in Brazil.”

List of robotics journals

List of robotics journals includes notable academic and scientific journals that focus on research in the field of robotics and automation. == Journals == Acta Mechanica et Automatica Advanced Robotics Annual Review of Control, Robotics, and Autonomous Systems IEEE Robotics and Automation Letters IEEE Transactions on Robotics IEEE Transactions on Field Robotics The International Journal of Advanced Manufacturing Technology International Journal of Humanoid Robotics International Journal of Robotics Research Journal of Cognitive Engineering and Decision Making Journal of Field Robotics Journal of Intelligent & Robotic Systems Paladyn Robotics and Autonomous Systems Robotics Science Robotics SLAS Technology

Odor source localization

Odor source localization (OSL) is the problem of locating the origin of an airborne or waterborne chemical plume using one or more mobile sensors, typically robots equipped with chemical sensors. The task sits at the intersection of robotics, fluid dynamics and machine olfaction. Chemical plumes in turbulent flows are intermittent and patchy, and most chemical sensors respond slowly and have limited selectivity, so the instantaneous reading available to a moving sensor is a poor proxy for the underlying time-averaged concentration field. Robotic OSL has been studied since the late 1980s and has applications including the detection of gas leaks, search and rescue after industrial accidents, and environmental monitoring of industrial emissions. == History == Robotic odor search emerged in the late 1980s and 1990s, drawing on earlier work in chemical ecology that had described how moths and other insects locate distant pheromone sources. R. A. Russell at Monash University was among the first to build mobile robots that followed chemical trails on the floor and tracked airborne odor plumes. Distributed and multi-robot odor search were investigated by Hayes, Martinoli and Goodman at the California Institute of Technology and EPFL, who studied cooperative plume-tracing on simulated and physical robot swarms. In 2007 Vergassola, Villermaux and Shraiman introduced infotaxis, an information-theoretic search strategy in which a sensor moves so as to maximize the expected information gain about source location, rather than following a chemical concentration gradient; the paper appeared in Nature and prompted substantial follow-up work in the robotics community. From the mid-2010s, multi-rotor unmanned aerial vehicles carrying lightweight chemical sensors became a common experimental platform for OSL research. == Problem formulation == OSL is generally decomposed into three sub-problems: plume detection (deciding whether a chemical signal is present), plume traversal (moving so as to remain in contact with the plume), and source declaration (deciding when the source has been reached). The mathematical difficulty depends strongly on the assumed dispersion model. In laminar or low-Reynolds number flows a Gaussian advection–diffusion model gives a smooth concentration field with a well-defined gradient. In turbulent flows, which dominate most realistic environments, the plume is filamentary: the sensor receives short, randomly spaced bursts of chemical separated by periods of zero signal, and the time-averaged field is not a useful guide on the time scales at which a robot must act. Source-term estimation, surveyed by Hutchinson and colleagues, additionally aims to recover both the position and the release rate of the source from the observed concentrations, often using probabilistic filters. == Biological inspiration == Many OSL strategies are explicitly modeled on the behavior of male moths flying upwind toward a pheromone source. As reviewed by Cardé and Willis, moths combine an upwind surge whenever they detect a filament of pheromone with a wider crosswind cast when contact is lost, producing a characteristic zig-zag trajectory that has been transposed onto mobile robots by several groups. Other biological models draw on the search behavior of dogs and of marine animals such as blue crabs and lobsters, which integrate chemical and bilateral hydrodynamic cues over much shorter ranges. == Algorithms and strategies == === Reactive strategies === Reactive strategies select the next motion as a direct function of the current sensor reading. Chemotaxis steers along the locally estimated concentration gradient, which is effective in laminar plumes but degrades severely in turbulence. Anemotaxis exploits a measured wind direction by surging upwind when chemical contact is made. The bio-inspired cast-and-surge family combines anemotaxis with a deterministic crosswind cast on contact loss, and is the dominant reactive approach for turbulent environments. === Probabilistic and information-theoretic strategies === Probabilistic methods maintain a posterior distribution over possible source locations and choose actions that improve that distribution. The infotaxis strategy of Vergassola, Villermaux and Shraiman selects the move that maximizes the expected reduction in entropy of the source-location posterior, and is effective in regimes where the spatial gradient is unusable. Bayesian source-term estimation extends this idea by inferring both source position and release rate, typically using particle filters or sequential Monte Carlo. === Map-based strategies === Map-based methods build a spatial model of the time-averaged gas distribution from sensor readings collected along the robot's trajectory and search for local maxima in that model. Lilienthal and colleagues describe a family of kernel-based gas distribution mapping techniques in which point measurements are convolved with a Gaussian kernel to produce a spatially extrapolated estimate. Such methods are most useful when the source can be assumed quasi-stationary and the robot is able to revisit locations. === Multi-robot and swarm strategies === Multiple robots searching cooperatively can shorten search times. Cooperative formations spread the sensors across the crosswind axis, making detection of an intermittent plume more likely. Swarm-based approaches, reviewed by Wang and colleagues, deploy larger numbers of simpler agents and rely on collective behavior rather than centralized planning; reported advantages include improved coverage of the search area and the possibility of locating multiple sources in parallel. == Sensors and platforms == Most OSL systems use metal-oxide semiconductor (MOX) sensors, photoionization detectors or electrochemical cells, which trade off sensitivity, selectivity, response time and power consumption. Ishida and colleagues describe how these sensors interact with airflow around the robot body, an effect that motivates careful aerodynamic design and active sampling. Mobile platforms include wheeled ground robots for indoor and structured outdoor environments, multi-rotor unmanned aerial vehicles for open spaces and elevated sources, and autonomous underwater vehicles for chemical plumes in the marine environment. == Notable systems == Among the early demonstrations, R. A. Russell's series of differential-drive robots at Monash University localized volatile sources in still and ventilated rooms during the 1990s. The Smelling Nano Aerial Vehicle reported by Burgués and colleagues used a Crazyflie nano-quadcopter (approximately 27 grams in mass and 10 cm across) carrying a custom MOX gas sensing board, and built three-dimensional gas distribution maps of indoor releases from sweeping flights of less than three minutes. The GADEN simulator, released by Monroy and colleagues, couples three-dimensional dispersion computed from an OpenFOAM CFD solver with models of MOX and photo-ionization gas sensors, and is widely used to test mobile-robot olfaction algorithms in simulation. == Applications == Reported applications include the localization of natural-gas and methane leaks in urban infrastructure, search for chemical contamination after industrial accidents, search and rescue, and environmental monitoring of industrial emissions. Drug- and explosives-detection robots are an adjacent application area, although these typically rely on close-range sniffing rather than long-range plume tracking. == Open challenges == Open challenges identified in recent reviews include the limited speed, selectivity and stability of available chemical sensors; the scarcity of standardized, large-scale benchmarks comparable to those available in computer vision; reliable handling of multi-source environments, where standard single-source assumptions fail; and the integration of OSL with other autonomous-vehicle subsystems such as obstacle avoidance and navigation in three-dimensional turbulent flow.

