Abstract: Cartographic data is represented using wavelet coefficients. Specifically, a cartographic shape point database consisting of shape points and nodes stored on a per geographic feature basis is converted to a cartographic wavelet database consisting of wavelet and scaling coefficients also stored on a per geographic feature basis. The shape of each geographic feature can be reconstructed from the stored wavelet and scaling coefficients for that geographic feature. The wavelet transform organizes the information in a function according to scale, a concept which is related to resolution. The wavelet-based representation facilitates operations such as line simplification (generalization) and zooming. Multi-resolution error metrics are defined using the wavelet representation for assessing the accuracy of sampled cartographic databases with respect to a ground truth database.

Abstract: Cartographic data is represented using polynomial splines. To improve representation accuracy and reduce storage requirements, a database storing data points (shape points and nodes) is converted into a database of spline control points. The spline control points are computed by fitting a polynomial spline to the geographic features using a least squares approximation. The control points associated with each geographic feature are stored in a computer-usable database. The geographic features can be displayed by computing the spline functions using the stored control points.

Abstract: A geographic database represents roads including an altitudinal component of the geometry of the roads. The altitudinal component of the geometry of roads is represented using data that indicate straight line segments and vertical curves, in particular parabolic vertical curves. The straight lines and vertical curves are determined by providing data, indicating the altitude at a plurality of locations along portions of roads, as an input to a Hough transform to determine the straight line segments and vertical curves that coincide with the portions of the roads vertically. Then, data that define the straight line segments and vertical curves are stored to represent the altitudinal component of the geometry of the portions of the roads in the geographic database. The altitudinal variation of roads is thus expressed in closed form. From this closed form representation, the slope or grade at any point along the road can be easily computed.

Abstract: A method for determining the line segments, circular arcs, and clothoidal arcs that form a complex curve along a length thereof is disclosed. A ?-s curve of the complex curve is determined, which is a plot of tangent angles, wherein the angle is made with a fixed line by a tangent to the complex curve along the length thereof. The straight line portions and parabolic portions of the plot of the ?-s curve are determined and used to determine the corresponding circular arcs and straight lines that form the complex curve and clothoidal arcs that form the complex curve, respectively. The ?-s curve can be used to identify the curves and straight lines that define the geometry of roads and therefore can be used to store data that indicate the geometry of roads in a geographic database that contains data representing the roads.

Abstract: A geographic database represents roads including an altitudinal component of the geometry of the roads. The altitudinal component of the geometry of roads is represented using data that indicate straight line segments and vertical curves, in particular parabolic vertical curves. The straight lines and vertical curves are determined by providing data, indicating the altitude at a plurality of locations along portions of roads, as an input to a Hough transform to determine the straight line segments and vertical curves that coincide with the portions of the roads vertically. Then, data that define the straight line segments and vertical curves are stored to represent the altitudinal component of the geometry of the portions of the roads in the geographic database. The altitudinal variation of roads is thus expressed in closed form. From this closed form representation, the slope or grade at any point along the road can be easily computed.

Abstract: A geographic database represents roads including an altitudinal component of the geometry of the roads. The altitudinal component of the geometry of roads is represented using data that indicate straight line segments and vertical curves, in particular parabolic vertical curves. The straight lines and vertical curves are determined by providing data, indicating the altitude at a plurality of locations along portions of roads, as an input to a Hough transform to determine the straight line segments and vertical curves that coincide with the portions of the roads vertically. Then, data that define the straight line segments and vertical curves are stored to represent the altitudinal component of the geometry of the portions of the roads in the geographic database. The altitudinal variation of roads is thus expressed in closed form. From this closed form representation, the slope or grade at any point along the road can be easily computed.

Abstract: A method for determining how closely two geometric shapes match is disclosed. After scaling the geometric shapes to equal length, corresponding pairs of measurement locations are determined along the linearly extending geometric shapes. Tangent vectors are determined at the measurement locations and the angle made by the tangent vectors associated with each corresponding pair of measurement locations is determined. After translating one of the geometric shapes by an angle equal to the mean of all the angles at the corresponding pairs of measurement locations, the area between the geometric shapes or the maximum deviation between the geometric shapes is determined. This is an indication of how closely the geometric shapes match. This indication can be used in various applications, including vehicle positioning, sign recognition, and evaluation of geographic database accuracy.

Abstract: The degree to which a linearly extending feature, such as a road, curves is indicated using a bowing coefficient. The bowing coefficient at a given location along a linearly extending feature is determined by comparing the distance along the feature between two points on either side of the given location (or an approximation of the distance) to a straight-line distance between these same two points. Bowing coefficient data can be used by various vehicle systems that require information about the curvature of linearly extending features, such as roads upon which the vehicle is traveling.

