Abstract: Specifying defective pixels can be done with higher precision. With the imaging apparatus 1, defective pixels are specified after NUC process with respect to initial good pixels, as well as correction with respect to initial defective pixels, has been done, and therefore it is possible to specify defective pixels with higher precision as compared with the case where defective pixels are specified without carrying out the NUC process and correction with respect to initial defective pixels. In addition, captured-image data acquired by defective pixels other than the initial defective pixels can be corrected in the controlling means 40, because pixels in which defect other than the initial defect is caused can be specified by specifying defective pixels after corrected captured-image data has been generated in a manner such that captured-image data which is acquired by the image capturing unit 10 is corrected on the basis of information for specifying an initial defective pixel.

Abstract: An image pickup apparatus having an image pickup element with a plurality of image pickup pixels and a plurality of focus detection pixels, a focus detector performing a focus detection based on the output from the focus detection pixels corresponding to a focus detection area, and a setter configured to set a usable F-number based on stored information of a defective pixel that exists in the focus detection pixels. When the defective pixel exists in the focus detection pixels corresponding to the focus detection area, if an F-number is within the usable F-number, the focus detector performs focus detection by using the output from the defective pixel, and if the F-number is out of the usable F-number, the focus detector performs focus detection without using such output.

Abstract: An image sensing apparatus comprises: an output unit which includes an output line group, a plurality of difference circuits, a first dummy line, and a second dummy line, and wherein the output line group is interposed between the first dummy line and the second dummy line, a readout unit includes a plurality of memory circuits, each of the plurality of memory circuits includes a first holding capacitance and a second holding capacitance, a gain determined by a ratio of a capacitance value of the first holding capacitance and a capacitance value of a first output line is applied to the first signal output to the first output line, and a gain determined by a ratio of a capacitance value of the second holding capacitance and a capacitance value of a second output line is applied to the second signal output to the second output line.

Abstract: A dust detection system, comprising a receiver, a dust extraction block, a memory and an image correction block, is provided. The receiver receives an image signal. The dust extraction block generates a dust image signal on the basis of the image signal. The memory stores an intrinsic-flaw image signal corresponding to an intrinsic-flaw image including sub-images of dust that the dust extraction block extracts in initializing. The image correction block generates a corrected dust-image signal on the basis of the intrinsic-flaw image signal and a normal dust-image signal. The normal dust-image signal corresponds to a normal dust image including sub-image of dust that the dust extraction block extracts after initializing. The corrected dust image is the normal dust image that sub-images of dust in the intrinsic-flaw image are deleted from.

Abstract: An image pickup apparatus includes: an image pickup device that outputs pixel signals picked up by a plurality of pixels arranged in a two-dimensional manner for picking up an image of an object; a white spot positional information storage portion that stores positional information of a white-spot pixel that exists in the image pickup device; an image pickup device drive portion; and a white spot correction portion that, based on positional information of the white-spot pixel that is read out from the white spot positional information storage portion, performs correction with respect to the pixel signal of the pixel that is determined to be the white-spot pixel based on a white spot correction value calculated based on seven pixels that surround a pixel that is determined to be the white-spot pixel.

Abstract: An image pickup apparatus includes an image pickup element 10 that includes unit cells capable of individually reading signals from pixels that receive light beams transmitting through different pupil positions of an image pickup lens 5, a detector 20 that generates a pair of image signals in a pupil division direction using a signal from a pixel corresponding to each of the unit cells to perform focus detection based on a phase difference, a defective pixel storage unit 22 that stores defective pixel information, and a defective pixel compensating unit 20 that compensates a signal of a defective pixel based on an output of the defective pixel storage unit. The defective pixel compensating unit 20 compensates the signal of the defective pixel using a signal obtained from a pixel disposed in a direction different from the pupil division direction with respect to the defective pixel.

Abstract: An adaptive image processing method includes: defining a pixel zone involving a target pixel according to a color corresponding to the target pixel; selecting a plurality of adjacent pixels from the pixel zone, wherein the adjacent pixels and the target pixel correspond to the same color; acquiring a defect pixel threshold value by calculating a product of a sum of absolute differences between each pixel of the plurality of adjacent pixels and a defected pixel compensation ratio; acquiring an adjacent difference value by calculating a sum of absolute differences between the target pixel and each pixel of the plurality of adjacent pixels; and determining whether the target pixel is a defect pixel by comparing the defect pixel threshold value with the adjacent difference value.

