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1.
The Interpretation of Line Drawings with Contrast Failure and Shadows   总被引:4,自引:0,他引:4  
In line drawings derived from real images, lines may be missing due to contrast failure and objects with curved surfaces may cast shadows from multiple light sources.This paper shows that it is the presence of shadows, rather than contrast failure, that renders the line drawing labelling problem NP-complete. However, shadows are a valuable visual cue, since their presence is formally shown to reduce the average ambiguity of drawings. This is especially true when constraints concerning shadow formation are employed to differentiate shadow and non-shadow lines.The extended junction constraint, concerning straight lines colinear with junctions, compensates the loss of information caused by contrast failure. In fact, we observe the contrast failure paradox: a drawing is sometimes less ambiguous when lines are partly missing due to contrast failure.It is known that the coplanarity of sets of object vertices can be deduced from the presence of straight lines in the drawing. This paper shows that these coplanarity constraints are robust to the presence of contrast failure.  相似文献   

2.
Interpreting line drawings of curved objects   总被引:6,自引:2,他引:4  
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.  相似文献   

3.
A shape-from-shading method of polyhedral objects using prior information   总被引:1,自引:0,他引:1  
We propose a new method for recovering the 3D shape of a polyhedral object from its single 2D image using the shading information contained in the image and the prior information on the object. In a strict sense, we cannot recover the shape of a polyhedron from an incorrect line drawing, even if it is practically almost correct. In order to overcome this problem, we propose a flexible face positioning method that can permit inconsistencies in the recovered shape that arise from vertex-position errors contained in incorrect line drawings. Also, we propose to use prior information about the horizontality and verticality of special faces and the convex and concave properties of the edges in order to attain good solutions and present a method of formulating such prior information as physical constraints. The shape-from-shading method is formulated as a minimization problem of a nonlinear cost function with the nonlinear constraints and its solution is searched by a global optimization algorithm. In the experiments with a synthetic image and three kinds of real images, shapes that are similar to those of the actual objects were recovered in all cases. As a result, the proposed method has proven to be effective in the shape recovery of simple-shape polyhedral objects.  相似文献   

4.
This paper presents a direct method to recover the geometry of the 3D polyhedron depicted in a single parallel projection. It uses two sets of information, the list of faces in the object, obtained automatically from the drawing, and a user-identified cubic corner, to compute for the coordinates of the vertices in the drawing and thus establish the 3D geometry of the whole polyhedron. The algorithm exploits the topological structure of the polyhedron, implicit in the connectivities between the faces, resulting in a complexity that is linear in the number of faces. The method is extended to objects with no cubic corners as well. The algorithm works well for recovering objects from accurate line drawings, producing accurate 3D objects. A simple extension to the algorithm allows it to handle inaccurate drawings such as sketches, and produce 3D objects that are consistent with our human perception of the drawings.  相似文献   

5.
Overcoming superstrictness in line drawing interpretation   总被引:1,自引:0,他引:1  
Presents an algorithm for correcting incorrect line drawings-incorrect projections of a polyhedral scene. Such incorrect drawings arise, e.g., when an image of a polyhedral world is taken, the edges and vertices are extracted, and a drawing is synthesized. Along the way, the true positions of the vertices in the 2D projection are perturbed due to digitization errors and the preprocessing. As most available algorithms for interpreting line drawings are "superstrict," they judge these noisy inputs as incorrect and fail to reconstruct a three-dimensional scene from them. The presented method overcomes this problem by moving the positions of all vertices until a very close correct drawing is found. The closeness criterion is to minimize the sum of squared distances from each vertex in the input drawing to its corrected position. With this tool, any superstrict method for line drawing interpretation is now practical, as it can be applied to the corrected version of the input drawing  相似文献   

6.
This paper presents a new method for recovering three-dimensional shapes of polyhedral objects from their single-view images. The problem of recovery is formulated in a constrained optimization problem, in which the constraints reflect the assumption that the scene is composed of polyhedral objects, and the objective function to be minimized is a weighted sum of quadric errors of surface information such as shading and texture. For practical purpose it is decomposed into the two more tractable problems: a linear programming problem and an unconstrained optimization problem. In the present method the global constraints placed by the polyhedron assumption are represented in terms of linear algebra, whereas similar constraints have usually been represented in terms of a gradient space. Moreover, superstrictness of the constraints can be circumvented by a new concept ‘position-free incidence structure’. For this reason the present method has several advantages: it can recover the polyhedral shape even if image data are incorrect due to vertex-position errors, it can deal with perspective projection as well as orthographic projection, the number of variables in the optimization problem is very small (three or a little greater than three), and any kinds of surface information can be incorporated in a unifying manner.  相似文献   

7.
8.
Floating point round-off causes erroneous and inconsistent decisions in geometric modelling algorithms. These errors lead to the generation of topologically invalid boundary models for CSG objects and significantly reduce the reliability of CAD applications. Previously known methods that guarantee topological consistency by relying on arbitrary precision rational arithmetic or on symbol-manipulation techniques are too expensive for practical purposes. This paper presents a new solution which takes as input a “fixed precision” regularized Boolean combination of linear half-spaces and produces a polyhedral boundary model that has the exact topology of the corresponding solid. Each half-space is represented by four homogeneous coefficients infixed precision format (La bits for the three direction cosines and Ld bits for the constant term, i.e. the distance from the origin). Exact answers to all topological and ordering questions are computed using a fixed length, 3 La+ Ld+ 2 bits, integer format. This new guaranteed tight limit on the number of bits necessary for performing intermediate calculations is achieved by expressing all of the topological decisions based on geometric computations in terms of the signs of 4 by 4 determinants of the input coefficients. The coordinates of intersection vertices are not required for making the correct topological decisions and hence vertices and lines are represented implicitly in terms of planes.  相似文献   

9.
In previous optimization-based methods of 3D planar-faced object reconstruction from single 2D line drawings, the missing depths of the vertices of a line drawing (and other parameters in some methods) are used as the variables of the objective functions. A 3D object with planar faces is derived by finding values for these variables that minimize the objective functions. These methods work well for simple objects with a small number N of variables. As N grows, however, it is very difficult for them to find expected objects. This is because with the nonlinear objective functions in a space of large dimension N, the search for optimal solutions can easily get trapped into local minima. In this paper, we use the parameters of the planes that pass through the planar faces of an object as the variables of the objective function. This leads to a set of linear constraints on the planes of the object, resulting in a much lower dimensional nullspace where optimization is easier to achieve. We prove that the dimension of this nullspace is exactly equal to the minimum number of vertex depths which define the 3D object. Since a practical line drawing is usually not an exact projection of a 3D object, we expand the nullspace to a larger space based on the singular value decomposition of the projection matrix of the line drawing. In this space, robust 3D reconstruction can be achieved. Compared with two most related methods, our method not only can reconstruct more complex 3D objects from 2D line drawings, but also is computationally more efficient.  相似文献   

10.
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