Abstract: The degree to which a linearly extending feature, such as a road, curves is indicated using a bowing coefficient. The bowing coefficient at a given location along a linearly extending feature is determined by comparing the distance along the feature between two points on either side of the given location (or an approximation of the distance) to a straight-line distance between these same two points. Bowing coefficient data can be used by various vehicle systems that require information about the curvature of linearly extending features, such as roads upon which the vehicle is traveling.

Abstract: The Hough Transform is used to identify the circular arcs and straight line segments that coincide with the horizontal curves of roads. The Hough Transform uses data indicating positions along the roads as an input in order to identify the circular arcs and straight line segments that coincide with the roads. Data indicating the circular arcs and straight line segments are stored in a geographic database and are used to represent the roads. Radius of curvature of the road is obtained as a by product of this representation. Because the Hough Transform yields a closed form representation of road segments, the heading at any point along a road can be computed by computing the tangent to the closed form representation. Thus, heading can be accurately obtained at any point along a road.

Abstract: A method for comparing geometric shapes to each other is disclosed. The method includes determination of a rotational variation metric. The shapes to be compared are scaled so that their lengths are equal and tangent vectors at corresponding locations along the geometric shapes are determined. The angle between each pair of corresponding tangent vectors for each of these locations is then plotted as a function of the length along the geometric shapes. The variation around the mean angle between the tangent vectors for the locations along the geometric shapes being compared is the rotational variation coefficient. This process defines a rotational variation metric which indicates how closely the two geometric shapes match. The rotational variation metric can be used in various geographic applications, including vehicle positioning, sign recognition, and evaluating geographic database accuracy.

Abstract: The degree to which a linearly extending feature, such as a road, curves is indicated using a bowing coefficient. The bowing coefficient at a given location along a linearly extending feature is determined by comparing the distance along the feature between two points on either side of the given location (or an approximation of the distance) to a straight-line distance between these same two points. Bowing coefficient data can be used by various vehicle systems that require information about the curvature of linearly extending features, such as roads upon which the vehicle is traveling.

Abstract: A method of determining geographic feature association between geographic features of a first geographic database and a second geographic database builds a proximity matrix having a proximity value element for each of the features of the first geographic database as compared to each of the features of the second geographic database. A singular value decomposition of the proximity matrix is computed, and the singular value decomposition is converted into an association matrix. Using the association matrix, the method identifies an associated feature pair having one feature of the first geographic database and one feature of the second geographic database.

Abstract: Methods for comparing three-dimensional space curves are provided. Such methods are particularly useful for map matching in in-vehicle navigation systems as well as for other applications that require accurate positioning of the vehicle with respect to the underlying map data referenced by the system. Additionally, they are useful in measuring and/or evaluating the accuracy of a geographic database. Two angles that define the angular orientation of a three dimensional space curve are determined at corresponding locations for each of a first space curve and a second space curve. The variance of the relationship between the angle pairs at corresponding locations along the first and second space curves is utilized to determine the similarity between the first and second space curves despite any spatial translation and angular rotation between the first and second space curves.

Abstract: A method for comparing geometric shapes to each other is disclosed. When used for vehicle positioning, the present method determines which map path of several candidate map paths best matches an actual path traveled by the vehicle as measured by sensors. The vehicle path and each candidate map path are generalized to a given degree of generalization, thereby yielding an overall trend of the vehicle path and overall trends of each of the candidate map paths. The trend of the vehicle path is compared to the trend of each of the candidate map paths. Based on these comparisons, one or more candidate map paths may be eliminated. If more than one map path remains, the vehicle path and each of the remaining map paths are generalized again, this time to a lesser degree of generalization, and comparisons are made between the trend of the vehicle path and the trend of each of the remaining map paths. Based on these comparisons, one or more map paths may be eliminated.

Abstract: Methods for comparing three-dimensional space curves are provided. Such methods are particularly useful for map matching in in-vehicle navigation systems as well as for other applications that require accurate positioning of the vehicle with respect to the underlying map data referenced by the system. Additionally, they are useful in measuring and/or evaluating the accuracy of a geographic database. Two angles that define the angular orientation of a three dimensional space curve are determined at corresponding locations for each of a first space curve and a second space curve. The variance of the relationship between the angle pairs at corresponding locations along the first and second space curves is utilized to determine the similarity between the first and second space curves despite any spatial translation and angular rotation between the first and second space curves.

Abstract: The degree to which a linearly extending feature, such as a road, curves is indicated using a bowing coefficient. The bowing coefficient at a given location along a linearly extending feature is determined by comparing the distance along the feature between two points on either side of the given location (or an approximation of the distance) to a straight-line distance between these same two points. Bowing coefficient data can be used by various vehicle systems that require information about the curvature of linearly extending features, such as roads upon which the vehicle is traveling.