Gapo

Gapo is a Vietnamese social networking service based in Hanoi, Vietnam. Users are able to create a personal profile and share text, photos and videos with others on the platform. Users can also use Gapo for live streaming, instant messaging, blogging, and online payments. Gapo was launched in July 2019 by Hà Trung Kiên and Duong Vi Khoa. == History == Gapo was founded in response to calls for Vietnam's Communist-led government to produce a domestic alternative to social media giants like Facebook and Google. Gapo officially launched on July 23, 2019 at an event in Hanoi. The company received 500 billion đồng (US$22 million) in funding from technology corporation G-Group to be utilized in the first phase of development. They also partnered with Sony Music Entertainment to provide music content to its services. == Features == Gapo features a news feed for posting content, livestreaming, instant messaging, and blogging. It also allows users to pay online and access public services. == Reception == Within two days of launch, Gapo received about 200,000 registrations. By September 2019, the user base increased to one million. Upon launch, Gapo experienced significant technical difficulties. Users complained about the inability to sign up for a new account and said that certain functions were not available for use at launch. This issue caused Gapo to temporarily suspend their services in order to perform upgrades and bug fixes. Gapo relaunched the next day, though many users reported that the access speed decreased. The mobile app also received mixed reviews from users in both the App Store and the Google Play Store, with an average rating of 3.1 and 3.5, respectively. Most users found the app to be a knockoff of Facebook, although some users praised the app for being locally developed. === Expert opinions on platform viability === Le Hong Hiep of the ISEAS - Yusof Ishak Institute was doubtful that a Vietnamese-owned social network service could be as powerful as a foreign-based service, stating that Vietnam might not be able to develop a viable social media network to compete with the likes of Facebook or Google. Others, like blogger Ann Chi, said that, due to local players complying with local censorship policy, there is a chance that locals might not trust Gapo and other local services in light of possible surveillance. Regarding the targeted user base figure for the end of 2019 and 2021, experts cautioned that the company might need an additional trillion đồng of funding to reach its planned user base targets. In response, the company stated that Gapo was never meant to compete with Facebook, but instead noted that the main difference between Gapo and Facebook is that Gapo provides a personalized user experience through customization. == Censorship == Gapo has the right to censor posts and news that are deemed offensive and inaccurate by users or not approved by the censorship curators.

