INFERENCE OF SEGMENTED, VOLUMETRIC SHAPE FROM INTENSITY IMAGES

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1 INFERENCE OF SEGMENTED, VOLUMETRIC SHAPE FROM INTENSITY IMAGES Parag Havaldar and Gérard Medioni Institute for Robotics and Intelligent Systems University of Southern California Los Angeles, California Abstract We present a method to infer segmented and volumetric descriptions of objects from intensity images. Our descriptions are in terms of Generalized Cylinders (GCs). We use three weakly calibrated images taken from slightly different viewpoints as input, where the object is only partially visible. There are parts of the object whose surfaces are facing away from the camera and parts are self occluded. Arriving at volumetric descriptions in these cases, with only partial data, requires the development of strong inference rules. These rules are based on the local properties of GCs.We first detect groups in each image based on proximity, parallelism and symmetry. The groups are matched and their contours are labelled as true and limb edges. We use the information about groups and the label associated with its contours to recover visible surfaces. We then use local properties of GCs to obtain the position of the GC axis and the cross sections to make a volumetric inference. The final descriptions are volumetric and in terms of parts. We demonstrate results on real images of moderately complex objects with texture and shadows. 1 Introduction Shape description of objects from one or few intensity images is an important problem in computer vision. Researchers have attempted to describe objects in terms of points, lines, surfaces and volumes. Among them, volumetric descriptions are the richest and most descriptive, but difficult to obtain because not all the object is visible from one, two or three images. In such cases, strong inference procedures need to be developed to recover a volumetric description. In this paper, we propose a method of inferring, volumetric, segmented (or part-based) descriptions in the presence of noise, texture, shadows. Such descriptions provide compact * This research was supported in part by the Advanced Research Projects Agency of the Department of Defense and was monitored by the Air Force Office of Scientific Research under Contract No. F The United States Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright notation hereon. representations which can be used to recognize objects, manipulate them, navigate around them and learn about new objects. We use as input three weakly calibrated (known epipolar geometry) intensity images of an object from slightly different view points and generate volumetric descriptions in terms of Generalized Cylinders (GCs). We start by motivating our approach in the light of existing theories of object recognition, and review relevant work. 1.1 Motivation Humans seem to understand the shape of objects from intensity images with little effort, even if the objects are occluded, novel, rotated in depth or extensively degraded. However, computer vision has made only a small progress in this direction. Here, we address a few issues which have motivated our work. The need for representing objects in terms of volumetric parts has been shown by Biederman [1] in the psychology field. Similar ideas based on Generalized Cylinders (GCs) have been proposed by Nevatia and Binford [12] in computer vision. However, deriving such descriptions from real images, in a data driven-fashion, poses many problems. Among them are discontinuous boundaries, the presence of texture and shadows, occlusion etc. In our case, we extract representations in terms of GCs. In the image, these GCs give rise to symmetries, which are extracted in a hierarchical fashion using grouping. The three views we use, help to label the contours of these groups as true edges or limb edges [2][5][16]. Volumes are then be inferred using the groups, the label associated with their contours and properties of a subclass of GCs. As a result of this representation scheme, however, objects which can be better described by statistical features, for example waves, bushes, cannot be dealt with. 1.2 Summary of previous work Mackworth [10] and Kanade [9] used skew symmetries as a basis for constraining face orientations of polyhedral objects. Ulupinar and Nevatia [15] have addressed the recovery of a certain class of objects - zero Gaussian curvature surfaces (ZGCs). They worked on texture-free perfect line drawings. Ponce et al [13] have

2 derived important projective invariant properties of another class of objects - straight axis, homogeneous cross section, generalized cylinders (SHGCs). Zerroug and Nevatia [18] [19] have addressed the segmentation and recovery of a class of GCs - SHGCs and PRCGCs. They have derived strong invariant properties for their detection in images, but the volumetric recovery is limited only to cases where cross sections can be clearly seen. Unlike the above approaches, which deal with only one image, our previous work [5] addresses a more general class of GCs. We use three weakly calibrated views of the object, which enables us to label edges as true edges and limb edges. This additional information helps in the volumetric recovery. However, the volumetric inference in [5] is limited to objects made of GCs have circular cross sections. Vaillant and Faugeras [16], Cippola and Blake [2] have shown how to compute the local structure along the occluding or limb contours using three calibrated images. They match corresponding points in three images and hence are able to give the surface structure only locally along the contour. Other approaches using structure from motion [14] also used point based tracking and hence do not address segmented descriptions. Joshi et al [8] estimate the structure of the silhouette contour using a trinocular stereo rig. Multiple estimates over time of the structure of such silhouettes are then integrated into a 3-D description of the objects. In conclusion, segmented, volumetric descriptions from intensity images have been derived only for specific classes of GCs [15][18][19] and only under restricted conditions. In section 2 we give an overview of our approach and explain properties of Generalized Cylinders which we make use of in the inference process. In sections 3 and 4, the complete volumetric inference and reasoning procedures have been presented. Sometimes enough information cannot be