Abstract: Display location calculation means and methods for calculating a display location are disclosed. It has become common for users to indicate a point on a display in order to communicate with a machine. It is therefore necessary to be able to calculate the location on the display that is being indicated by the user. A display generator (123) is arranged in operation to generate a display in response to display data generated by a machine (111). A camera operable to generate image data representing at least part of the scene within the field of view of the camera (which part, includes at least a portion of the display) is carried in a pointer device (103). Computation means (111, 113, 115) are arranged in operation to receive the image data and the display data and to calculate from these data sets the position and/or orientation of the pointer device (103) relative to the display. A display location can then be calculated from the calculated position and/or orientation.

Abstract: In order to simply generate an accurate three-dimensional shape model, the generating method has the step (#1) of arranging a three-dimensional shape model in an initial state in a virtual space, the step (#2) of projecting points on the three-dimensional shape model onto photographed images and specifying pixels on the respective photographed images corresponding to the points, the step (#3) of evaluating scattering of pixel values of the respective pixels on the photographed images corresponding to the points on the three-dimensional shape model, and the step (#4) of deforming the three-dimensional shape model so that the scattering of the pixel values of the respective pixels becomes small.

Abstract: A semi-automatic reconstruction method of 3-D building models using building outline segments is introduced. The core technology of the present invention is called the “Split-Merge-Shape” algorithm. The Split and Merge processes sequentially reconstruct the topology between any roof-edges of the buildings and then reform them as enclosed regions. The Shape process uses height information and consecutive-coplanar analysis to determine the shapes and heights of the roofs. After generating polyhedral building models, prismatic building models can also be generated by using a semi-automatic procedure. An existing digital topographic map of buildings can be directly used to reconstruct their 3-D models without any excess stereo-measurements. In addition to cost reduction, high efficiency, high quality, and minimization of manual operations, the integration of photogrammetric mapping with 3-D building modeling in one procedure is possible, which is the most cost-effective approach for 3-D mapping.

Abstract: The invention relates to a method for detecting an object (1) in relation to a surface (2). A synthetic image (3c, 4c) is produced from at least two distinct viewpoints (3, 4), for each of said viewpoints, by means of a geometrical transformation comprising at least one perspective projection (3a, 4a) of the object on the surface (2), each synthetic image being associated with the viewpoint concerned. By discriminating between the synthetic images, it is possible to detect the presence of and determine the position of the object (1) in relation to the surface (2), by searching for contrast inversions. The invention can be used for surveying a swimming pool.

Abstract: An image forming process for easily making an image drawing (ortho-image) in an actual place while confirming it in real time. Measuring of control points (at least three points) is performed (S110), and preparation is made for forming an ortho-image based on image data thereof and survey data. Where photographing is carried out from a plurality of directions, additional image measuring is performed (S140). Then, ortho-image formation is performed on a PC (S160). Here, if a formed ortho-image is not what is desired, ortho-image correction is performed (S180). After a satisfactory image is obtained (S200), the process moves to a next area to be measured, and the same operation is repeated. On the other hand, unless a satisfactory image is obtained, additional image measuring (S140) is performed again.

Abstract: In accordance with a specific embodiment of the present invention, an image is projected upon a surface. The image can include a pattern having a plurality of individual shapes used to measure and map the surface. The plurality of individual shapes include features that are detectable in a direction parallel to the plane formed by a projection axis of the projected shapes and a point associated with a view axis. The image further comprises a feature containing an encoding information for identifying the plurality of shapes individually. The feature containing encoding information can be a separate feature from each of the plurality of individual shapes, or may be a feature integral to the plurality of individual shapes. The feature containing encoding information is oriented such that the encoding information is retrieved along a line perpendicular to a plane formed by the projection axis and the point along the view axis. The use of the feature is used to perform multiframe reference independent scanning.

Abstract: An automated system and/or method is disclosed for rapidly, accurately, and efficiently processing bulk three-dimensional digital image data of both path/corridor and area scenes to discriminate different structures or classifications of objects from within the image. The method first decomposes the three-dimensional digital imagery coordinate points into simple local structures and then extracts the globally complex structures from the local structures. The system and/or method incorporates procedures for sub-dividing the three-dimensional image data into rectilinear and/or ellipsoidal finite element cells, mathematically analyzing the contents (point coordinates) of each individual cell to classify/define the local structure, and extracting the globally complex structure or object from the image.

