Abstract: A method to conduct fingerprint verification provides a sector distribution based on the position and angle of every minutiae vector, wherein the number of further minutiae vectors of the template in any sector of the sector distribution is determined and a feature vector is generated for every minutiae vector of both templates. The two feature arrays are matched by calculating the scalar product for every combination of said vectors generating a matrix. Mated pairs of minutiae from the first second template are found by searching the maximum element in every column of the matrix finally issuing a value representing identification information of the fingerprint. Additionally a false finger identification method and a fingerprint verification system are disclosed.

Abstract: A method and system of obtaining a ten-print plain impression fingerprint includes scanning a print image, processing the scanned image, separating the processed image into individual fingerprint images, and determining how many print images have been scanned. The method also includes comparing the print image to a previously scanned print image, quality classifying the separated images, indicating a quality classification of the print image based on the classifying step, and determining whether the print image is of a good quality. The system can include a ten-print scanner having a finger guide and a platen used to position four finger slaps onto the platen.

Abstract: Method and system for reconstructing seamless fingerprint image from set of image slices, or frames, from fingerprint swipe sensor. Robust normalized cross-correlation procedures are used for frame evaluation and image matching. Efficient use of device processing resources including memory by keeping only data frames that indicate moving finger and discards frames where no finger exists at sensor during acquisition or finger has not moved since last frame was acquired. Capability to adjust sensor settings during acquisition process to obtain optimal results. Logic ensures operation across different physical systems and sensor characteristics with varying acquisition speeds. Statistics regarding resulting reconstructed image and finger swiping process are computed and embedded in reconstructed image and are useful to the downstream fingerprint matching system, and by embedding in image, inventive system and method ensure that any fingerprint processing system can use information if when called upon to do so.

Abstract: In a capacitive biometric sensor, in particular, a fingerprint sensor, to determine the maximum contrast that can actually be achieved in that application in the gray scale values, in particular, of a fingerprint (dynamic resolution of the sensor), at least one measurement point composed of a dielectric material is integrated above each of the sensor electrodes on a sensor array.

Abstract: This invention relates to the use of holographic optical elements in the design and application of biometric scanning instruments used typically for capturing biometric information such as fingerprints and handprints. A system and method for capturing print images from select areas of a platen are presented. The system includes a reference beam source that provides a reference beam, holographic material that receives the reference beam, a platen on a surface of the holographic material that receives a biometric object, and an image sensor. Variations in orientation of the reference beam cause differing areas of the platen to be mapped onto the image sensor, thereby obtaining both different image translations and magnifications of at least a portion of the biometric object.

Abstract: The invention relates to a device for determining the non precise placement of measuring sites on measuring sensors and for reducing measuring errors, which result from the movement between the measuring sites and the measuring sensors when measuring the most diverse quantities to be measured, with the aim of creating robust measuring systems for recording measured values under real or challenging conditions. The invention is characterized by: detecting whether and which sensor elements are covered and thus in contact with the site to be measured; tracking and/or adapting the sensor elements so that the contact is not interrupted even during movements, and; the resilient arrangement of the contacts for constantly maintaining the mechanical bearing pressure when measuring the electrical skin resistance.

Abstract: A computer-implemented method is provided for generating a quality field representation of a collection of image data. The method includes receiving the collection of image data and identifying a target point along a ridge in the collection of image data. A directional field representation is estimated by assigning an angle value to the ridge indicative of an angle with respect to a reference line. Also, a covariance between the target point and a corresponding point along a line orthogonal to the angle value is calculated.

Abstract: After processing, a target feature point is detected. Information about a target feature point includes the position of the ridge containing a vicinal feature point relative to the position of the ridge containing the target feature point in addition to the position, type, and direction of the target feature point. Then, the information is checked in a matching process, and the vicinal feature point is checked on a feature point contained in a ridge matching in position the ridge of the target feature point. When the target feature point and the vicinal feature point match in position and direction, and are different in type only, the mark has a value indicating a matching level. Then, a matching result of the vicinal feature points is obtained as a matching mark, and it is determined whether the target feature point is matching by determining whether the matching mark is equal to or larger than a threshold.