extracted from the edge images to make volumetric inferences. This has been explained in section 4. Finally in section 5 we give our conclusions and directions for required future work. 2 Overview of our approach The flowchart illustrating our approach is shown in Figure 1. We start with three weakly calibrated (known epipolar geometry) intensity images of an object from close viewpoints. Groups are extracted for each view based on proximity, parallelism and symmetry. Next, these groups are matched in all the images and their contours are labelled as occluding or limb edges which are viewpoint dependent, and true edges which are due to surface discontinuities and surface marking. Groups having contours labelled as limb edges are hypothesized to come from smooth surfaces, while those with true edges are hypothesized to come from surfaces. These surfaces are then reasoned with to image 1 image 2 image 3 Extraction of groups Matching groups of three images using epipolar geometry Label contours of matched groups Figure 1 Groups with True edges Hypothesize surfaces in 3-D Extraction of groups Groups with Limb edges Inference of Volumes Hypothesize smooth GCs in 3-D Description of approach Extraction of groups 3-D volumetric descriptions in terms of parts Axes (a) (b) (c) Figure 2Examples of GCs - with straight and curved axes. make volumetric inferences by using local properties of generalized cylinders. Volumetric inferences are made for all types of groups - having all edges true, all limb or a combination of both. Properties of Generalized Cylinders To uncover the underlying volume or GC requires identifying and delineating the cross section, the axis of the GC and the scaling function. To compute these entities we use properties of GCs. The generic GC representation is too general to give specific invariant properties for every type (or class) of GCs. An observation to be made here is that when the GC axis is straight, it can be locally approximated as a straight homogeneous cross section GC (SHGC). When the axis is curved (planar or non-planar), the GC can be locally approximated as a Planar Axis, Constant cross section GC (PRCGC). We therefore use some of the properties of these subclasses of GCs, to locally infer the position of the axis and the volume. Researchers [13][15][17][18][19] have used these properties to group contours in a image. Here we use them to infer volumes in 3-D. We consider two cases:. GC axis is straight. Figure 2 (a) and (c) show examples of this case where the GC axis is straight. Here the surface axes may be straight or curved (Figure 3). For a GC whose axis is

3 V U Lines of correspondence co-intersect - Property 1 Meridians (a) Three views of a monitor and detected edges S Figure 3 GC with straight axis straight and the cross section is homogeneous, we have the following properties. Property 1 - In 3-D, the lines of correspondence (lines joining co-cross sectional points, see Figure 2) between any pair of cross section curves are either parallel or intersect the GC axis at the same point. (proved in [18]). Property 2 - In 3-D, the meridians of the GC are planar and the axis of the GC lies in this plane. Proof - Since the axis is straight, the GC may be parameterized as follows - S( t, s) = ( u()r t ( s) sinα, v ()r t ( s), s+ u()r t ( s) cosα) where u() t, v() trepresent the cross section plane and s is the axis direction as shown in Figure 2. α is the angle the cross section makes with the axis. Now meridians are curves of constant t, - ar ( s), br ( s), s+ cr( s), where a, b and c are constants. To prove that the meridians are planar, we show that the normal to the plane formed by any point on the meridian P(s) and two points on the axis, say A(0, 0, 0) and B(0, 0, s o ) is constant. The normal is defined as the cross product of vectors P(s)-A and P(s)-B. n( s) = ( P( s) A) ( P( s) B) n( s) = P( s) B, because P( s) P( s) is 0 and A is the origin (0, 0, 0) n( s) = bs r( s), as r( s), 0, or when normalized o o n( s) = bs, as, 0, which is a constant, Q.E.D o o GC axis is curved. Here the surface axes of the GC are curved. An example is shown in Figure 3(b). As stated above, we may consider such volumes to be locally composed of PRCGCs. For such GCs, we have the following property. Property 3 - The meridians of a PRCGC are parallel symmetric. (proved in [15][19]) 3 Inferring volumetric primitives In the following subsections, we describe inference mechanisms to deduce volumetric primitives using these properties. First, in section 3.1 we give a brief explanation of extracting groups and labelling their con- True (c) Labelled edge (b) Example of a matched skew symmetry (above) and parallel symmetry (below) Figure 4 Three views of a monitor (a), matched groups (b), labelled edges (c) tours. Then we describe the inference procedure, which depends on the type of groups formed - having contours with only true edges (3.2), with limb edges (3.3) or both (3.4). Here we locally infer the shape of the GC axis, the cross section and the volume using the above properties. 3.1 Extracting groups and labelling contours We start with three weakly calibrated (known epipolar geometry [3]) intensity images of an object from close viewpoints. Groups are extracted for each view based on proximity, parallelism and symmetry in a hierarchical manner. The efficient extraction of such a grouping hierarchy is described in [6] and [7]. Next, these groups are matched in all the images and their contours are labelled as occluding or limb edges and true edges. Three views are required for deciding the labels of contours in the image [2][5][16]. An example of the matching and labelling procedure (which is detailed in [5]) is shown in Figure 9. Most of the edges are labelled as true here. The rest of the edges remain unlabeled because no correspondences for groups with these edges could be found. Once the groups are extracted and the contours labelled we can then proceed to infer volumetric parts. 3.2 Inferring volumetric parts for groups with true edges Groups with contours labelled as true edges are hypothesized to come from surfaces in 3-D. These surfaces are obtained by disparity measurements between the respective contours in any two images after ensuring that the two image planes are parallel. Examples of some generated surfaces are shown in Figure 5. Other surfaces generated were found to lie on one of these surfaces and hence were interpreted as texture groups.