Abstract: A method and system are provided for constructing a virtual three-dimensional model of an object using a data processing system, and at least one machine-readable memory accessible to the data processing system. A set of at least two digital three-dimensional frames of portions of the object are obtained from a scanner or other source comprising a set of point coordinates in a three dimensional coordinate system providing differing information of the surface of the object. The frames provide a substantial overlap of the represented portions of the surface of the object, but do not coincide exactly. Data representing the set of frames are stored in the memory and processed by the data processing system so as to register the frames relative to each other to thereby produce a three-dimensional virtual representation of the portion of the surface of the object covered by the set of frames.

Abstract: Disclosed is a 3-dimension (3D) scanning system for a computer-aided tooth modeling capable of extracting a configuration of a tooth into a 3D configuration data in a short time. The 3D scanning system includes an image detecting part for extracting an image data of a tooth plaster model, a moving part for changing a location and a position of the tooth plaster model measured by the image detecting part, and a control part for changing and controlling the location and the position of the tooth plaster model by controlling the moving part to measure the tooth plaster model using the image detecting part.

Abstract: A method and system providing a transfer container crane with container code recognition of a container identified by a container code to a container inventory management system is disclosed. The system and method are capable of performing these tasks without the use of non-standard container tagging.

Abstract: The present invention discloses a stereo image measuring device capable of carrying out high-speed and highly reliable three-dimensional measurement for a stereo image, easily correcting any omitted measurement, measurement errors or the like, and achieving a much higher speed, efficiency and reliability for measurement as a whole. A survey instrument measures a number of control points on site. A camera is, for example a digital camera, a film camera or the like. A control point search unit executes correlation between a control point measured beforehand by the instrument survey and an image. A search area setting unit sets a search area to be used for image correlation processing based on the control points correlated by the control point search unit, and sets respective data blocks, i.e., a reference data block and a search data block. An arithmetic operation unit executes orientation calculation, and image correlation processing (stereo matching) for the search area set by the search area setting unit.

Abstract: A method of enhancing a source image for analysis. The method comprises the steps of digitizing the source image to obtain pixel data comprising location data and density data, generating a three-dimensional model of the pixel data with the location data represented in first and second axes and the density data represented in a third axis, and analyzing the three-dimensional model to determine features of the source image.

Abstract: Creation of a computer representation of a three-dimensional object surface is described. The viewing cones for camera positions at which images of the object were taken are determined and the intersection of these viewing cones is used to define an initial three-dimensional space within which the object surface lies. This initial space is divided into voxels. Each non-occluded voxel is checked for photoconsistency by comparing the colors (or average colors) of the pixel patches in the images to which that voxel projects. Photo-inconsistent voxels are removed. A voxel may be determined to be photo-inconsistent if there exists no set of photoconsistent pixel regions or the pixel patches do not share a color value range. The pixel patch into which each voxel projects in a further image may be compared with the stored color for that voxel and any photo-inconsistent voxels removed. This process can then be repeated for further images.

Abstract: A distance correcting apparatus of a surroundings monitoring system includes a stereo imaging means for stereoscopically taking a pair of images of a frontal scenery, a parallax calculating means for calculating a parallax based on the pair of images, a distance calculating means for calculating a distance to an object based on the parallax and a parameter for correcting distance, an approximation line calculating means for calculating a plurality of approximation lines extending in the distance direction in parallel with each other based on the images, a vanishing point calculating means for calculating a vanishing point of the images from a point of intersection of the approximation lines and a parameter correcting means for correcting the parameter based on the calculated vanishing point.

Abstract: A 3-D model of an object is created by processing images taken from a series of camera positions. An initial sequence of the images is processed to define respective image co-ordinates of matching features to generate a set of model data defining model points in a 3-D space of the model and to obtain respective camera solutions representative of positions and orientations of virtual cameras in the 3-D space defining views of the model corresponding to the images. A new image is added to the sequence and processed to obtain a camera solution for a corresponding new virtual camera for use in generating further model data.

Abstract: A method and apparatus capable of using two or more capture methods to create three-dimensional representations of a target captured. Elements of the three-dimensional digital representation generated from the plural capture method are combined to yield a single digital three-dimensional representation having improved quality.

