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![Some impossible figures: (a) is adapted from Penrose and Penrose [9], (b) from Draper [10], (c) from Huffman [11], and (d) from Ernst [12].](profile/Federico-Thomas/publication/3193374/figure/fig10/AS:668658363822099@1536431985797/Some-impossible-figures-a-is-adapted-from-Penrose-and-Penrose-9-b-from-Draper.png)
Some impossible figures: (a) is adapted from Penrose and Penrose [9], (b) from Draper [10], (c) from Huffman [11], and (d) from Ernst [12].
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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 d...
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... the years, several methods have been proposed to test the correctness of line drawings and give their possible reconstructions [2], [3], [4], [5], [6], [7]. These tests succeed in judging as incorrect such impossible figures as those in Fig. 2. However, even when the drawings come from a picture of a real scene, the tests usually judge them as incorrect, failing to derive a spatial reconstruction. To see why, consider the examples in Fig. 1d, showing the projections of two truncated pyramids. These drawings can only be correct when the three edge lines l, m, and n meet at a ...
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Citations
... Junc on points, however, have an essen al role in the interpreta on of the drawing and thus, if the vectorisa on does not find the junc on loca ons directly, these are o en es mated from the intersec on points of lines (Ramel et al., 1998). This approach, while suitable for neat, machinegenerated line drawings, is not suitable for human sketches which are typically drawn sloppily with poorly located junc ons (Ros et al., 2002) as illustrated in Figure 2. Moreover, these algorithms typically assume that the drawings consist predominantly of straight lines and circular arcs. ...
... The problem remains in deducing the hidden, unsketched part of the drawing. Algorithms such as that described in Ros et al., (2002) obtain the full 3D structure by solving planar equa ons of the object surfaces, and assume that a wireframe drawing of the object is available. However, when people sketch, they typically draw only the visible part of the object such that the wireframe drawing is not always readily available. ...
Sketching is a natural and intuitive communication tool used for expressing concepts or ideas which are difficult to communicate through text or speech alone. Sketching is therefore used for a variety of purposes, from the expression of ideas on two-dimensional (2D) physical media, to object creation, manipulation, or deformation in three-dimensional (3D) immersive environments. This variety in sketching activities brings about a range of technologies which, while having similar scope, namely that of recording and interpreting the sketch gesture to effect some interaction, adopt different interpretation approaches according to the environment in which the sketch is drawn. In fields such as product design, sketches are drawn at various stages of the design process, and therefore, designers would benefit from sketch interpretation technologies which support these differing interactions. However, research typically focuses on one aspect of sketch interpretation and modeling such that literature on available technologies is fragmented and dispersed. In this paper, we bring together the relevant literature describing technologies which can support the product design industry, namely technologies which support the interpretation of sketches drawn on 2D media, sketch-based search interactions, as well as sketch gestures drawn in 3D media. This paper, therefore, gives a holistic view of the algorithmic support that can be provided in the design process. In so doing, we highlight the research gaps and future research directions required to provide full sketch-based interaction support.
... The junction position is then found mathematically through line fitting [28]. While this approach works well for neat, machine-generated drawings, human sketches are sloppy, and thus lines do not usually intersect neatly at the junctions, resulting in poorly located junctions [29]. ...
... A better approach would be to take the centroid of the detected points. However, such an approach is known to displace the location of the junction point [29]. We, therefore, configure a set of 11 cosfire filters that are selective for the complete junctions shown in Figure 4, and apply them to a small region around the detected junction points. ...
Engineering design makes use of freehand sketches to communicate ideas, allowing designers to externalise form concepts quickly and naturally. Such sketches serve as working documents which demonstrate the evolution of the design process. For the product design to progress, however, these sketches are often redrawn using computer-aided design tools to obtain virtual, interactive prototypes of the design. Although there are commercial software packages which extract the required information from freehand sketches, such packages typically do not handle the complexity of the sketched drawings, particularly when considering the visual cues that are introduced to the sketch to aid the human observer to interpret the sketch. In this paper, we tackle one such complexity, namely the use of shading and shadows which help portray spatial and depth information in the sketch. For this reason, we propose a vectorisation algorithm, based on trainable cosfire filters for the detection of junction points and subsequent tracing of line paths to create a topology graph as a representation of the sketched object form. The vectorisation algorithm is evaluated on 17 sketches containing different shading patterns and drawn by different sketch-ers specifically for this work. Using these sketches, we show that the vectorisation algorithm can handle drawings with straight or curved contours containing shadow cues, reducing the salient point error in the junction point location by 91% of that obtained by the off-the-shelf Harris-Stephen's corner detector while the overall vectorial representations of the sketch achieved an average F-score of 0.92 in comparison to the ground truth. The results demonstrate the effectiveness of the proposed approach.
