Estimation and photogrammetric treatment of linear features

David Mulawa, Purdue University


The three dimensional space of our experience contains many forms of object features. The forms of these object features include point features, linear features, surface features and volume features. The emphasis in this thesis is on the linear features as contained in a three dimensional object space. Theory was developed for linear features to address the following aspects: modeling, efficient least squares adjustment techniques, quality assessment, and geometric interaction among several linear features. All together, this thesis forms a basis for a synoptic theory for the estimation of linear features. Included is specific modeling for selected representative forms of linear features. These are: the straight line, the conic sections, the polynomial, the spline, and the general parametric linear feature. Least squares adjustment is the basis for the estimation of the values of the linear feature descriptors. Efficient computational techniques are needed for a practical theory and are an integral part of this thesis. In particular, a method of immediate folding of the normal equations is developed which makes it possible to use a parametric representation of a linear feature in a practical way. Two quality assessment methods are developed for the linear feature. One method is a determination of an equal probability surface that surrounds an estimated linear feature as contained in a three dimensional object space. Another method determines the root mean square (rms) of the distance from an estimated linear feature to a true (or reference) linear feature. Also included is specific modeling for geometric interaction among linear features in the form of: space intersection of linear features; equal linear features and cofeatural linear features; parallel linear features; and coplanarity of linear features. From the general theory, several efficient photogrammetric relationships are developed as a special application. These relationships are used to perform the standard photogrammetric treatments of space intersection, space resection, and triangulation. These treatments are possible without the need to perform a point-to-point (conjugate points) matching among the images. The relationships are suitable for all direction preserving photogrammetric sensors of which the frame camera and the linear CCD array are examples.




Mikhail, Purdue University.

Subject Area

Civil engineering

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