Abstract: An apparatus (2) for matching features in images of objects taken from different viewpoints is provided comprising: an image buffer (60) for receiving image data; and output buffer (62) for outputting pairs of matched features and processing means (64–78) for processing received image data to determine matched pairs of features in images.

Abstract: In an image processing apparatus 20 an input sequence 130 of video images is processed to determine the different positions and orientations at which the images were recorded in an efficient and accurate manner. A subset of the input images are selected as keyframes to form a sequence 250 of keyframes. Respective triples of keyframes having different, non-overlapping positions in the sequence 250 are selected and processed to determine the relative positions and orientations at which the keyframes in each triple were recorded to form respective sets of keyframes. The positions and orientations of keyframes between the keyframes in each triple are then calculated to form expanded sets of keyframes 266, 276, 286. The sets are further expanded by calculating the positions and orientations of keyframes which lie between sets in the sequence 250. The sets are merged by calculating the relationship between the coordinate systems in which the positions and orientations of the keyframes in each set are defined.

Abstract: A three-dimensional shape modeling of a real object that reduces the limitations on the target shape and color. The rough shape of the target object is determined by a silhouette method (which has limitation on the target shape) and, at the same time, the detailed shape of the target object is determined by a triangulation method or the like (which has limitation on the target color). By using both sets of information, the consistency between the rough and detailed shape information are checked. For the portions where the consistency is not satisfied (points where detailed shape information is absent or points where detailed shape section is present outside the rough shape), rough shape is assumed to be the final object information and for other portions, the detailed shape is taken as the final object information. In this manner, three-dimensional shape modeling with reduced limitations on the target shape and color can be performed.

Abstract: A plurality of sets of range data and texture data obtained at different visual points are generated with respect to a measuring object, and relative shift processing of the range data is carried out. At a point to which the range data is shifted, corresponding points of the range data are calculated, and the correlation of the texture data is calculated on the basis of the calculated corresponding points. The minute shift of the range data, the corresponding point calculation processing, and the calculation of the correlation value of the texture data are repeatedly carried out for each minute shift of the range data. The corresponding point for the data exhibiting the highest texture correlation is outputted and the shift quantity of the range data is calculated on the basis of the outputted corresponding point.

Abstract: The invention is a stereoscopic shutter system having a single liquid crystal (LC) cell. The system may have flexible substrates or non-flexible substrates. The system requires only two electrical conductors to shutter both eyes. The system uses twisted nematic liquid crystal, ferro-electric liquid crystal, pi-cell technology, or other similar shuttering technologies. The system includes only one LC cell, a single large laminated linearly polarizing filter P1, and two smaller linear polarizing analyzers oriented in the P1 and P2 states. The shutters may be bent into a one-dimensional curved shape about the vertical or horizontal axis.

Abstract: A stereo digital camera which generates a three-dimensional image or stereograph having one file structure, and records the three-dimensional image on a recording medium includes a stereo adapter having optical axes corresponding to parallax, an imaging lens for transferring an object image via the stereo adapter, and a single CCD pickup unit having monocular regions on which the monocular images of the object image are projected by the imaging lens. Two monocular region images from the monocular regions form one multocular stereo image, and are compressed as one image data. This image data is appended with header information which contains an item indicating that this image data is a stereo image, an item corresponding to the number of monocular images which form the stereo image, and an item associated with addresses of the first and second monocular images, and is stored in a recording medium as one file.

Abstract: A system for localizing objects has two or more measurement units. Calibration methods provide transformations to a common reference frame by locating calibration features in local reference frames of the measurement units. A calibration target spanning measurement fields of the measurement units may be used. The measurement units may have overlapping measurement fields. The measurement units may comprise stereo vision units or other units capable of locating objects or object features.

Abstract: Imaging apparatus for obtaining depth information of an object to be imaged. An image capturing part for obtaining three or more parallactic or steroscopic images of the object as viewed from three or more different viewpoints which are not arrayed on the same line; a displacement detector for detecting plural displacements with respect to a specific region of the object, each displacement being detected between any two of the three or more steroscopic images; and a depth calculator for calculating the depth information with respect to the specific region, based on the plural displacements detected by the displacement detector.

