Abstract: A calibration system comprises control circuitry and waveform capture circuitry. The control circuitry selects a first calibration waveform for input to a digital predistortion circuit of a transmitter. The capture circuitry captures a first waveform output by the transmitter in response to the first calibration waveform. The control circuitry compares the first calibration waveform to the captured first waveform. The control circuitry selects a first one of a plurality of mapping circuit configurations based on the result of the comparison, wherein the mapping circuit is configured to map outputs of a plurality of delay circuits among inputs of a plurality of filter taps. The control circuitry stores the one of the mapping circuit configurations in nonvolatile memory associated with the transmitter.

Abstract: A position specifying section obtains an observation distance by specifying the position of an irradiated region from a picked-up image that is obtained from the image pickup of a subject on which the irradiated region is formed by auxiliary measurement light. An image processing section sets the amount of offset, which corresponds to a height of the irradiated region of a convex portion of the subject, for the observation distance, and generates an offset measurement marker on the basis of the offset distance that obtained by adding the amount of offset to the observation distance. A specific image in which the offset measurement marker is superimposed on the picked-up image is displayed on a display unit.

Abstract: Methods, techniques, apparatus, and algorithms are described for robustly measuring real-world distances using any mobile device equipped with an accelerometer and monocular camera. A general software implementation processes 2D video, precisely tracking points of interest across frames to estimate the unsealed trajectory of the device, which is used to correct the device's inertially derived trajectory. The visual and inertial trajectories are then aligned in scale space to estimate the physical distance travelled by the device and the true distance between the visually tracked points.

Abstract: An electronic device displays a field of view of a camera with a view of a three-dimensional space and updates the field of view based on changes detected by the camera. While a measurement-point-creation indicator is over a determined anchor point in the field of view, the device changes a visual appearance of the indicator to indicate that a measurement point will be added at the anchor point if a touch input meets first criteria. In response to a touch input that meets the first criteria, a measurement point is added at the anchor point if the indicator is over the anchor point, and at a location away from the anchor point if not. In response to movement of the camera changing the field of view, if the field of view does not include a feature to which measurement points can be added, the measurement-point-creation indicator ceases to be displayed.

Abstract: An ultrasonic diagnosis apparatus according to one embodiment includes an ultrasonic probe, an image generating processor, a monitor, a database, and a calibration information generation processor. The image generating processor generates an ultrasonic image, based on an echo signal obtained through the ultrasonic probe. The monitor displays the ultrasonic image. The database stores image data including the ultrasonic image displayed on a screen of the monitor. The calibration information generation processor generates calibration information including a conversion value for performing a predetermined measurement with respect to the ultrasonic image included in the image data, based on the database storing image data including the ultrasonic image displayed on a screen of the monitor, and a positional relationship between at least one scale mark existing in the image data and the ultrasonic image.

Abstract: A method for a terminal to measure an angle, includes: displaying a horizontal reference line, a measurement line, and an object being imaged by a camera on a display interface of the terminal, a plane determined by the measurement line and the horizontal reference line being parallel with the display interface, and the measurement line being relatively static with respect to the display interface; during a process in which the terminal is turned to cause, on the display interface, an edge of the object to be parallel with the measurement line, obtaining one or more angles between the measurement line and the horizontal reference line; and determining an angle obtained when the edge of the object is parallel with the measurement line as an angle between the object and a horizontal plane.

Abstract: Methods, systems, and computer readable media are disclosed for determining a pixel-to-length ratio between a number of pixels disposed over a predetermined length of a reference object within an image of a siding sample and the predetermined length of the reference object. A first and second distance between respective first and second pairs of points within the image corresponding to respective first and second length measurements of the siding sample are determined, as well as a first and second number of pixels disposed between the first and second pair of points, respectively. Furthermore, the method, system, and computer readable medium disclose determining the first length measurement based on the pixel-to-length ratio and the first number of pixels, determining the second length measurement based on the pixel-to-length ratio and the second number of pixels, and identifying a siding product associated with the first and second length measurements.

Abstract: The invention relates to an image capturing system with a camera unit for capturing images of the outside area of a motor vehicle, and with a protective element, wherein at least the camera unit and/or the protective element can be moved via a mechanism by means of a drive from at least a closed position (Ia) into at least an open position (IIa), wherein in the closed position (Ia) of the protective element at least one lens of the camera unit is located behind the protective element so as to be inaccessible from the outside, and in the open position (IIa) at least the lens of the camera unit is exposed for image capture by the protective element. It is essential to the invention that at least the deflecting element is arranged on the mechanism, the deflecting element serving to change the direction of force applied to the mechanism, thus allowing a compact installation space to be realized.