Abstract: An image processing method includes: acquiring a mosaic image photographed by image pickup means including an image pickup element in which a basic array pattern is repeatedly arranged in horizontal and vertical directions, storing first correction data containing a coordinate of a defective pixel and correction information associated with a position of the defective pixel in the basic array pattern, and second correction data containing a correction pattern corresponding to the correction information and indicating positions, relative to the defective pixel, of plural peripheral pixels that have a same color as the defective pixel, reading the correction pattern based on the correction information, calculating coordinates of the peripheral pixels based on the first correction data and the read correction pattern, extracting pixel values corresponding to the peripheral pixels at the calculated coordinates from the mosaic image, and calculating the pixel value of the defective pixel.

Abstract: A method of processing image signals comprises determining whether each of multiple units of input pixel data received from an image sensor is bad pixel data generated by a bad pixel of the image sensor or normal pixel data generated by a normal pixel of the image sensor, and performing interpolation to generate image data corresponding to the bad pixel using only normal pixel data and omitting bad pixel data.

Abstract: Among defective pixels of an image sensor, defective pixels which need to be corrected are determined depending on the type and defect level for individual defective pixels and on image capturing conditions. Depending on the types of the defective pixels, the correspondences between the image capturing conditions and the defect levels of the defective pixels to be corrected are prepared in advance, thereby carrying out appropriate defective pixel correction in view of the fact that the dependence of the abnormal signal output level on the image capturing conditions differs depending on the type of defective pixel.

Abstract: There is provided a denoising method of an image system that detects a brightness variation cycle of ambient light sources, records a brightness variation of at least one noise area within the brightness variation cycle and compensates the brightness variation from current images thereby removing interference from the ambient light sources. There is further provided an image system.

Abstract: A method and apparatus that allows for the correction of multiple defective pixels in an imager device. In one exemplary embodiment, the method includes the steps of selecting a correction kernel for a defective pixel, determining average and difference values for pixel pairs in the correction kernel, and substituting an average value from a pixel pair for the value of the defective pixel.

Abstract: According to certain embodiments, alpha image data of an alpha frame corresponding to an alpha portion of a scene is accessed. Beta image data of a beta frame corresponding to a beta portion of the scene is accessed. The alpha frame and the beta frame have an overlapping region. Alpha-beta pairs are generated for the overlapping region. Each alpha-beta pair comprises an alpha value of the alpha image data and a beta value of the beta image data that both correspond to the same portion of the scene. A function is applied to each alpha-beta pair to determine first frame image data for the overlapping region. The first frame image data comprises information to generate a first frame of the scene.

Abstract: An apparatus includes an image sensor, a detection unit, and a control unit. The image sensor photoelectrically converts an incident light from an object. The detection unit detects a defective pixel of the image sensor based on an image signal generated by the image sensor. The control unit controls, when a first defective pixel for irregularly outputting an abnormal level and a second defective pixel for regularly outputting an abnormal level in the image sensor are detected, storage time of the image sensor at the detection time of the first defective pixel to be longer than storage time of the image sensor at detection time of the second defective pixel and a number of image signals used for detection to be larger.

Abstract: An imaging device includes an imaging unit having an imaging element to conduct photoelectric conversion on incident light from a subject and output an electric signal, a signal gain control unit for controlling an output signal level of the imaging unit, a plurality of defective pixel correction units for correcting defective pixels contained in a signal output from the signal gain control unit, an image signal processing unit for generating an image signal from a signal which is output from the defective pixel correction units, a temperature measurement unit for measuring temperature in the vicinity of the imaging element, and a system control unit for generally controlling the imaging unit, the signal gain control unit, the correction units, and the image signal processing unit. The system control unit uses the plurality of defective pixel correction units jointly and causes them to operate according to occurrence causes of defective pixels.

Abstract: Provided are an apparatus and method for executing sensitivity difference correction processing of an image signal, which is generated by a single plate-type image sensor through a color filter. The sensitivity difference correction is executed for Gr and Gb signals included the image signal, for example, an RGB signal, which is generated by the single plate-type image sensor through the color filter. A pixel value of a color filter unit which has the same color as a correction target pixel and is present in surroundings of the correction target pixel is acquired. An additional value is calculated by adding a difference between weighted mean pixel values “a” and “b” of two kinds of pixel groups “A” and “B” classified according to positions of pixels to the pixel value of the correction target pixel in which the weighted mean values correspond to distances of the pixel groups from the correction target pixel.