4 Figure 5 Examples of surfaces generated from groups with edges labelled true. To recover the volume comprised of these surfaces, we need to reason about which surface plays the role of the cross section (if visible), which are the sides, where the axis of the volume is located and those which have nothing to do with the volumetric description. The scaling function for the cross-section also needs to be computed. As mentioned before, all the surfaces and the cross section forming the primitive may not be visible. Even if they are visible, they could be partially occluded. Rigid deduction rules have to be developed to perform the required task. The properties discussed earlier are used to recover all the parameters, the cross section, the sides and the axis of the GC primitive. Next we explain how to compute the GC axis, the sides and the cross section Computing the GC axis (and sides) Surfaces with their respective surface axes have been computed. We make a distinction between straight and curved axis. GC axis is straight. If the GC axis is straight, then we assume that the GC locally obeys properties of an SHGC. If the surface axes are straight, they may be either parallel or the intersect at a common point (Property 1). If curved, then the lines joining their respective endpoints intersect at a common point (Property 1). We group the surfaces whose axes obey these properties and say that their corresponding surfaces form the sides of the GC. Since meridians are planar with the GC axis (Property 2), the GC axis can be computed as the intersection of two (or more) planes (see Figure 6-a). The computed axis for the monitor example is shown in Figure 7. In certain cases, the axes computed might not correspond to the intuitive axis of the volume, but would generate a correct description as long as the cross section is swept relative to it. Planes perpendicular to sides Surface Axes Surface and plane perpendicular to sides GC Axes (a) GC axis is straight (b) GC axis is curved Figure 6 Computation of the GC axis for GCs with true edges. GC axis is (a)straight (b) curved. GC axis is curved. If the GC axis is curved, then we assume that the GC locally obeys properties of a PRCGC. The meridians (and hence surface axes) are locally parallel symmetric (Property 3). We group together all surface axes which are locally parallel symmetric. Their respective surfaces form the sides of the GC. For any two side surfaces we may define another surface which is perpendicular to it and passing though the surface axis. The GC axis then is the intersection of two (or more) such surfaces. An example of this computation is shown in Figure 6 (b) Computing the cross section The cross sections of the various parts forming an object may or may not be completely visible. Here we discuss how to recover and/or infer the cross section in such cases: Cross section is visible If the cross section is visible in the edge images, and it forms a high level group, then it will be recovered as one of the surfaces forming the volume. While all the other axes of sides obey specific properties (section 3.2.1), the cross section surface will be the surface whose axis has a direction nearly orthogonal to the GC axis. In cases, where the GC axis is not unique, multiple interpretations are formed as shown in Figure 3 (c). Here, there are three possible GC axis, and correspondingly three cross-section surfaces. The inferred cross section for the PC monitor example is shown in Figure 7. Figure 7 Computed GC axis and cross section for the PC monitor example Cross section is not visible If the cross section is not visible, or if it is visible and does not form a high level group, then it will not be recovered as one of the surfaces forming the volume. In this case, the cross section is recovered in a two step process as shown in Figure 8. First the GC axis is computed using the observed surfaces and their corresponding surface axes as explained in section Next, at any given point on the GC axis a plane perpendicular to the axis is defined, which intersects the surfaces to give part of the cross section. The object shown in Figure 8 is made of three parts. No cross section curves can be observed for the middle part. However, the visible contour of the cross-section can be inferred. In the absence of further information, this partial cross section may then be completed using

5 Surface axes Plane perpendicular to GC axis Object made of three parts. For the middle part, no cross section can be seen. Recovered GC axis Hypothesized part of cross section cross section completed assuming symmetry (a) Recovered volume shown from different viewpoints Figure 8 Hypothesizing cross sections simple regularity measures such as symmetry or reflection.the scaling function for the cross section can be obtained from the surfaces which form the sides and the volume can then be generated. In Figure 9 we show multiple views of the inferred volume for the PC monitor example. There were 13 high level, matched groups computed in all the views. Groups with contours labelled as true edges were hypothesized as surfaces in 3-D. These resulting surfaces were reduced to 5 because some were subsumed by