Abstract: A failsafe monitoring device for monitoring a spatial area comprises at least one image recording unit. A three-dimensional image of the spatial area is recorded and a representation of said three-dimensional image is displayed in order to configure the monitoring device. A configuration plane is defined using a plurality of spatial points which have been determined within the three-dimensional image. Subsequently, at least one variable geometry element is defined relative to the configuration plane. A data record which represents a transformation of the geometry element into the spatial area is generated and transferred to the monitoring device.

Abstract: An apparatus may include a motion sensing device, a communication interface; and a processor. The processor may receive a point of origin that corresponds to a spatial position of the apparatus. The processor may determine, responsive to detecting a user interface command and based on a plurality of values received from the motion sensing device, a spatial position of the apparatus relative to the point of origin, and to acquire an image of an object in a field of view of the apparatus. The processor may also determine a scale factor of the image based on at least the spatial position of the apparatus relative to the point of origin.

Abstract: The disclosure includes a system and method for distinguishing between items of similar appearance that vary in size. An image recognition application receives an image including a plurality of items, identifies each item in the image, generates a region of interest for each identified item in the image, determines a dimension of the region of interest for each identified item in pixels, determines a plurality of pixel-to-physical dimension ratios for each identified item, identifies a selected pixel-to-physical dimension ratio among the plurality of pixel-to-physical dimension ratios, and determines a stock keeping unit identifier of each identified item in the image based on the selected pixel-to-physical dimension ratio and the dimension of the region of interest for each identified item.

Abstract: A positioning method continuously determines the spatial position of an auxiliary measuring instrument having several auxiliary-point markings in a fixed, known spatial distribution relative to one another. Camera images of the auxiliary-point markings are continually recorded using a camera having a surface sensor that includes pixels, and read-out processes are continually performed by reading out the pixels with regard to a respective current exposure value. Image positions of the imaged auxiliary-point markings in the respective current camera image are determined, with which the current spatial position of the auxiliary measuring instrument is derived. Respective current areas of interest on the surface sensor are continually set using image positions determined in at least one previously recorded camera image.

Abstract: A timing system that includes a glyph associated with an object to be timed and at least one camera for capturing images of the glyph or associated object. A computer generates a virtual line, associates the virtual line with at least one of the images, and determines when the glyph or associated object intersects, crosses or has crossed the virtual line. A database records the identity of the glyph and the time that the glyph or associated object intersected or crossed the virtual line. The invention also relates to a related method for determining the time a glyph or object associated therewith passes a predetermined point or line.

Abstract: An image-based georeferencing system comprises an image receiver, an image identification processor, a reference feature determiner, and a feature locator. The image receiver is configured for receiving a first image for use in georeferencing. The image comprises digital image information. The system includes a communicative coupling to a georeferenced images database of images. The image identification processor is configured for identifying a second image from the georeferenced images database that correlates to the first image. The system includes a communicative coupling to a geographic location information system. The reference feature determiner is configured for determining a reference feature common to both the second image and the first image. The feature locator is configured for accessing the geographic information system to identify and obtain geographic location information related to the common reference feature.

Abstract: A road calibration system and a method for calibration of a road surveillance system are disclosed. Said road surveillance system is adapted to monitor a surveillance area of a road and comprises a plurality of vehicle surveillance means. Said plurality of vehicle surveillance means are adapted to measure a position of a vehicle passing said surveillance area and are synchronized with a global timing signal. The method comprises, in order to calibrate said plurality of vehicle surveillance means such that a position determination of said plurality of vehicle surveillance means is equal, passing a calibration vehicle with a plurality of predefined calibration markers through said surveillance area. During the passage each measurement means measures a position of an assigned calibration marker at a predetermined time and compares a measured distance between the positions of said calibration markers with a reference distance between the positions of said calibration markers.