Abstract: A carrier for a sweep-type fingerprint sensor and a method of operation are disclosed. The carrier has a recess for receiving and mounting the fingerprint sensor and one or more tactile elements for assisting the user in positioning a finger, and in correctly moving the finger across the sensor being read. In one embodiment the tactile element consists of an oval ridge, or a portion thereof, defining a major axis which is lies in the sweep direction. The tip of the finger is initially positioned in the arcuate portion of the oval ridge and is moved across the sensor, generally along the axis of the oval. The side walls of the ridge assist the user in correctly moving the finger across the sensor.

Abstract: Embodiments of a method and/or apparatus to provide a binary image are disclosed.

Abstract: The present invention provides technologies for narrowing down fingerprints images, which will be used for identity determination, without extracting auxiliary information such as a fingerprint pattern, thereby shortening the time required for fingerprint verification. The device according to the present invention includes a storage means 26 for storing characteristic information extracted from fingerprint images of registered persons, and a collection means 10 for collecting a fingerprint image. First, a extraction means 14 extracts characteristic information from the fingerprint image collected by the collection means 10. Next, a narrowing means 16 calculates a similarity between part of the characteristic information of the person to be identified, which was extracted by the extraction means 14, and corresponding part of the characteristic information of each of the registered persons, which is stored in the storage means 26.

Abstract: A fingerprint verification device includes a fingerprint sensor including an imaging surface. The fingerprint sensor is configured to capture images of a user's finger when the finger is swiped against the imaging surface. A memory stores fingerprint data. A controller compares minutiae in the captured images with the stored fingerprint data to verify the user's identity. The controller is configured to determine whether the finger is a real human finger based on the spacing of minutiae in the captured images.

Abstract: A method of using an electronic locking system to access one of a plurality of lockers includes programming the system by recording at least one biometric characteristic of a user, storing the recorded biometric characteristic of the user in memory, and associating the recorded biometric characteristic of the user with one of the lockers so that the user is authorized to access the locker. The method also includes locking the locker, re-recording the biometric characteristic of the user, after the re-recording step, comparing the re-recorded biometric characteristic of the user with the recorded biometric characteristic of the user and unlocking the locker if the re-recorded biometric characteristic of the user matches the recorded biometric characteristic of the user. The system is newly reprogrammed for each subsequent user of the locker.

Abstract: A system and a method for minutiae record matching is claimed that includes the processing a first plurality of ordered minutiae match values with weighting values corresponding to a function of at least the number of minutiae in the corresponding latent print and the corresponding print in the tenprint for a given unweighted match value to define a second plurality of weighted match values. The second plurality of weighted match values may be further normalized based at least on the highest unweighted match value to generated a third plurality of weighted match values.

Abstract: Systems and methods perform access control and mobile identity verification utilizing a memory, maybe on a handheld device, that stores at least biometric data, such as minutia. The handheld device may also store other data, such as a threshold value and Wiegand data. The data may be stored in a memory, a magnetic strip, a code, a bar code, or in all of these devices associated with the handheld device. The handheld device may be a SmartCard or the like. The threshold value may be a required value or parameter generated from input criteria based on biometric data read and extracted by an extracting system during an enrolling process. The threshold value is used during extracting, matching, or both, to most accurately determine the identity and characteristics of an individual wanting access to an accessed system or being questioned by law enforcement in the field.

Abstract: The present invention determines whether fingerprint ridgeline information is contained within the fingerprint image using a simple method by considering the properties of the fingerprint ridgeline. In this fingerprint image evaluation method, a density is obtained of a reference point provided within the fingerprint image and a density is obtained of a comparison point that is shifted from the reference point by a predetermined distance. The amount of fingerprint ridgeline information contained within the fingerprint image is evaluated based upon a difference between the density of the reference point and the density of the comparison point. In this fingerprint image evaluation method, the characteristic of the fingerprint ridgeline, in which a fingerprint furrow line exists proximally to the fingerprint ridgeline, is utilized. Therefore, erroneous determinations can be prevented in which an image, which is not in fact a fingerprint image, is determined to be a fingerprint image.

Abstract: A system and a method for segmenting slap fingerprints is described. The method includes providing a print image, optionally pre-processing the print image, detecting at least a plurality of image components of the print image, determining at least one segmentation boundary for the print image, and computing the convex hull of the image components. The orientation, relative orientation and placement of the image components are detected. The zone lines of each component are found and zone areas are defined. The components under the top component of each zone are deleted. The finger numbers are assigned in accordance with the anchor print component, the geometrical relationship among the components. The slap print image is segmented in accordance with the segmentation boundary and its neighboring boundaries.