Abstract: A system, method, and computer-readable medium for detecting and eliminating correspondence errors associated with image occlusions. In a first embodiment of the invention, the method applies traditional correspondence methods for matching points in two images, a left image (FIG. 1A) and a right image (FIG. 1B), taken of the same scene. The method applies the correspondence method to locate a matching a point (310) in the right image (FIG. 1B) with a “best match” point (320) in the left image (FIG. 1A). A set of matching points (310, 320) is generated. A second search is then performed by using the best match point (320) in the right image (FIG. 1B) as the basis for an additional correspondence search in the left image (FIG. 1A). The range of match candidates in the second search is such that points to the left of the starting point (310) are not tested as match candidates.

Abstract: Pairs of stereo Xray radiographs are obtained from an X-ray imaging system and are digitized to form corresponding pairs of stereo images (602, 604). The pairs of stereo images (602, 604) are adjusted (410) to compensate for gray-scale illumination differences by grouping and processing pixel groups in each pair of images. Distortion in the nature of depth plane curvature and Keystone distortion due to the toed-in configuration of the X-ray imaging system are eliminated (412). A screen parallax for the pair of stereo images is adjusted (414) to minimize depth range so as to enable a maximum number of users to view the stereoscopic image, and particular features of interest.

Abstract: We present a method and apparatus for local and superficial measurement of the optical properties of turbid media. The depth probed is on the order of 1 transport mean free path of the photon. The absorption coefficient, reduced scattering coefficient and the phase function parameter ?=(1?g2)/(1?g1) are optical parameters computed from a single measurement of the spatially resolved reflectance close to the source. Images of superficial structures of the medium can be obtained by performing multi-site measurements. An important application of this technique is the characterization of biological tissues, for example for medical diagnostic purposes. Measurements on biological tissues can be achieved using a probe of diameter less than 2 mm, and the average volume probed is on the order of 1 mm3. Separate images of absorption and tissue structure can be achieved with a resolution of approximately one transport mean free path of the considered tissue.

Abstract: A method is described for determining a 2D gradient magnitude image from a range image of an object. The range image includes intensity values at pixel locations. The intensity values correspond to distances to a surface of the object. For each pixel (i,j) in the range image, a horizontal central difference dx value and a vertical central difference dy value are determined. Then, the 2D gradient magnitude image value at each pixel (i,j) is set to 0.5*sqrt(dx2+dy2+4). The range image can be scaled so that a unit intensity value at each pixel corresponds to a unit distance value. The magnitude of a gradient at a 3D point p can then be determined from the scaled range image and the gradient magnitude image. First, a perpendicular projection (x,y) of p onto the scaled range image is computed. Next, a gradient magnitude at (x,y) is interpolated from the corresponding values of the 2D gradient magnitude image near the location (x,y).

Abstract: A three-dimensional information processing apparatus for obtaining three-dimensional information from an object having a three-dimensional shape, and performing predetermined information processing, comprises: a camera for sensing images of the object from a plurality of coordinate positions using an image sensing system having one or a plurality of optical systems. A plurality of depth information are extracted from image sensing related information sensed by the camera at the plurality of coordinate positions, and the plurality of extracted depth information are converted and unified into depth information expressed by a unified coordinate system.

Abstract: Apparatus and a method for producing a stereoscopic line-scan image of an object in which a detector camera is used to view the object, means are provided to move relative to one another the surface of the object past the detector in a direction which is at right angles to the scanning lines direction of the detector, and means are provided to select the outputs from two spaced lines in each picture frame produced by the detector and store those lines in a frame store to build up individual pictures from each of the two lines, so that one individual picture constitutes a left hand picture of a stereoscopic pair and the other individual picture constitutes a right hand image of a stereoscopic pair. Preferably the detector camera is a television camera or a full field digital.

Abstract: In accordance with a specific embodiment of the present invention, an image is projected upon a surface. The image can include a pattern having a plurality of individual shapes used to measure and map the surface. The plurality of individual shapes include features that are detectable in a direction parallel to the plane formed by a projection axis of the projected shapes and a point associated with a view axis. The image further comprises a feature containing an encoding information for identifying the plurality of shapes individually. The feature containing encoding information can be a separate feature from each of the plurality of individual shapes, or may be a feature integral to the plurality of individual shapes. The feature containing encoding information is oriented such that the encoding information is retrieved along a line perpendicular to a plane formed by the projection axis and the point along the view axis. The use of the feature is used to perform multiframe reference independent scanning.