Abstract: A method, system and reference target for estimating spectral data on a selected one of three spectral information types is disclosed. Spectral information types comprise illumination of a scene, spectral sensitivity of an imager imaging the scene and reflectance of a surface in the scene. The method comprises obtaining a ranking order for plural sensor responses produced by the imager, each sensor responses being produced from a reference target in the scene, obtaining, from an alternate source, data on the other two spectral information types, determining a set of constraints, the set including, for each sequential pair combination of sensor responses when taken in said ranking order, a constraint determined in dependence on the ranking and on the other two spectral information types for the respective sensor responses and, in dependence on the ranking order and on the set of constraints, determining said spectral data that optimally satisfies said constraints.

Abstract: A device for measuring three dimensional shape includes a first irradiation unit, a first grating control unit, a second irradiation unit, a second grating control unit, an imaging unit, and an image processing unit. After performance of a first imaging operation as imaging processing of a single operation among a multiplicity of imaging operations performed by irradiation of said first light pattern of multiply varied phases, a second imaging operation is performed as imaging processing of a single operation among a multiplicity of imaging operations performed by irradiation of said second light pattern of multiply varied phases. After completion of the first imaging operation and the second imaging operation, shifting or switching operation of the first grating and the second grating is performed simultaneously.

Abstract: Systems, methods, and other embodiments associated with producing spatially varying spectral response calibration data are described. One example method includes controlling a digital camera to capture characteristic data arrays from light sensors in the digital camera in response to the digital camera being exposed to light stimuli from a multi-spectral reference display. The data arrays will be acquired multiple times at multiple locations in multiple stimuli provided from the multi-spectral reference display. The method also includes controlling a calibration logic to manipulate characteristic data arrays to produce spatially varying spectral response calibration data as a function of using characteristic data arrays and known wavelengths of the light in light stimuli. The method may also include providing the spatially varying spectral response calibration data to a downstream consumer (e.g., correction process, quality control process), displaying the data, or storing the data.

Abstract: Methods, systems, and computer readable media are disclosed for determining a pixel-to-length ratio between a number of pixels disposed over a predetermined length of a reference object within an image of a siding sample and the predetermined length of the reference object. A first and second distance between respective first and second pairs of points within the image corresponding to respective first and second length measurements of the siding sample are determined, as well as a first and second number of pixels disposed between the first and second pair of points, respectively. Furthermore, the method, system, and computer readable medium disclose determining the first length measurement based on the pixel-to-length ratio and the first number of pixels, determining the second length measurement based on the pixel-to-length ratio and the second number of pixels, and identifying a siding product associated with the first and second length measurements.

Abstract: A volume determining method for an object on a construction site is disclosed. The method may include moving a mobile camera along a path around the object while orienting the camera repeatedly onto the object. The method may include capturing a series of images of the object from different points on the path and with different orientations with the camera, the series being represented by an image data set; performing a structure from motion evaluation with a defined algorithm using the series of images and generating a spatial representation; scaling the spatial representation with help of given information about a known absolute reference regarding scale; defining a ground surface for the object and applying it onto the spatial representation; and calculating and outputting the absolute volume of the object based on the scaled spatial representation and the defined ground surface.

Abstract: Embodiments of the present invention disclose a method and an apparatus for obtaining a video quality parameter and an electronic device. The method includes dividing a target video segment into at least one video subsegment, where duration of every video subsegment is at least time perceivable by human eyes; obtaining a video quality parameter of the video subsegment; and processing the video quality parameter of the video subsegment, and obtaining a video quality parameter of the target video segment.

Abstract: Methods, systems, and computer readable media are disclosed for determining a pixel-to-length ratio between a number of pixels disposed over a predetermined length of a reference object within an image of a siding sample and the predetermined length of the reference object. A first and second distance between respective first and second pairs of points within the image corresponding to respective first and second length measurements of the siding sample are determined, as well as a first and second number of pixels disposed between the first and second pair of points, respectively. Furthermore, the method, system, and computer readable medium disclose determining the first length measurement based on the pixel-to-length ratio and the first number of pixels, determining the second length measurement based on the pixel-to-length ratio and the second number of pixels, and identifying a siding product associated with the first and second length measurements.

Abstract: A method of sighting a target includes receiving an initial condition of an optical device. The initial condition includes a size of a ranging element and a range associated with the size of the ranging element. The method further includes receiving a ballistic information and receiving an image from an imaging sensor. At least a portion of the image is displayed on a display. The ranging element is overlaid on the displayed portion of the image. A first zoom input is received to set a first zoom value that corresponds to a first distance from the optical device. The method also includes determining a first projectile position based on the first distance and the ballistic information.