Abstract: A digital image captured by a digital camera module is scaled to a smaller size, and separately horizontal direction filtered and vertical direction filtered using one-dimensional spatial filters. The horizontal direction filtered image and the vertical direction filtered image are combined, wherein edge regions and corner regions of the combined filtered image are created differently than its middle region. The combined filtered image is then thresholded selected pixels of the thresholded image are marked as a blemish region. Other embodiments are also described and claimed.

Abstract: An information processing apparatus that causes display of anomalous pixels of images includes acquisition means for acquiring positions of anomalous pixels in a captured image using a plurality of acquisition schemes for acquiring anomalous pixels; and display control means for causing a display unit to display an image showing the positions of anomalous pixels obtained by the acquisition means so that the relative position between the anomalous pixels in the captured image is maintained and that the display format for each of the positions of anomalous pixels is changed in accordance with the acquisition schemes.

Abstract: A pedestal level compensation method includes calculating a dark level difference error depending on temperature, calculating a pedestal level offset depending on an analog gain, and compensating a pedestal level according to the dark level difference error and the pedestal level offset.

Abstract: A method for assisting users with channel entry utilizes channel tuning history to simplify the channel entry process. According to an exemplary embodiment, the method includes steps of storing a list of channel numbers previously tuned by the apparatus; receiving a first input selecting a most significant digit of a channel number; and enabling a display of channel numbers in response to the first input, wherein the displayed channel numbers comprise at least one channel number included in the stored list and having the most significant digit and at least one other channel number not included in the stored list and having the most significant digit.

Abstract: An image reading apparatus includes a sheet feeding unit configured to sequentially feed documents loaded on a document positioning plate, a reading sensor configured to read a document of the plurality of documents fed by the sheet feeding unit, an acquisition unit to acquire an interval of the document between a trailing edge of a preceding document and a leading edge of a next document conveyed through the conveyance path, and a reading unit to execute a first reading mode using the reading sensor to read the document conveyed at a first conveyance speed, and a second reading mode using the reading sensor to read the document conveyed at a second conveyance speed that is lower than the first conveyance speed, wherein the reading unit executes the second reading mode after the first reading mode when the interval of the document is less than a predetermined interval.

Abstract: Among defective pixels of an image sensor, defective pixels which need to be corrected are determined depending on the type and defect level for individual defective pixels and on image capturing conditions. Depending on the types of the defective pixels, the correspondences between the image capturing conditions and the defect levels of the defective pixels to be corrected are prepared in advance, thereby carrying out appropriate defective pixel correction in view of the fact that the dependence of the abnormal signal output level on the image capturing conditions differs depending on the type of defective pixel.

Abstract: An image blemish detecting system includes an image capturing module, a brightness adjusting module, and a blemish detecting module. The image capturing module captures an image. The brightness adjusting module adjusts the brightness of the image to obtain a second image having substantially uniform brightness. The blemish detecting module calculates a brightness ratio of each pixel in the second image, marks the pixels of which the brightness ratios are not smaller than a predetermined reference value as “1”, and marks the other pixels as “0”. The blemish detecting module calculates the quantity of the pixels in a continuous area in which all pixels are marked as “1”, and determines that the continuous area is a blemish if the quantity of the pixels in the continuous area is greater than or equal to the predetermined pixel quantity.

Abstract: An image processing apparatus comprises: a storage unit storing a first group of defective pixel data including positional information on a defective pixel of an image sensor and information on a type of defect; a detection unit which detects a defective pixel of the image sensor and generates a second group of defective pixel data; a combining unit which combines the first and second groups to generate a third group; and a correction unit which corrects an image signal output from a defective pixel of the image sensor using the third group, wherein the combining unit assigns a priority level corresponding to the type of defect to each piece of defective pixel data, and if there are multiple pieces of defective pixel data including common positional information, leaves the defective pixel data in the order of priority level, the highest the first and the lowest the last.

Abstract: An image processing apparatus includes: a holding section holding a pixel value input thereto; a basic pixel value calculating section calculating a basic pixel value from the pixel values of a plurality of pixels which are neighboring pixels located around a pixel of interest having the pixel value held by the holding section and which have the same color as the pixel of interest; a different color pixel difference calculating section calculating a different color pixel difference which is a difference between the pixel values of neighboring pixels having a color different from the color of the pixel of interest; a combining section combining the basic pixel value and the different color pixel difference to calculate an estimated pixel value of the pixel of interest; and a correcting section correcting the pixel value of the pixel of interest to the estimated value.