Abstract: A system and method for sending a packet with a position address and line scan data from a first device over a 1394 interface to a second device. The present invention loads a camera, an illuminator, and a microprocessor with set-up instructions and a start pulse. The camera captures a line-by-line image of an object placed on the surface of a sliding prism. Position data, corresponding to the captured line-by-line image, is logged as the position address. The position address is combined with the line-by-line image to form a packet. The packet is sent to the second device for processing and viewing the image.

Abstract: In a fingerprint image, this fingerprint matching method extracts as skeleton stability the area of a zone which is drawn around a pre-determined attention point and which does not contain any minutiae that are bifurcations or endpoints in ridges forming a fingerprint pattern, and calculates similarity by collating said skeleton stability thus extracted with skeleton stability already registered.

Abstract: Fingerprint verification matching a claimant fingerprint with one of a number of recorded enrollee fingerprints uses various adaptations of model alignment techniques involving affine transformation to provide an algorithm providing relatively fast and accurate verification suitable for realtime applications. These techniques involve sampling minutiae into subsets based on geometrical proximity to a particular index minutiae for each subset, eliminating minutiae which are near the fingerprint boundary, ordering the minutiae of each subset in a predetermined manner, classifying each subset in bins which discriminate on the properties of the subsets, checking transformations proposed as matches between fingerprints for consistency with each other, and checking the topological as well as the geometrical correspondence of potentially matching fingerprints. In a preferred form, a score indicative of the correlation between fingerprints is used to ultimately decide whether the fingerprints match.

Abstract: The pattern-collating device includes as feature point pairs, among feature points which are portions indicating respective features of an examination target graphic which is the graphic to be compared and a model graphic which is the reference graphic, those which mutually correspond in said examination target graphic and said model graphic and a similarity determination section which calculates the similarity between the examination target graphic and the model graphic based on correspondence of the feature points by the feature point pair formation section, wherein the similarity determination section calculates the similarity between the examination target graphic and the model graphic based on a probability that the number of the feature point pairs between an arbitrary graphic and the model graphic, is not less than the number of the feature point pairs between the examination target graphic and the model graphic previously obtained by the feature point pair formation section.

Abstract: A system comprising means, which stores, regenerates, or matches shape of curves, by using a specified group of data in length to express a shape of curve. The system uses a sequence of several measure points on the curve, which are determined so as to make the same distances between those adjacent measure points. They are the data of lengths of arcs between starting measure point and ending measure points among every three consecutive measure points on the curve.

Abstract: In a fingerprint/palmprint image processing system and method, for local regions other than a highly reliable region, a ridge line image which can be estimated to represent a ridge line is selected from ridge line candidate images, and whether or not each of the selected ridge line images is valid as an image representing a ridge line is discriminated. Thus, a whole image is generated on the basis of the ridge line image in the highly reliable region and the ridge line images which were discriminated to be valid in the other regions.

Abstract: A pattern collation device for comparing and collating graphic forms includes a deformation estimating unit for estimating deformation generated in a graphic form to be examined which is a graphic form as an object of examination based on information about a feature point indicative of features in each of the graphic form to be examined in question and a model graphic form as a graphic form based on which comparison is made, a deformation correcting unit for correcting the graphic form to be examined in question based on information about the deformation estimated by the deformation estimating unit and a similarity determining unit for comparing the graphic form to be examined whose deformation is corrected by the deformation correcting unit with the model graphic form as a graphic form based on which comparison is made to calculate similarity therebetween.

Abstract: The method of recognizing fingerprints comprises an analysis step (21) in which an expert analyses characteristic points of a fingerprint image so as to be able to differentiate the fingerprint whose image is presented to him. The method comprises a modification step (19) in which the said print image available with various levels from a grey scale is modified into a second image in which at least one grey range of the first image is parameterized so as to be represented with various levels from a colour scale. The modification makes it possible to identify the characteristic points on an unknown fingerprint image more accurately and also to compare the said image to other known fingerprint images more easily.