Abstract: A 3D positioning apparatus is used for an object that includes feature points and a reference point. The object undergoes movement from a first to a second position. The 3D positioning apparatus includes: an image sensor for capturing images of the object; and a processor for calculating, based on the captured images, initial coordinates of each feature point when the object is in the first position, initial coordinates of the reference point, final coordinates of the reference point when the object is in the second position, and final coordinates of each feature point. The processor calculates 3D translational information of the feature points using the initial and final coordinates of the reference point, and 3D rotational information of the feature points using the initial and final coordinates of each feature point. A 3D positioning method is also disclosed.

Abstract: A motion calculation device includes an image-capturing unit configured to capture an image of a range including a plane and outputs the captured image, an extraction unit configured to extract a region of the plane from the image, a detection unit configured to detect feature points and motion vectors of the feature points from a plurality of images captured by the image-capturing unit at a predetermined time interval; and a calculation unit configured to calculate the motion of the host device based on both of an epipolar constraint relating to the feature points and a homography relating to the region.

Abstract: A camera-equipped electronic apparatus by which an actual dimension of a subject can be easily known immediately at the time of capturing an image of the subject is provided. The camera-equipped electronic apparatus detects a size of an image of a marker and a size of the image of the subject in the captured image displayed on a display. Based on an actual dimension of the marker, the detected size of the image of the marker, and the detected size of the image of the subject, the actual dimension of the subject is computed, and the computed actual dimension is displayed on the display.

Abstract: A method is for monitoring the electrical integrity of lines of photosites of an imaging device with matrix array of photosites. The control lines of photosites may include for each line of photosites an emission of elementary electrical control signals for the photosites of the line. The method may include diagnosis of the elementary electrical control signals emitted.

Abstract: An image capturing apparatus for capturing the image of the physical object and displaying the captured image is provided for combining and displaying in real time the shape-distorted graded scale with the captured image, the apparatus comprising a graded scale generating part for generating the graded scale to be used for indicating the dimension of the physical object in the captured image; a data storing part for storing the data for correction to be used in order to correct the graded scale shape by adding the distortion to the generated graded scale in the similar degree to the distortion caused by the distortion aberration; a graded scale shape correcting part for generating the shape-distorted graded scale by correcting the graded scale shape according to the data for correction; and an image combining part for combining the generated shape-distorted graded scale with the captured image, and displays the captured image combined with the shape-distorted graded scale.

Abstract: A projector (1) for imaging an original image on a projection area (5) includes projection optics (2) having an adjustable image width (L) for imaging the original image on the projection area (5). A camera device (6) is used for imaging the projection area (5) and generating a projection area image. A comparison device (12) compares the original image with the projection area image and adjusts the image width (L) of the projection optics (2) as a function of the comparison such that the comparison device (12) is configured to determine the position of the original image in the projection area image. The position of the original image in the projection area image is then used as a measure for determining the image width of the projection optics (2).

Abstract: A method and apparatus for digital image correlation. A camera system is used to obtain larger scale images of a larger scale dot pattern on a surface of a workpiece and smaller scale images of a smaller scale dot pattern on the surface of the same workpiece. The smaller scale dot pattern forms a larger dot in the larger scale dot pattern in the larger scale images. The larger scale images and the smaller scale images may be used to determine a measurement of the workpiece.

Abstract: Systems and methods that improve farmers' ability to measure quantities of dry agricultural materials and rates of change of those quantities are disclosed. Also disclosed are systems and methods to rapidly and effectively communicate materials quantities and rates between farm equipment operators.

Abstract: Embodiments of the present invention disclose a method and an apparatus for obtaining a video quality parameter and an electronic device. The method includes dividing a target video segment into at least one video subsegment, where duration of every video subsegment is at least time perceivable by human eyes; obtaining a video quality parameter of the video subsegment; and processing the video quality parameter of the video subsegment, and obtaining a video quality parameter of the target video segment.

Abstract: An apparatus and method for insuring the proper alignment of a detected vein pattern and a projected vein pattern are disclosed. The apparatus enhances the visual appearance of veins so that an error that can lead to improper patient care or injury can be avoided.