Abstract: An image processing apparatus that processes image data output from an image sensing device including a plurality of pixels, comprises: a storage unit that stores defect data at least including first information showing grades of defective pixels that are subject to correction and, with respect to each defective pixel among the plurality of pixels, address information, second information showing a grade of the defective pixel; an acquisition unit that acquires an imaging condition and an imaging environment at a time of image sensing; a determination unit that compares the first information and the second information, and determines whether defect correction of each defective pixel is necessary or not based on a comparison result; and a correction unit that performs the defect correction on image data output from a defective pixel for which the determination unit determines that defect correction is necessary.

Abstract: A solid-state imaging device according to an embodiment includes: a first optical system configured to form an image of an object on an image formation plane; an imaging element comprising an imaging area which includes a plurality of pixel blocks each including a plurality of pixels; a second optical system configured to include a microlens array including a plurality of microlenses provided to correspond to the plurality of pixel blocks and reduce and re-form an image scheduled to be formed on the image formation plane, in a pixel block corresponding to an individual microlens; and a signal processing unit configured to perform image signal processing with an optical position relation between each microlens and the pixel block corrected, by using an image signal of the object obtained by the imaging element.

Abstract: An electronic device includes a memory configured to receive data representing light intensity values from pixels in a focal plane array and a processor that analyzes the received data to determine which light values correspond to triggered pixels, where the triggered pixels are those pixels that meet a predefined set of criteria, and determines, for each triggered pixel, a set of neighbor pixels for which light intensity values are to be stored. The electronic device also includes a buffer that temporarily stores light intensity values for at least one previously processed row of pixels, so that when a triggered pixel is identified in a current row, light intensity values for the neighbor pixels in the previously processed row and for the triggered pixel are persistently stored, as well as a data transmitter that transmits the persistently stored light intensity values for the triggered and neighbor pixels to a data receiver.

Abstract: A method of pixel correction is disclosed. The method generally includes the steps of (A) generating a plurality of pixel values from a sensor in response to an optical signal, (B) generating a temperature signal representing a temperature of the sensor and (C) generating a plurality of corrected values by applying a per-pixel correction model to the pixel values, wherein the per-pixel correction model is responsive to the temperature.

Abstract: An image processing apparatus includes a first defect interpolation unit that interpolates a defective pixel using a pixel value of a first pixel near a specific first pixel or a pixel value of a second pixel near a specific second pixel, a second defect interpolation unit that interpolates the defective pixel using a rate of pixel values of a first pixel and a second pixel in the same micro lens near the specific first pixel and the specific second pixel, an in-focus level evaluation unit that evaluates an in-focus level using outputs of the first and second pixels, a synthesis rate switching unit that switches a synthesis rate of outputs of the first and second defect interpolation units, and a signal processing unit that generates a shot image using an output of the synthesis rate switching unit.

Abstract: A solid-state imaging device includes: a normal pixel disposed in a pixel section capable of performing a global shutter, and including at least a photoelectric conversion part and a memory part adjacent to the photoelectric conversion part; and a leak-light correcting pixel disposed in the pixel section to correct degradation of an image quality originated from leak light leaked into the memory part.

Abstract: A solid-state imaging device includes: an imaging unit; a row selection circuit; a column circuit unit; and a control unit configured to supply a row address signal which designates a pixel row to be selected to the row selection circuit, in which the imaging unit includes: a valid part including first pixels; and a peripheral part including second pixels, and the control unit includes an output adjustment unit which adjusts an output order of row address signals, the output adjustment unit adjusts the output order of the row address signals so that orders and combinations of the numbers of rows to be outputted per unit row are equal to each other in a first row selection sequence and in a second row selection sequence, and generate the first and second row selection sequences, and the control unit supplies the first and second row selection sequences to the row selection circuit.

Abstract: An image processing apparatus that processes image data output from an image sensing device including a plurality of pixels, comprises: a storage unit that stores defect data at least including first information showing grades of defective pixels that are subject to correction and, with respect to each defective pixel among the plurality of pixels, address information, second information showing a grade of the defective pixel; an acquisition unit that acquires an imaging condition and an imaging environment at a time of image sensing; a determination unit that compares the first information and the second information, and determines whether defect correction of each defective pixel is necessary or not based on a comparison result; and a correction unit that performs the defect correction on image data output from a defective pixel for which the determination unit determines that defect correction is necessary.