Abstract: A computer-implemented method and system for adjustment and matching of stereoscopic images (206, 208) of the eye fundus (106). Illumination errors between the images are eliminated, such as by adjusting groups of pixels so that the mean and variance of a group (306) from the left image (206) will have the same mean intensity and variance as the corresponding group (308) from the right image (208). An epipolar line adjustment is performed, such as by shifting points in the images based on matched points in the images. Image occlusion errors are detected and removed, such as by matching point analysis. Once these adjustment steps have been completed, a matching analysis can be preformed using the corrected images.

Abstract: A method of taking three-dimensional measurements of an object surface by means of a camera movable between initial and terminal positions relative to the object surface in which object coordinates are determined by gray scale curves of images formed on sensors of the camera. Tracking of characteristics of an image taken at an initial position to an image taken at a terminal position is made safer and simpler by incremental tracking over one or more images taken at camera positions intermediate the initial and terminal positions.

Abstract: The acquisition of 3-D scenes by a single hand-held camera is disclosed. The camera is preferably mounted on a lens attachment with four mirrors, enabling stereo capturing of the scene. The signal processing tasks involved, camera calibration and correspondence estimation, are each disclosed. Both fixed and self-calibration methods benefit from the use of the lens attachment to acquire a scene. Specifically, full self-calibration of the camera is enabled, without loss of absolute scale as seen in prior art stereo self-calibration methods. Accurate 3-D models are obtained with the method of the invention.

Abstract: Displacement of a first block of pixels from a first to a second image of a scene is determined for applications of automated distance computation. The selection of corresponding blocks in the two images is performed and verified as follows. A first block is taken from the first image. A first region is selected from a set of first regions in the second image, so that a difference between an image content of the first region and of the first block is minimal among the set of first regions. A second block is taken from the second image, the second block containing at least part of the selected first region. A second region is selected from a set of second regions in the first image, so that a difference between an image content of the second region and of the second block is minimal among the set of second regions. A first displacement between the first block and the selected first region is compared with a second displacement between the second block and the selecting second region.

Abstract: A system and method are described for aligning a locally-reconstructed three-dimensional object, whose local reconstruction is relative to a local coordinate system, to a global coordinate system by using pre-mapped control points which are projected onto one or more of the images that may be used to generate the local reconstruction. A system includes a control point information generator and an alignment generator. The control point information generator is configured to identify in at least image associated with a local reconstruction of the object a projection of at least one control point in the scene onto the at least one image, and generate local projected coordinate information indicating coordinates of the projection in the at least one image.

Abstract: Method for acquiring a three-dimensional shape or image of a scene, wherein a predetermined pattern of lines is projected onto the scene and the shape is acquired on the basis of relative distances between the lines and/or intersections of the lines of the pattern.

Abstract: A potting compound for use in the fabrication of fiber optic gyro sensor coils utilizes a silver-filled silicone base to reduce gyro sensitivity to changes in heat rate and thereby improve gyro performance during warm-up and periods of thermal cycling.

Abstract: A method of 3-dimensional structure estimation of the invention, making use of a plurality of stereo-pictures, repeats, for each pixel of a first picture, a step of extracting corresponding small regions (4) corresponding to the concerning pixel according to a depth estimation (68); a step of calculating a neighboring correspondence value for each of the corresponding small regions representing correspondence among neighboring corresponding small regions of picures taken by neighboring cameras; a step of obtaining a sum (61) of the neighboring correspondence values; and selecting a value of the depth estimation (68) which gives a singular value of the sum (61) representing correspondence among the corresponding small regions.

Abstract: The present invention relates to a method for aligning an object, whose image is to be recorded, with an image capture apparatus and a coupling eyepiece. Said method consists in using a light source, said light source being positioned in the place of the object and emitting luminous dots through a mask and through the coupling eyepiece towards the capture apparatus. The invention also consists in verifying whether the images of said luminous dots are split into two on the image plane, then, using all the development functions determined for the various alignment settings, in determining a particular setting in which the distances between the images of the luminous dots are minimal.

Abstract: A perspective image characteristic value is extracted from a 2D input image signal for each of plural parallax calculation regions defined in a one-field screen on a field-by-field basis. Parallax information per predetermined unit area of the one-field screen is generated by using the perspective image characteristic value extracted per parallax calculation region. A first image signal and a second image signal are generated from a signal of the 2D input image signal which resides in each predetermined unit area, the first and second image signals having a horizontal phase difference therebetween based on the parallax information on the predetermined unit area.