Abstract: A method of hash string extraction from biometric information is disclosed. The method comprises the steps of providing a biometric information sample in the form of a fingerprint for example, extracting features from the biometric information sample and encoding the features based on their location within the biometric information sample; and, generating a string of values based on the extracted features and their determined locations. The method further comprises the steps of hashing the string of symbols to produce a plurality of hash values for comparing the plurality of hash values against a stored hash value for identifying a user.

Abstract: The invention relates to a method for registering fingerprint information via a sensing surface A. The method comprises scanning part surfaces A?1 in the sensing surface A, checking whether the centre point P1, with its immediate surrounding area A?1, of each scanned part surface A?1 is unique within the part surface A?1, and registering a first number of centre points P1 which, with their respective immediate surrounding areas A?1, are unique within their respective part surfaces A?1. The respective immediate surrounding areas A?1 of the points and the respective part surfaces A?1 of the points are also registered. The invention also relates to a method for verifying fingerprint information, in which verification is carried out on the basis of registered information relating to a fingerprint which is to be approved in the verification method.

Abstract: A system and method for counting ridges in a captured print image frame is described. A pixel path through the captured print image frame is traversed. A hysteresis band for the pixel path is determined. A number of crossings of the determined hysteresis band is counted while traversing the pixel path. A number of print ridges based on the counted number of hysteresis band crossings is determined.

Abstract: An image capturing apparatus includes an image capturing section and capture control section. The image capturing section converts the shape of an object into an electrical quantity in accordance with the parameter value set in a parameter setting section, and outputs image data representing an image corresponding to the shape of the object. The capture control section receives the image data output from the image capturing section, calculates an evaluation index for evaluating the image quality of the image from the image data. If the evaluation index falls outside the range of a preset reference value, the capture control section changes the parameter value set in the parameter setting section so as to make the evaluation index fall within the range of the reference value to output the image data which is received from the image capturing section and the evaluation index of which falls within the range of the reference value.

Abstract: A method including the steps of:) receiving (202) a search record; generating (206) at least one hierarchical cluster, each having a different minimum quality level; for each cluster, generating (210) at least one corresponding search package having a first set of search prints; selecting the highest quality cluster (218), a search package (222) and corresponding file records for performing a search (226); determining (230) whether a hit was found between any file print in the corresponding file records and any search print in the selected search package; and proceeding with the search process through the remaining quality clusters in an order based on decreasing quality until a match is found or until there are no remaining file records against which to compare a search package.

Abstract: The invention achieves stabilization of the verification performance and augmentation of the verification performance. The fingerprint data synthesis apparatus includes a fingerprint data extraction section for extracting minutiae from each of a plurality of fingerprint images to produce fingerprint data, a fingerprint data storage section for storing the fingerprint data, a common minutia searching section for investigating a correspondence of the minutiae between the plurality of fingerprint data to search for the same minutiae included commonly in two or more of the plurality of fingerprint data as common minutiae, a fingerprint data synthesis section for selecting one of the common minutiae as a minutia representative of the common minutiae to produce one synthetic fingerprint data, and a validation section for validating the synthetic fingerprint data. The apparatus is applied to production of fingerprint data used in a system which identifies an individual.

Abstract: The disclosed invention herein is a method for extracting fingerprint feature data using a ridge orientation model. The fingerprint feature data extracting method includes the steps of inputting a fingerprint image, extracting ridge orientations according to regions, calculating ridge qualities according to regions and separating background region from the fingerprint image, extracting regions having a core and a delta, setting an initial ridge orientation model, calculating a ridge orientation function, and extracting the ridge orientations and the core and delta positions of the fingerprint image.

Abstract: A fingerprint recognizing device having patterned floating electrodes is disclosed. The fingerprint recognizing device includes a transparent electrode layer to which one terminal of an AC power source is connected; a light emitting layer for forming an electric field between the transparent electrode layer and a finger forming a ground contact when being contacted with the finger and emitting light by this electric filed for generating an optical fingerprint image according to ridge lines of a fingerprint image; a plurality of patterned floating electrodes arranged on the light emitting layer at a predetermined interval and turned on/off to output the optical fingerprint image; and a transparent insulating layer for transmitting the optical image generated from the light emitting layer.

Abstract: A method of fast fingerprint search space partitioning and prescreening is disclosed. The method comprises the steps of: inputting the contents of a fingerprint repository comprising file fingerprints for index creation; creating an index based on each minutia and selected neighbors of each minutia in each file fingerprint in the repository; searching the index to identify all minutiae which correspond to the minutiae in a search fingerprint; and analyzing results of this search to determine which file fingerprints contributed the most minutiae with the best correspondence to the minutiae in the search fingerprint.