... The reconstruction of a 3D model from a single freehand sketch may be resolved in two different ways. One approach is to create a system of equations which represents each plane in the drawing, solving the equations to obtain the 3D coordinates of each vertex [11]. Alternatively, optimisation based approaches, driven by heuristics derived from the principals of human understanding of drawings, can be used to determine the optimal 3D co-ordinates of the vertices [12]- [14]. ...
This paper focuses on the identification of hidden lines and junctions from natural sketches of drawings that exhibit an extended-trihedral geometry. Identification of hidden lines and junctions is essential in the creation of a complete 3D model of the sketched object, allowing the interpretation algorithms to infer what the unsketched back of the object should look like. This approach first labels the sketched visible edges of the object with a geometric edge label, obtaining a labelled junction at each of the visible junctions of the object. Using a dictionary of junctions with visible and hidden edges, these labelled visible junctions are then used to deduce the edge interpretation and orientation of some of the hidden edges. A genetic algorithm is used to combine these hidden edges into hidden junctions, evolving the representation of the hidden edges and junctions until a feasible hidden view representation of the object is obtained.
... Many methods have been proposed for automatically reconstructing 3D objects from single line drawings [5,7,9,10,11,15,17,19,20]. Among these methods, the two in [11] and [20] can handle more complex objects than the others. ...
Reconstructing 3D objects from single line drawings is often desirable in computer vision and graphics applications. If the line drawing of a complex 3D object is decomposed into primitives of simple shape, the object can be easily reconstructed. We propose an effective method to conduct the line drawing separation and turn a complex line drawing into parametric 3D models. This is achieved by recursively separating the line drawing using two types of split faces. Our experiments show that the proposed separation method can generate more basic and simple line drawings, and its combination with the example-based reconstruction can robustly recover wider range of complex parametric 3D objects than previous methods.
... Machine interpretation of diagrams, specifically, the 3D construction of objects depicted in drawings can be achieved by either solving planar equations [LCLT08,RT02] obtained from the diagram or by optimizing some cost function related to the ideal geometry of an object [CGC99, LF92, LS96, PMC03]. While these methods determine the depth coordinates of salient points of the object, other techniques, namely line labelling techniques provide an initial interpretation of the drawing from which an initial inflation of the diagram can be obtained. ...
Artistic cues help designers to communicate design intent in sketches. In this paper, we show how these artistic cues may be used to obtain a line labelling interpretation of freehand sketches, using a cue-based genetic algorithm to obtain a labelling solution that matches design intent. In the paper, we show how this can be achieved from off-line or paper based sketches, thereby allowing designers greater flexibility in the choice of sketching medium.
... Though it takes more effort for the user to draw such line drawings, compared with line drawings without hidden lines, they allow the reconstruction of complete and more complex objects. Much work concerning line drawings with hidden lines has been published in the computer vision literature [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], and in CAD and graphics [13], [14], [15], [16], [17], [18], [19], [20], [21]. The applications of 3D reconstruction from this kind of line drawings include: 1) providing a flexible sketching interface in current CAD systems [14], [16], [18], 2) providing a 2D sketch query interface for 3D object retrieval from large databases or from the internet [19], [22], [23], 3) interactive generation of 3D models from images [9], [17], [20], 4) automatic conversion of existing industrial wireframe models to solid model [13], [14], and 5) building rich databases for object recognition systems and reverse engineering algorithms for shape reasoning [13], [14]. ...
... The earliest work towards 3D reconstruction from single line drawings is line labeling, which focuses on finding a set of consistent labels from a line drawing to test the correctness and/or realizability of the line drawing [3], [4], [5], [16], [24], [25], [26], [27], [28], [29], but it does not explicitly recover a 3D object from a line drawing. Most 3D reconstruction methods from a line drawing assume that the face topology of the line drawing is known in advance. ...
... One example is shown in Fig. 6, which has 15 real faces. From this line drawing, Algorithm 1 finds three internal faces C 1 = (1, 2, 3, 4, 5, 6, 7, 8, 1), C 2 = (1, 2, 3, 4, 5, 8, 1), and C 3 = (5, 8,9,10,5). Since C 1 and C 2 are incompatible according to Property 4, the algorithm finally outputs two solutions: one is C 1 and C 3 and the other is C 2 and C 3 . Note that when C 1 is an internal face, C 1 and the real face (5,6,7,8,5) are on the same plane; when C 2 is an internal face, C 2 and this real face are on different planes. ...