Abstract: A three-dimensional information processing apparatus for obtaining three-dimensional information from an object having a three-dimensional shape, and performing predetermined information processing, comprises: a camera for sensing images of the object from a plurality of coordinate positions using an image sensing system having one or a plurality of optical systems. A plurality of depth information are extracted from image sensing related information sensed by the camera at the plurality of coordinate positions, and the plurality of extracted depth information are converted and unified into depth information expressed by a unified coordinate system.

Abstract: A method and apparatus to capture stereoscopic images is disclosed. A light source having a diffracting device to project a structured light unto a target object is provided. A plurality of imaging devices to capture images of the target object is provided.

Abstract: A furnace-type atomic absorption spectrophotometer heats a sample by controlling a heating current passed to the tube inside which the sample is held. The temperature of the tube is monitored and the heating current is controlled, say, by a phase control method, such that the monitored temperature will approach a specified target temperature. The spectrophotometer includes a control unit which determines a quantity of a specified operation for the heating control such as a firing angle by a PID control calculation on the difference between the monitored temperature and a target temperature value. PID parameters are determined such that the minimum detectable quantity can be reduced.

Abstract: Method and apparatus are provided for generating two dimensional images representing scenes of three dimensional spaces as viewed for arbitrary observing point. In a specific embodiment of the method and apparatus, consecutive virtual images, computed from four dimensional reference images are consecutively displayed on a multimedia screen in order to convey motion of a body.

Abstract: In the image monitor apparatus, a plurality of images are respectively inputted through a plurality of TV camera from each view position. An image projection section projects each of the plurality of images onto a predetermined plane in three-dimensional space. A comparison section compares the projected image data of two images by unit of predetermined area on the plane, and extracts the predetermined areas, each of which two projected image data are different, from the plane. An extraction section extracts an existence position of a monitored object from the predetermined areas extracted. An integration section integrates the existence positions of the monitored object extracted for the projected image data of all of two images in the plurality of images as all existence positions of the monitored objects on the plane.

Abstract: An aerial reconnaissance system generates imagery of a scene that meets resolution or field of view objectives automatically and autonomously. In one embodiment, a passive method of automatically calculating range to the target from a sequence of airborne reconnaissance camera images is used. Range information is use for controlling the adjustment of a zoom lens to yield frame-to-frame target imagery that has a desired, e.g., constant, ground resolution or field of view at the center of the image despite rapid and significant aircraft altitude and attitude changes. Image to image digital correlation is used to determine the displacement of the target at the focal plane. Camera frame rate and aircraft INS/GPS information is used to accurately determine the frame to frame distance (baseline). The calculated range to target is then used to drive a zoom lens servo mechanism to the proper focal length to yield the desired resolution or field of view for the next image.

Abstract: An object of the invention is to provide a method for easily determining an integral interval when detecting inclinations of a subject in pixel units and reconstructing a shape of said subject by integrating said detected inclinations. This method photographs the subject with a left camera and a right camera, and obtains gradational images from the respective positions. This method obtains in pixel units parallaxes for the subject between these positions. This method determines as one integral interval each domain in which pixels showing the same parallax appear in succession.

Abstract: A coincidence and stereoscopic binocular rangefinder is disclosed for measuring distance to sighted targets. The rangefinder preferably has three optical windows for receiving radiation from a sighted target allowing the user to use both his ability to align separated images in one of the eyepieces of the rangefinder, and his ability to stereoscopically sense and compare apparent target depths using both eyepieces of the rangefinder. The rangefinder also includes a novel feature whereby the binocular portion may be easily and conveniently detached from the rangefinder and used separately, and then easily reattached when distance measurement is again desired.

Abstract: A method for making it possible to simply reduce accumulation of integral errors when obtaining a directing measured result by integrating measured values in a measured value group. Integrated values Ye(i) up to each measured value are obtained by means of the partial integrating method by using the even-numberth measured values in a measured value group as the respective reference values, respectively. Integrated values Yo(i) up to each measured value are obtained by means of the partial integrating method by using the odd-numberth measured values in a measured value group as the respective reference values, respectively. An average value of Ye(i) and one of the odd-numberth-reference integrated values Yo(i-1), Yo(i), and Yo(i+1) is taken as a final integrated result Y(i) up to each measured value, where i is a place number in a row of measured values.