Apache ORC

Apache ORC (Optimized Row Columnar) is a free and open-source column-oriented data storage format. It is similar to the other columnar-storage file formats available in the Hadoop ecosystem such as RCFile and Parquet. It is used by most of the data processing frameworks Apache Spark, Apache Hive, Apache Flink, and Apache Hadoop. In February 2013, the Optimized Row Columnar (ORC) file format was announced by Hortonworks in collaboration with Facebook. A calendar month later, the Apache Parquet format was announced, developed by Cloudera and Twitter. Apache ORC format is widely supported including Amazon Web Services' Glue,Google Cloud Platform's BigQuery, and Pandas (software). == History ==

Plotting algorithms for the Mandelbrot set

There are many programs and algorithms used to plot the Mandelbrot set and other fractals, some of which are described in fractal-generating software. These programs use a variety of algorithms to determine the color of individual pixels efficiently. == Escape time algorithm == The simplest algorithm for generating a representation of the Mandelbrot set is known as the "escape time" algorithm. A repeating calculation is performed for each x, y point in the plot area and based on the behavior of that calculation, a color is chosen for that pixel. === Unoptimized naïve escape time algorithm === In both the unoptimized and optimized escape time algorithms, the x and y locations of each point are used as starting values in a repeating, or iterating calculation (described in detail below). The result of each iteration is used as the starting values for the next. The values are checked during each iteration to see whether they have reached a critical "escape" condition, or "bailout". If that condition is reached, the calculation is stopped, the pixel is drawn, and the next x, y point is examined. For some starting values, escape occurs quickly, after only a small number of iterations. For starting values very close to but not in the set, it may take hundreds or thousands of iterations to escape. For values within the Mandelbrot set, escape will never occur. The programmer or user must choose how many iterations–or how much "depth"–they wish to examine. The higher the maximal number of iterations, the more detail and subtlety emerge in the final image, but the longer time it will take to calculate the fractal image. Escape conditions can be simple or complex. Because no complex number with a real or imaginary part greater than 2 can be part of the set, a common bailout is to escape when either coefficient exceeds 2. A more computationally complex method that detects escapes sooner, is to compute distance from the origin using the Pythagorean theorem, i.e., to determine the absolute value, or modulus, of the complex number. If this value exceeds 2, or equivalently, when the sum of the squares of the real and imaginary parts exceed 4, the point has reached escape. More computationally intensive rendering variations include the Buddhabrot method, which finds escaping points and plots their iterated coordinates. The color of each point represents how quickly the values reached the escape point. Often black is used to show values that fail to escape before the iteration limit, and gradually brighter colors are used for points that escape. This gives a visual representation of how many cycles were required before reaching the escape condition. To render such an image, the region of the complex plane we are considering is subdivided into a certain number of pixels. To color any such pixel, let c {\displaystyle c} be the midpoint of that pixel. We now iterate the critical point 0 under P c {\displaystyle P_{c}} , checking at each step whether the orbit point has modulus larger than 2. When this is the case, we know that c {\displaystyle c} does not belong to the Mandelbrot set, and we color our pixel according to the number of iterations used to find out. Otherwise, we keep iterating up to a fixed number of steps, after which we decide that our parameter is "probably" in the Mandelbrot set, or at least very close to it, and color the pixel black. In pseudocode, this algorithm would look as follows. The algorithm does not use complex numbers and manually simulates complex-number operations using two real numbers, for those who do not have a complex data type. The program may be simplified if the programming language includes complex-data-type operations. for each pixel (Px, Py) on the screen do x0 := scaled x coordinate of pixel (scaled to lie in the Mandelbrot X scale (-2.00, 0.47)) y0 := scaled y coordinate of pixel (scaled to lie in the Mandelbrot Y scale (-1.12, 1.12)) x := 0.0 y := 0.0 iteration := 0 max_iteration := 1000 while (xx + yy ≤ 22 AND iteration < max_iteration) do xtemp := xx - yy + x0 y := 2xy + y0 x := xtemp iteration := iteration + 1 color := palette[iteration] plot(Px, Py, color) Here, relating the pseudocode to c {\displaystyle c} , z {\displaystyle z} and P c {\displaystyle P_{c}} : z = x + i y {\displaystyle z=x+iy\ } z 2 = x 2 + 2 i x y {\displaystyle z^{2}=x^{2}+2ixy} - y 2 {\displaystyle y^{2}\ } c = x 0 + i y 0 {\displaystyle c=x_{0}+iy_{0}\ } and so, as can be seen in the pseudocode in the computation of x and y: x = R e ⁡ ( z 2 + c ) = x 2 − y 2 + x 0 {\displaystyle x=\mathop {\mathrm {Re} } (z^{2}+c)=x^{2}-y^{2}+x_{0}} and y = I m ⁡ ( z 2 + c ) = 2 x y + y 0 . {\displaystyle y=\mathop {\mathrm {Im} } (z^{2}+c)=2xy+y_{0}.