Abstract: A method of processing image signals comprises determining whether each of multiple units of input pixel data received from an image sensor is bad pixel data generated by a bad pixel of the image sensor or normal pixel data generated by a normal pixel of the image sensor, and performing interpolation to generate image data corresponding to the bad pixel using only normal pixel data and omitting bad pixel data.

Abstract: An imaging apparatus detects and registers fixed-noise pixels as those pixels of the image sensor which produce fixed pattern noise, and includes an optical element which disperses light that is incident on the image sensor. The detection is performed by identifying isolated high-luminance pixels within captured images and, for each isolated high-luminance pixel, evaluating the luminance values of peripherally adjacent pixels. A judgement is made as to whether an isolated high-luminance pixel is a fixed-noise pixel based upon comparing luminance values of the peripherally adjacent pixels with a predetermined threshold value, the judgement preferably being performed only while images are captured during hours of darkness.

Abstract: An image processing apparatus for processing image signals output from an image sensor having a plurality of unit cells each including a plurality of photoelectric conversion elements for receiving light passing through different pupil regions and each of which can be read out separately, wherein: a detection unit detects a phase difference between a plurality of images each formed on the basis of image signals of photoelectric conversion elements located in a same position in each of the plurality of unit cells; a determination unit determines a defective photoelectric conversion element; and a correction unit corrects a defective image signal of a defective photoelectric conversion element using an image signal corresponding to the defective image signal and constituting another of the plurality of images that does not include the defective image signal, based on the phase difference detected by the detection unit.

Abstract: An image sensing apparatus includes an image sensing unit having an image sensor, an optical member which is arranged in front of the image sensor, a foreign substance detection unit which detects, from a foreign substance detection image including the image of a foreign substance adhered to the surface of the optical member, a recording unit which, when shooting a moving image, records moving image data generated based on image signals successively output from the image sensing unit, and records foreign substance information and lens information in addition to the moving image data, and a lens information obtaining unit which, when the lens information is updated by operating the imaging lens by a user during moving image shooting, obtains the updated lens information. When the lens information obtaining unit obtains the updated lens information, the recording unit records the updated lens information in addition to the moving image data.

Abstract: A method, apparatus and system that allows for the identification of defective pixels, for example, defective pixel clusters, in an imager device. The method, apparatus and system determine, during use of the imager device, that a pixel defect, e.g., cluster defect, exists and accurately maps the location of the defective pixel. By analyzing more than one frame of an image, the method increases the accuracy of the defect mapping, which is used to improve the quality of the resulting image data.

Abstract: A spectral anomaly detection method includes the steps of segmenting a panchromatic image, obtained from a hyperspectral sensor into cluster data sets. Principal component analysis can be separately performed on each of the cluster data sets to produce a plot of principal components. An anomaly detection algorithm can be applied to an adaptively selected subset of principal components for each of the cluster data sets to produce cluster detection scores. Finally, separate detection thresholding algorithms can be applied to each of the cluster detection scores, and the results of the detection thresholding algorithms can be combined into a single detection plane.

Abstract: A method for monitoring inactive pixels in a scene imaging system may include determining a location of at least one inactive pixel in a focal plane array. The method may include sensing an environment image based upon a surrounding environment of an aircraft. The method may include generating an image associated with the environment image. The method may include evaluating a location for one or more inactive pixels in the generated image in comparison to a location for the at least one inactive pixel in the focal plane array. The method may include determining whether a fault exists in image generation or image display based upon the evaluation.

Abstract: A defect pixel detection apparatus includes an image sensor which includes an effective pixel configured to have a photoelectric conversion element and an output unit configured to output a pixel signal generated by the photoelectric conversion element, a first reference pixel configured to have the same pixel configuration as the effective pixel and be optically shielded, and a second reference pixel configured to have a pixel configuration different from that of the effective pixel, a defect level acquiring unit configured to acquire a defect level of a target pixel in the image sensor, and a defect pixel determination unit configured to determine whether the target pixel is a defect pixel by comparing a defect level of the target pixel with a defect detection threshold according to a type of the pixel.

