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18-Geom-A7 Geospatial Information Systems · December 2015

Question 6 of 12: Removing Residual Geometric Distortions on Merge

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

National Exams — December 2015 — 04-Geom-A7 Geospatial Information Systems. Closed-book; an approved Casio or Sharp calculator is permitted. Format: twelve short-answer questions of varying value totalling 100 marks; all questions constitute a complete exam and are solved in full below. Datum and coordinate conventions follow the Canadian spatial reference framework — NAD83(CSRS) horizontally and CGVD2013 vertically.

Reference texts: P. A. Longley, M. F. Goodchild, D. J. Maguire & D. W. Rhind, Geographic Information Systems and Science (4th ed., Wiley, 2015); P. Bolstad, GIS Fundamentals: A First Text on Geographic Information Systems (6th ed., XanEdu, 2019); P. A. Burrough, R. A. McDonnell & C. D. Lloyd, Principles of Geographical Information Systems (3rd ed., Oxford, 2015); M. Worboys & M. Duckham, GIS: A Computing Perspective (2nd ed., CRC, 2004); J. P. Snyder, Map Projections — A Working Manual (USGS PP 1395); ISO 19115 Geographic information — Metadata.

Question 6: Removing Residual Geometric Distortions on Merge (10 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Residual geometric distortions on merge mean that, after each layer has been brought to a common datum and projection, features that should coincide still do not — a road in one dataset is offset from the same road in another. The procedure is a systematic registration / conflation with rubber sheeting:

  1. Establish a reference (base) dataset. Choose the layer of highest known positional accuracy (e.g., a survey-control or orthophoto layer) as the "truth" to which the others will be adjusted, and confirm all layers share one datum, projection and units so only local distortion remains.
  2. Diagnose the distortion. Overlay the datasets and inspect the misalignment: quantify it (magnitude, direction, whether it is a uniform shift, a rotation/scale, or a spatially varying warp). A global systematic error is removed by a single transformation; a varying error needs a local (elastic) fit.
  3. Identify and match control (link) points. Select clearly identifiable common features — road intersections, monuments, building corners — well distributed across the whole area and matched correctly between the source and the reference. Distribution matters more than sheer number: gaps and clusters leave regions poorly constrained.
  4. Apply a global transformation first. Fit a similarity or affine transformation by least squares to remove the systematic component (shift, rotation, differential scale) and examine the residuals to detect blunders and gauge what distortion remains.
  5. Rubber-sheet the residual local distortion. Apply a local elastic (piecewise/triangulated finite-element or spline) warp anchored on the link points so features are pulled onto the reference; displacement is largest at the links and blends smoothly between them, correcting local misfit a global transformation cannot.
  6. Edge-match and reconcile topology and attributes. Snap coincident features across sheet/dataset boundaries, rebuild topology, remove slivers and duplicate geometry, and reconcile conflicting attributes; conflation transfers the best attributes to the merged geometry.
  7. Validate. Check residuals at independent check points, confirm no over-fitting has degraded previously correct areas, and document the accuracy achieved in the metadata/lineage.

The essence is: unify the reference frame, remove the global error by transformation, then remove the remaining local error by rubber sheeting, and finally clean topology and attributes.