Abstract: The invention offers a technique for personal identification which reduces the amount of computation required to match fingerprints, thereby shortening the processing time, while simultaneously improving the precision of the match. A press-type fingerprint sampler 1 reads a 1 cm2 area in the central portion of a fingerprint which has been pressed flat, and supplies fingerprint information representing a two-dimensional image of the fingerprint to a fingerprint match processing device 2. At the fingerprint match processing device 2, a minutiae extracting portion 21b extracts eight types of minutiae (starting points, end points, bifurcation points, juncture points, dots, short lines, islands and scars) from the fingerprint information and writes these into the memory portion 22 to register the fingerprint. When matching the fingerprints, the fingerprints are similarly sampled by the press-type fingerprint sampler 1 to extract the minutiae, which are then supplied to a match computing portion 21c.

Abstract: A method and system for the extraction of linear features from digital imagery is described herein. The proposed methodology is based on the tridimensional Radon transformation and on the generation of a multi-layer database having separate layers containing different types of information to allow the reconstruction of an output image where the linear features of the input image are restored.

Abstract: A method and system for performing automated biological identification. The system including a preprocessing module with a histogram transform for locally and globally enhancing biological data such as fingerprints. An enhancement module with a fast smoothing and enhancement function. A feature extraction module with a fingerprint oriented thinning function. A matching module with a resolution-enhanced Hough transform function for fingerprint registration and matching score function.

Abstract: Methods and procedures for improving the performance and reliability of image analysis within an image identification system include a series of image qualification functions designed to quickly process a fraction of available image data and to provide feedback to a system user pertaining to image quality and authenticity. Functions designed to produce image models based on original image data and to catalogue such image models into a searchable database are included in the present invention. The present invention also includes functions for comparing one image model to another. Finally, the present invention provides functions for making a quick determination as to which, if any, of a potential thousands (or more, i.e., millions) of image models within a searchable database exhibit a desired level of similarity, as compared to a target image model.

Abstract: A fingerprint authentication apparatus has a combined visible/infrared light source, which illuminates a finger placed on an optical image sensor with both infrared light and visible light. The optical image sensor has a block with infrared sensitivity and a block within infrared sensitivity, and generates a fingerprint image from light scattered by the finger. The infrared sensitivity of the infrared-sensitive block of the optical image sensor is such that a clear image is obtained from a living organism, and an unclear image is obtained from a replica. If the finger is an actual living finger, the fingerprint images from both blocks are clear, but in the case of a replica, the image from the block having infrared sensitivity is clear, and the image from the block without having infrared sensitivity is unclear.

Abstract: A method of analyzing and recognizing fingerprint images that utilizes vector processing of a vector field that is defined as the tangential vector of the fingerprint ridge curves is disclosed. The raw fingerprint image is divided into blocks, filtered to remove noise, and the orientation direction of each block is found. This allows the ridge curves to be enhanced and approximated by piece-wise linear approximations. The piece-wise linear approximations to the ridge curves allow the minutiae to be extracted and classified and a fingerprint minutiae template to be constructed. An enrollment process gathers multiple fingerprint images, creates fingerprint minutiae templates corresponding to the acquired fingerprint images, and stores the templates and other data associated with the respective individual or the enrolled fingerprint in a fingerprint database.

Abstract: A portable biometric device enables a designated person to unlock any one portal exclusive of other portals of a secure entity and or a secure service by choosing which of their personal biometric characteristics is presented to the portable biometric device. The portable biometric device includes a biometric sensor such that a biometric characteristic of a person for example a finger pattern is read dependent upon the person presenting the biometric characteristic to the biometric sensor. The reading is encoded in order for a processor to determine if the biometric characteristic has been predesignated for access via a predesignated one of the plurality of portals. If so, the processor selects an appropriate authorization code which is communicated by wireless transmission for unlocking the predesignated one of the portals, to the exclusion of any other of the portals. In an alternate example the processor is a central controller remote from the biometric device.