Abstract: A camera has a focus detection sensor that includes a plurality of first focus detection pixels and a plurality of second focus detection pixels, and that has a plurality of focus detection pixel pairs each including a first focus detection pixel and a second focus detection pixel, and stores defect information indicating a defective pixel. The camera corrects a value of the defective pixel and a value of one of the first focus detection pixel and the second focus detection pixel that forms the focus detection pixel pair with the defective pixel based on a value of a focus detection pixel of the same type that is not the defective pixel. The camera detects focusing status based on a phase difference between a first focus detection image obtained from the first focus detection pixels and a second focus detection image obtained from the second focus detection pixels after the correction.

Abstract: A defective pixel correction apparatus includes a defect pattern acquisition unit configured to acquire, as a defect pattern, a pattern of positions of a plurality of defective pixels in a group of pixels used to correct a noted pixel, a pixel selection unit configured to select one or more pixels from among pixels other than the defective pixels in the group of pixels on the basis of the defect pattern, and a defective pixel correction unit configured to correct the noted defective pixel using the selected pixels.

Abstract: A first generation unit generates a RAW image reduced in the horizontal direction from a RAW image including pixels each having single-color signal information, by limiting the band of spatial frequencies in the horizontal direction and decreasing the number of pixels in the horizontal direction. The RAW image reduced in the horizontal direction is stored in a line memory. A second generation unit generates a reduced RAW image by decreasing, at least in the vertical direction, the number of pixels of the RAW image reduced in the horizontal direction. This makes it possible to generate a reduced RAW image using little memory capacity.

Abstract: A method of processing image signals comprises determining whether each of multiple units of input pixel data received from an image sensor is bad pixel data generated by a bad pixel of the image sensor or normal pixel data generated by a normal pixel of the image sensor, and performing interpolation to generate image data corresponding to the bad pixel using only normal pixel data and omitting bad pixel data.

Abstract: There is provided an image processing apparatus including a first storage unit for storing a first correction data for correcting a defective pixel signal outputted from a defective pixel of an image sensor, a detecting unit for detecting a defective pixel signal outputted from a defective pixel of the image sensor in accordance with a designation set by a user, a creating unit for creating a second correction data based on the defective pixel signal detected by the detecting unit, a determination unit for determining whether the second correction data is used with the first correction data, in accordance with a designation set by a user; and a correction unit for correcting a pixel signal output from the image sensor in accordance with a determination result of the determination unit.

Abstract: An automated RAW image processing method and system are disclosed. A RAW image and metadata related to the RAW image are obtained from a digital camera or other source. The RAW image and the related metadata are automatically processed using an Operating System service of a processing device to produce a resulting image in an absolute color space. The resulting image is then made available to an application program executing on the processing device through an application program interface with the Operating System service.

Abstract: An imaging apparatus includes: an imaging unit configured to image an image using an imaging device; an image obtaining unit configured to obtain a plurality of images equivalent to the time of dark, imaged by the imaging unit; a registering unit configured to register, with an image obtained by the image obtaining unit, the address and change amount of a pixel where the output value of the pixel changes so as to exceed a predetermined threshold; and a correcting unit configured to correct, when taking a pixel corresponding to an address registered by the registering unit as a processing object pixel, the pixel value of the processing object pixel based on comparison between difference of the output values of the processing object pixel and a peripheral pixel of the processing object pixel, and the change amount of the processing object pixel.

Abstract: An image processor which is capable of performing correction of defective pixels without degrading image quality when synthesizing a plurality of still images. When a plurality of image data items are synthesized, a first reference value which is smaller than a second reference value for use in determining whether or not to correct pixel data forming the image data is compared with a pixel value indicated by each of synthesized pixel data items forming the synthesized image data, and first correction processing is performed in which the synthesized pixel data of the synthesized image data is corrected according to a result of comparison.

Abstract: A shader can include a series of instructions, among which are horizontal instructions and vertical instructions. Executing such shader for rendering animation information may mean many redundant computations on millions of graphic data points. Thus, vertical instructions are separated out from horizontal instructions and executed in a vertical manner, thereby reducing rendering time and cache space used during the process. That is, a block of instructions is recursively subdivided until a number of instructions that are to be executed in a horizontal manner are approximately minimized in each sub-block. All of the identified vertical sub-blocks can process each data point individually and independently from other data points, thereby achieving various advantages, including, but not limited to, temporary processing, index processing, efficient caching and the like.