Three-dimensional object reconstruction from a single 2D line drawing is an important problem in computer vision. Many methods have been presented to solve this problem, but they usually fail when the geometric structure of a 3D object becomes complex. In this paper, a novel approach based on a divide-and-conquer strategy is proposed to handle the 3D reconstruction of a planar-faced complex manifold object from its 2D line drawing with hidden lines visible. The approach consists of four steps: 1) identifying the internal faces of the line drawing, 2) decomposing the line drawing into multiple simpler ones based on the internal faces, 3) reconstructing the 3D shapes from these simpler line drawings, and 4) merging the 3D shapes into one complete object represented by the original line drawing. A number of examples are provided to show that our approach can handle 3D reconstruction of more complex objects than previous methods.
... Some related work is about testing the correctness of a line drawing based on algebraic or geometric tests [23], [24], [25], [26], [27] that apply to a line-labelled version of the line drawing. The algorithm presented in [28] tries to overcome the superstrictness problem in this line drawing interpretation. ...
Varley [1] made comments on our paper in [2] section by section. We answer them in this response paper.
... How to bestow this ability on a computer vision system is an important topic. A number of publications have been devoted to this research in the major computer vision literature [8], [15], [20], [21], [22], [23], [25], [29], [30], [31], [32], [33]. The applications of this research include: flexible sketching input for conceptual designers who tend to prefer pencil and paper to mouse and keyboard [3], [19], [22]; providing rich databases to object recognition systems and reverse engineering algorithms for shape reasoning [2], [3]; automatic conversion of industrial wireframe models to solid models [2], [14]; interactive generation of 3D models from images [13], [20], [35]; friendly user interface for 3D object retrieval [5], [27] . ...
... There have been a number of papers discussing 3D reconstruction from single 2D line drawings [6], [8], [15], [19], [20], [25], [28], [29], [30], [32], [33], [35], [36]. However, they handle only line drawings of planar objects. ...
An important research area in computer vision is developing algorithms that can reconstruct the 3D surface of an object represented by a single 2D line drawing. Previous work on D reconstruction from single 2D line drawings focuses on objects with planar faces. In this paper, we propose a novel approach to the reconstruction of solid objects that have not only planar but also curved faces. Our approach consists of four steps: (1) identifying the curved faces and planar faces in a line drawing, (2) transforming the line drawing into one with straight edges only, (3) reconstructing the 3D wireframe of the curved object from the transformed line drawing and the original line drawing, and (4) generating the curved faces with Bezier patches and triangular meshes. With a number of experimental results, we demonstrate the ability of our approach to perform curved object reconstruction successfully.
... Hence, the study of polyhedra is important and useful in many applications of computer vision. However very few elegant methods [20], [21], [18], [16], [17], [19] and [7] have been proposed for the reconstruction of polyhedral objects. The degree of freedom of a planar surface of a polyhedral object is three which can be reduced either by using more than one image or by imposing some extra constraints. ...
... Ros et al. [16] have given a method to correct the incorrect line drawing, in which all vertices are moved in their small neighborhood until a close correct line drawing is found. The problem is formulated as a nonlinear minimization problem. ...
This paper presents a robust approach for the reconstruction of polyhedral objects from line drawings. Minimization technique has been used in this approach by exploiting the shading information contained in the image. The minimization energy function has been formulated between observed and calculated value of image intensity under the Lambertian reflectance model. Various constraints e.g. the surface normal coplanarity and edge length proportionality constraints are used to get the unique solution for the depth values. The minimization problem is nonlinear with nonlinear constraints, which is solved by using Genetic Algorithm. The proposed algorithm produces satisfactory results even in the case of slight error in computation of vertex positions caused in image processing. The algorithm has been tested on synthetic images and the results are shown.
... Sugihara (1999) further proposed the concept " resolvable sequences " for polyhedra and proved that they always exist for spherical polyhedra, i.e., polyhedra which are homeomorphic to a sphere. This result is used by Ros and Thomas (2002) to overcome the super-strictness in scene analysis. In the combinatorial geometry society, the realization problem was studied in a different approach. ...
Polyhedral scene analysis studies whether a 2D line drawing of a 3D polyhedron is realizable in the space, and if so, parameterizing the space of all possible realizations. For generic 2D data, symbolic computation with Grassmann-Cayley algebra is needed in the analysis. In this paper, we propose a method called parametric calotte propagation to solve the realization and parameterization problems for general polyhe- dral scenes at the same time. In algebraic manipulation, parametric propagation is more e-cient than elimination. In application, it can lead to linear construction sequences for non-spherical polyhedra whose resolvable sequences do not exist.