Abstract: The present invention is a personal computer system and method including a biometric sensor which is protected from environmental forces and which resists certain attacks by sensing whether a living person is providing the biometric identification. A second sensor provides an input as to whether the biometric input is from a living person, through the sensing of a life-indicative parameter such as an appropriate level of blood oxygen in the sensed item, and the sensors are covered by a removal cover which provides electrostatic discharge when the cover is opened.

Abstract: An apparatus for supporting a combined substrate structure, comprising first and second substrates combined, includes: level-adjustable supporting mechanisms for supporting plural supporting points of a bottom surface of the combined substrate structure; a level-detecting system for detecting respective levels of corresponding points of a top surface of the combined substrate structure to the plural supporting points of the bottom surface; and a control system for receiving the detected levels from the level-detecting system and for controlling the plurality of level-adjustable supporting mechanism in respective level-adjustment operations in accordance with the detected levels.

Abstract: Embodiments of an architecture for processing gray-level images is disclosed.

Abstract: A buffer assisted data storage method and system has built-in fingerprint recognition function. Recognized data is provided with a high hit-rate in a short time with the assistanace of a buffer, when a user processes his/her identity recognition through the built-in fingerprint recognition module of the data storage device. As a result, the entire identification and verification process is faster and more efficient. In addition, with the aim of enhancing flexibility of usage, an operation setup interface is introduced to optimize the overall performance of the buffer.

Abstract: A method for determining reference points in a fingerprint image is used for determining similarity values using a determination of orientation patterns and a comparison with reference orientation patterns, in which the similarity values are compared with a first threshold value to determine whether a reference point is identified or not. Whorl, delta or core points are identified as core points. Both a linear and a nonlinear reference orientation pattern are used for core points. The orientation pattern for an image area is converted into a vector field for comparison with the reference orientation patterns. A scattering is computed from the spectral power density, which is determined for computation of orientation patterns, and severely distorted image areas are thereby eliminated from the determination of reference points.

Abstract: A method and apparatus generates fingerprint data for a fingerprint area larger than a sensing area of a fingerprint sensor. A fingerprint of a user is enrolled by generating fingerprint data sets responsive to placing a finger of a user on a sensing area of the fingerprint sensor a plurality of times with the finger being slightly repositioned on successive placements. The method also includes processing the fingerprint data sets to generate a composite fingerprint data set over an area of the fingerprint larger than the sensing area of the fingerprint sensor. The method may also be extended to the matching of a new fingerprint to an enrolled fingerprint based upon at least one sensing of the new fingerprint and the composite fingerprint data sets.

Abstract: An apparatus and method for enrolling at least one fingerprint and determining a match of a new fingerprint thereto uses data related to fingerprint ridge flow for matching a desired area segment of a new fingerprint to a corresponding area segment stored in a database. The apparatus generates and stores enrollment data based upon fingerprint ridge flow over a plurality of area segments for the at least one fingerprint, senses a new fingerprint, and generates sensed data based upon fingerprint ridge flow of the new fingerprint over at least one desired area segment of the plurality of area segments. The method also preferably includes comparing the enrollment data and sensed data to determine whether the new fingerprint matches an enrolled fingerprint. The generating of sensed data preferably comprises identifying and generating sensed data for only a single desired area segment in one embodiment.

Abstract: The present invention relates to a method, system and computer program product for enabling the remote authentication of fingerprints over an insecure network using a client-server architecture by generation of a set of random queries relating to fingerprint patterns based on stored fingerprint data at the server, to which the client responds based on the observed fingerprint patterns, followed by the issuing of a randomly generates set of challenges pertaining to geometrical relationships between the fingerprint patterns for which confirm responses are received by their server, the final authentication being determined by the proportion of correct responses by the client to said challenges.

Abstract: A prescreen filtering method and algorithm based upon Attributed Relational Graph (ARG) techniques are employed in a node-by-node matching to individually determine a best alignment of the sets of minutia of a pair of search and file fingerprints. First, the directional components of each and every different pair of minutia from the two sets are compared to ensure that they are within a given angular tolerance, which is selected to allow for a reasonable variation in possible rotational misalignments. After this directional alignment tolerance criteria has been passed, a Distance Matrix (DM) score is generated for each passed [u,v] minutia pair by performing a virtual alignment of the [u,v] minutia pair in location and direction, and then by comparing the distances and relative orientations between each of four pairs of minutia neighbors in each of the four local quadrants, which represents how well each different [u,v] minutia pair match each other.