\ } To get colorful images of the set, the assignment of a color to each value of the number of executed iterations can be made using one of a variety of functions (linear, exponential, etc.). One practical way, without slowing down calculations, is to use the number of executed iterations as an entry to a palette initialized at startup. If the color table has, for instance, 500 entries, then the color selection is n mod 500, where n is the number of iterations. === Optimized escape time algorithms === The code in the previous section uses an unoptimized inner while loop for clarity. In the unoptimized version, one must perform five multiplications per iteration. To reduce the number of multiplications the following code for the inner while loop may be used instead: x2:= 0 y2:= 0 w:= 0 while (x2 + y2 ≤ 4 and iteration < max_iteration) do x:= x2 - y2 + x0 y:= w - x2 - y2 + y0 x2:= x x y2:= y y w:= (x + y) (x + y) iteration:= iteration + 1 The above code works via some algebraic simplification of the complex multiplication: ( i y + x ) 2 = − y 2 + 2 i y x + x 2 = x 2 − y 2 + 2 i y x {\displaystyle {\begin{aligned}(iy+x)^{2}&=-y^{2}+2iyx+x^{2}\\&=x^{2}-y^{2}+2iyx\end{aligned}}} Using the above identity, the number of multiplications can be reduced to three instead of five. The above inner while loop can be further optimized by expanding w to w = x 2 + 2 x y + y 2 {\displaystyle w=x^{2}+2xy+y^{2}} Substituting w into y = w − x 2 − y 2 + y 0 {\displaystyle y=w-x^{2}-y^{2}+y_{0}} yields y = 2 x y + y 0 {\displaystyle y=2xy+y_{0}} and hence calculating w is no longer needed. The further optimized pseudocode for the above is: x:= 0 y:= 0 x2:= 0 y2:= 0 while (x2 + y2 ≤ 4 and iteration < max_iteration) do x2:= x x y2:= y y y:= 2 x y + y0 x:= x2 - y2 + x0 iteration:= iteration + 1 Note that in the above pseudocode, 2 x y {\displaystyle 2xy} seems to increase the number of multiplications by 1, but since 2 is the multiplier the code can be optimized via ( x + x ) y {\displaystyle (x+x)y} . == Coloring algorithms == In addition to plotting the set, a variety of algorithms have been developed to efficiently color the set in an aesthetically pleasing way show structures of the data (scientific visualisation) === Histogram coloring === A more complex coloring method involves using a histogram which pairs each pixel with said pixel's maximum iteration count before escape/bailout. This method will equally distribute colors to the same overall area, and, importantly, is independent of the maximum number of iterations chosen. This algorithm has four passes. The first pass involves calculating the iteration counts associated with each pixel (but without any pixels being plotted). These are stored in an array IterationCounts[x][y], where x and y are the x and y coordinates of said pixel on the screen respectively. The first step of the second pass is to create an array NumIterationsPerPixel[n], where the array size n is the maximum iteration count. Next, one must iterate over the array of pixel-iteration count pairs IterationCounts[x][y], and retrieve each pixel's saved iteration count, i, via e.g. i = IterationCounts[x][y]. After each pixel's iteration count i is retrieved, it is necessary to index the NumIterationsPerPixel array at i and increment the indexed value (which is initially zero) -- e.g. NumIterationsPerPixel[i] = NumIterationsPerPixel[i] + 1. for (x = 0; x < width; x++) do for (y = 0; y < height; y++) do i:= IterationCounts[x][y] NumIterationsPerPixel[i]++ The third pass iterates through the NumIterationsPerPixel array and adds up all the stored values, saving them in total. The array index represents the number of pixels that reached that iteration count before bailout. total: = 0 for (i = 0; i < max_iterations; i++) do total += NumIterationsPerPixel[i] After this, the fourth pass begins and all the values in the IterationCounts array are indexed, and, for each iteration count i, associated with each pixel, the count is added to a global sum of all the iteration counts from 1 to i in the NumIterationsPerPixel array . This value is then normalized by dividing the sum by the total value computed earlier. hue[][]:= 0.0 for (x = 0; x < width; x++) do for (y = 0; y < height; y++) do iteration:= Iteration