Abstract: An apparatus for evaluating the fit of a modular window assembly into a simulated vehicle body opening includes a base member, a vehicle body opening/sheet metal simulator mounted to the base member, one or more light sources disposed in the vehicle body opening/sheet metal simulator and one or more devices for securing the vehicle window to the vehicle body opening/sheet metal simulator. A method of utilizing the apparatus is also a part of the invention.

Abstract: A one-dimension position measurement system includes: a first ruler having a first one-dimension binary code si applied thereon, a camera for acquiring a picture of a portion of the code si, the portion having a length of I bits, and some processing elements. Each codeword of length I of the one-dimension code si is unique within the whole code si. A codeword ai is read from the acquired picture, and the processing elements are implemented for computing an absolute position p of the codeword ai of the code si from: (I). An ad-hoc interpolation method is used to obtain a precision way below the distance between two bits of the codewords. The code si may be applied on the ruler by using some geometric primitives, a geometric primitive for encoding a “1” being different from a geometric primitive for encoding a “0”, both having the same horizontal projection. The horizontal projection is then used for fine interpolation, achieving nanometer-scale resolution.

Abstract: Provided is a hardness tester and method including an indentation former creating an indentation in a sample surface with an indenter; a first area calculator calculating an area of the indentation during application of pressure, the indentation being formed in the sample surface while the indenter is pressed against the sample; an image capture controller controlling a CCD camera to obtain image data of the sample surface; a second area calculator calculating the area of the indentation remaining in the sample surface based on the obtained image data; an elasticity index calculator calculating an elasticity index of the sample based on the area of the indentation during application of pressure and the area of the indentation calculated by the second area calculator; and a hardness value calculator calculating a hardness value of the sample based on the indentation remaining in the sample surface.

Abstract: A system for determining the absolute position of a first object with respect to a second object includes a scalar element attached to the first object and a measuring device attached to the second object. The scalar element comprises a series of coded regions. The coded region represents a number designating a position along an axis of the scalar element. The measuring device includes a two-dimensional optical sensor array configured to capture an image of a portion of the scalar element. The system also includes a processor configured to receive the image and determine an absolute position of the first object with respect to the second object based on at least one coded region of the series of coded regions.

Abstract: A geodetic apparatus for performing measurements using a target and a method for controlling the geodetic apparatus is disclosed. The apparatus comprises a detector for measuring a position of the target relative to a sighting axis of the apparatus, a light emitter for outputting to an outside of the geodetic apparatus a first cone of light having a first wavelength and a second cone of light having a second wavelength different from the first wavelength, and a controller connected to both the detector and the light emitter. The first cone of light overlaps with the second cone of light at the distance of one meter from the apparatus by at least 30%. The controller is configured to control the light emitter based on the detected position of the target to output at least one of the first cone of light and the second cone of light.

Abstract: A centrifuge is provided. The centrifuge includes a power source, the power source configured to generate electrical power from a renewable power source. At least one battery electrically coupled to the power source. A motor is electrically coupled to the at least one battery. A rotor is coupled to the motor. The rotor has a generally cylindrical body and a pair of opposing openings opposite the motor, and a pair of holders each disposed in one of the pair of opposing openings, each of the holders having an opening on one end sized to receive a capillary tube.

Abstract: An object tracking method includes steps of obtaining multiple first classifications of pixels within a first focus frame in a first frame picture, wherein the first focus frame includes an object to be tracked and has a first rectangular frame in a second frame picture; performing a positioning process to obtain a second rectangular frame; and obtaining color features of pixels around the second rectangular frame sequentially and establishing multiple second classifications according to the color feature. The established second classifications are compared with the first classifications sequentially to obtain an approximation value, compared with a predetermined threshold. The second rectangular frame is progressively adjusted, so as to establish a second focus frame. By analyzing color features of the pixels of the object and with a classification manner, the efficacy of detecting a shape and size of the object so as to update information of the focus frame is achieved.

Abstract: A method and a device for the accurate measurement of objects, where, according to the invention, a camera (4) is arranged on a manually operated portable jointed arm (1) in order to take two-dimensional images of the object that is to be measured and where the measurements are carried out based on the two-dimensional images taken with the camera (4) and based on the displacements that are carried out by the jointed arm (1) during the measurements.

