Interpreting line drawings of curved objects

In this paper, we study the problem of interpreting line drawings of scenes composed of opaque regular solid objects bounded by piecewise smooth surfaces with no markings or texture on them. It is assumed that the line drawing has been formed by orthographic projection of such a scene under general viewpoint, that the line drawing is error free, and that there are no lines due to shadows or specularities. Our definition implicitly excludes laminae, wires, and the apices of cones.A major component of the interpretation of line drawings is line labelling. By line labelling we mean (a) classification of each image curve as corresponding to either a depth or orientation discontinuity in the scene, and (b) further subclassification of each kind of discontinuity. For a depth discontinuity we determine whether it is a limb—a locus of points on the surface where the line of sight is tangent to the surface—or an occluding edge—a tangent plane discontinuity of the surface. For an orientation discontinuity, we determine whether it corresponds to a convex or concave edge. This paper presents the first mathematically rigorous scheme for labelling line drawings of the class of scenes described. Previous schemes for labelling line drawings of scenes containing curved objects were heuristic, incomplete, and lacked proper mathematical justification.By analyzing the projection of the neighborhoods of different kinds of points on a piecewise smooth surface, we are able to catalog all local labelling possibilities for the different types of junctions in a line drawing. An algorithm is developed which utilizes this catalog to determine all legal labellings of the line drawing. A local minimum complexity rule—at each vertex select those labellings which correspond to the minimum number of faces meeting at the vertex—is used in order to prune highly counter-intuitive interpretations. The labelling scheme was implemented and tested on a number of line drawings. The labellings obtained are few and by and large in accordance with human interpretations.

[1]  Takeo Kanade,et al.  Recovery of the Three-Dimensional Shape of an Object from a Single View , 1981, Artif. Intell..

[2]  Takeo Kanade,et al.  A Theory of Origami World , 1979, Artif. Intell..

[3]  Harry G. Barrow,et al.  Interpreting Line Drawings as Three-Dimensional Surfaces , 1980, Artif. Intell..

[4]  H. Whitney.  On Singularities of Mappings of Euclidean Spaces. I. Mappings of the Plane Into the Plane , 1955 .

[5]  David L. Waltz,et al.  Understanding Line drawings of Scenes with Shadows , 1975 .

[6]  Indranil Chakravarty,et al.  A Generalized Line and Junction Labeling Scheme with Application to scene Analysis , 1979, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[7]  Stephen W. Draper,et al.  The Use of Gradient and Dual Space in Line-Drawing Interpretation , 1981, Artif. Intell..

[8]  Kokichi Sugihara,et al.  Mathematical Structures of Line Drawings of Polyhedrons-Toward Man-Machine Communication by Means of Line Drawings , 1982, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[9]  R. Millman,et al.  Elements of Differential Geometry , 2018, Applications of Tensor Analysis in Continuum Mechanics.

[10]  Alan L. Yuille,et al.  An Extremum Principle for Shape from Contour , 1983, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[11]  Vishvjit S. Nalwa,et al.  Edgel aggregation and edge description , 1987, Comput. Vis. Graph. Image Process..

[12]  S. Sutherland.  Seeing things , 1989, Nature.

[13]  A. Macworth.  Interpreting pictures of polyhedral scenes , 1973 .

[14]  J J Koenderink,et al.  What Does the Occluding Contour Tell Us about Solid Shape? , 1984, Perception.

[15]  Thomas O. Binford,et al.  Inferring Surfaces from Images , 1981, Artif. Intell..

[16]  Katsushi Ikeuchi,et al.  Numerical Shape from Shading and Occluding Boundaries , 1981, Artif. Intell..

[17]  Andrew P. Witkin,et al.  Intensity-Based Edge Classification , 1982, AAAI.

[18]  J. Koenderink,et al.  The Shape of Smooth Objects and the Way Contours End , 1982, Perception.

[19]  Alan K. Mackworth.  Interpreting Pictures of Polyhedral Scenes , 1973, IJCAI.

[20]  Herbert Freeman,et al.  Computer Description of Bodies Bounded by Quadric Surfaces from a Set of Imperfect Projections , 1978, IEEE Transactions on Computers.

[21]  Alan K. Mackworth.  Consistency in Networks of Relations , 1977, Artif. Intell..

[22]  Christos H. Papadimitriou,et al.  The complexity of recognizing polyhedral scenes , 1985, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

[23]  Martin C. Cooper.  Interpreting line drawings of curved objects with tangential edges and surfaces , 1997, Image Vis. Comput..

[24]  Gilbert Falk,et al.  Interpretation of Imperfect Line Data as a Three-Dimensional Scene , 1970, Artif. Intell..

[25]  Takeo Kanade,et al.  Gradient space under orthography and perspective , 1982, Comput. Vis. Graph. Image Process..

[26]  Robert M. Haralick,et al.  Understanding Objects with Curved Surfaces from a Single Perspective View of Boundaries , 1985, Artif. Intell..

[27]  Andrew P. Within.  Intensity-based edge classification , 1982, AAAI 1982.

[28]  William S. Havens,et al.  Hierarchical arc consistency: exploiting structured domains in constraint satisfaction problems , 1985 .

[29]  Kent A. Stevens,et al.  The Visual Interpretation of Surface Contours , 1981, Artif. Intell..

[30]  Eugene C. Freuder,et al.  The Complexity of Some Polynomial Network Consistency Algorithms for Constraint Satisfaction Problems , 1985, Artif. Intell..

[31]  A. Rosenfeld,et al.  Edge and Curve Detection for Visual Scene Analysis , 1971, IEEE Transactions on Computers.

[32]  J. M. Rubin,et al.  Color vision and image intensities: When are changes material? , 1982, Biological Cybernetics.

[33]  Kenneth J. Turner,et al.  Computer perception of curved objects using a television camera , 1974 .

[34]  Steven A. Shafer,et al.  Using color to separate reflection components , 1985 .