Abstract: A device for measuring a shape of a surface. The device includes a first monodirectional-pattern gauge illuminated by first lighting mechanism, thereby making it possible to measure the shape in relation to a first direction, and a second gauge with monodirectional pattern perpendicular to the pattern of the first gauge making it possible to measure the shape in relation to a second direction perpendicular to the first direction. The second gauge is produced in the same plane as the first gauge by an additional lighting mechanism that is only turned on when the first lighting mechanism is turned off.

Abstract: A surveying apparatus comprises an observation optical system having an image sensor for outputting a digital image signal and a zoom optical system, a reference-pattern projection optical system for making a reference pattern enter the observation optical system in an infinity state and for forming an image on the image sensor, a rotation mechanism capable of rotating in two directions, a horizontal angle detector and a vertical angle detector for detecting a horizontal angle and a vertical angle of rotation in the two directions of the rotation mechanism, and an arithmetic control unit. The arithmetic control unit measures the horizontal angle and the vertical angle of a sighting point based on detection results of the horizontal angle detector and the vertical angle detector and based on a difference between the reference pattern on the image sensor and the sighting point of the observation optical system.

Abstract: System and method for tridimensional cartography of a structural surface. Two wires are extended in front and along the structural surface so as to define a reference surface. A measuring unit comprising a laser arrangement and a camera is moved in front of the structural surface so as to progressively scan the surface. Tow distinct light planes directed toward the structural surface are projected by means of the laser arrangement. Images of the structural surface containing lines resulting from an intersection of the light planes with the structural surface and four reference points resulting from an intersection of the light planes with the wires are captured by means of the camera. The images are processed to determine the 3D coordinates of the lines defining the mapping in a reference system bound to the reference surface considering the position and the orientation of the measuring unit based on the reference points.

Abstract: A method for three-dimensional mapping of an object, including projecting with a projector a set of fringes on the object and capturing an image of the object in a camera. The method further includes processing the captured image so as to detect a Moiré pattern associated with the object and so as to extract depth information from the Moiré pattern, and configuring the projector and the camera so that a locally unambiguous characteristic of the Moiré pattern is related to a depth of the object.

Abstract: Provided is an in-vehicle image display device capable of providing, from among images of the peripheral area of a vehicle that can change in accordance with the driving state, an image of a part needed by the driver at an appropriate timing so that the driver can recognize the positional relationship between the vehicle and the peripheral area of the vehicle. Images captured with in-vehicle cameras are acquired, and a vehicle periphery image is generated from such images. Then, a collision-warned part of the vehicle that has a possibility of hitting a nearby object is selected based on the vehicle driving state, and the acquired image is processed to generate an enlarged image of the peripheral area of the collision-warned part of the vehicle selected by the collision-warned part selection part. Then, a composite display image, in which the positions of the enlarged image and the vehicle periphery image are displayed in a correlated manner, is generated and displayed.

Abstract: A video processing device includes a video accumulating unit configured to accumulate video data obtained by capturing video of a specific area, event occurrence data indicating an event that has occurred in a video image corresponding to the video data, and object specifying data for specifying an object relating to the event, a video processing unit configured to apply a predetermined effect to the video data accumulated in the video accumulating unit in accordance with the event occurrence data and the object specifying data that are added to the video data accumulated in the video accumulating unit to produce a modified video image, and a video output unit configured to output the modified video image to which the effect has been applied by the video processing unit.

Abstract: There is disclosed a method in a mobile communications device, wherein the method comprises displaying a main image, selecting an object in the main image, displaying a plurality of object images comprising the selected object, selecting a target object image from the plurality of object images, and displaying a target candidate image associated with the target object image.

Abstract: An apparatus and method are provided for measuring the end surface of a disk-shaped semiconductor wafer based on its projection image, without the influence of contaminants on the end surface. A rotation supporting mechanism supports a wafer between a first supporting position rotated by +?relative to a predetermined reference position and a second supporting position rotated by ??degrees at two or more supporting positions. An image sensor picks up a projection image of the wafer's end surface. An index value for the end surface is calculated for each of a plurality of obtained projection images. One representative value of the calculated index values or an aggregate value is obtained, and a shape measurement of the wafer's end surface corresponding to the reference supporting position is derived. When the wafer's radius and a chamfer width are set as r and k, ??cos?1 ((r-k)/r) is satisfied.

Abstract: Systems and methods that improve farmers' ability to measure quantities of dry agricultural materials and rates of change of those quantities are disclosed. Also disclosed are systems and methods to rapidly and effectively communicate materials quantities and rates between farm equipment operators.