others since they formed the same surface in 3-D. The final 5 surfaces were analyzed to find the position of the axis and the cross section of the underlying GC.The corresponding scaling function for the cross section was obtained from the groups forming the sides and the GC axis. An observation to be made here is that the cross sections are slightly warped (and may appear so in some of the views). This is because all reconstruction is done with uncalibrated views and hence it will be correct up to a projective reconstruction. In Figure 10 and Figure 11, we show another example of the performance of our system. Three views of a tool part are shown in Figure 10 (a). There were 14 high level, matched groups computed in all the views and their contours were labelled. Groups with contours labelled true edges generated surfaces. The surfaces were analyzed to find the position of the axis and the cross section of the underlying GC. The inferred volumetric parts are shown in Figure 11. The cross section of the first part (a), which could not be observed in the images, was inferred and completed using regularity. Volumetric inference for groups with limb edges, which formed the smooth GCs, is described in the next section. The recovered volume is shown projected from different viewpoints in (b) and with texture of the visible part mapped on the surfaces in (c). In the textured images, the black areas indicate portions where no texture was visible in any of the views. (b) Recovered volume shown with texture mapped Figure 9 Inferred volumetric shape of the PC monitor Figure 10 (a)three views of a tool and detected edges (b) Recovered volume shown from different viewpoints (c) Recovered volume shown with mapped texture Inferred volumetric description for a tool Figure 11 shows the inferred volumetric parts and the computed symbolic description. Here nodes indicate the part detected and the edges specify the adjacency relationships. 3.3 Inferring volumetric parts for groups with limb edges In this section, we deal with groups having contours labelled as limb or occluding edges. We make use of quasi invariant properties of straight and curved axis

6 (d) (c) (a) (b) (c) (d) Figure 11 Segmented parts of the tool and the computed symbolic description GCs described by Zerroug and Nevatia [17] to reconstruct the volume, namely, the projection of the axis of the smooth GC coincides with the axis of the projection. Therefore, the 3-D-axis of the volumetric part is first recovered by a disparity computation [5] on the axes in the two images. If the cross section can be seen in the two images, which is rarely the case, then it can be computed in 3-D. If absent, we assume the cross section to be circular. In the presence of additional data, such as texture on the surface, circular cross sections are then globally modified to fit this texture data. (a) Three views of a bottle and detected edges (b) (a) Body before correction (b) Body after correction Figure 13 Parts of bottle(above) and viewpoints with texture mapped on surface (below) 3.4 Inferring volumetric parts for groups with a mixture of both edges In this section we address the problem of extracting the volumetric shape of GC primitives whose surfaces are both planar and smooth. The edge image of such objects gives rise to groups with contours having both labels - true and limb. Examples of such volumetric GCs are shown in Figure 14. Computing the GC axis can be done similar to section However the cross section here needs to be well approximated when it is not visible. We therefore have the following two case: Cross-section is visible: In case the cross-section is visible, and it forms a high level group in all three images, then it will be recovered as one of the surfaces forming the volume (as explained before). The GC axis can be approximated as explained in The cross section then is the surface whose axis is almost orthogonal to the GC axis. Limb edge (c) Top Recovered volume with the two parts shown from different viewpoints Figure 12 Inferred volumetric description of a bottle An example of this process is shown in Figure 12 and Figure 13. In this case 9 high level groups were formed. The groups with limb edges were first hypothesized as GCs with circular cross sections, which resulted in two parts - the body with a circular cross section shown and the in Figure 13 (a) and (c). The groups with contours labelled as true edges, were hypothesized as surfaces in 3-D. These surfaces were found to lie inside the hypothesized body. The cross sections of the body were then globally modified to fit the texture data. The body after such a correction is shown in Figure 13 (b).the recovered bottle is shown shaded from three different viewpoints in Figure 12 (below) and with texture of the visible portion mapped on its surface Figure 13 (below). Here parts where texture information is not available appears black. True edge Figure 14 Examples of GCs which generate groups with a combination of true and limb edges Cross-section is not visible: It is more interesting to recover the volume if the cross section cannot be seen. Since the side surfaces are made of true and limb edges, the cross section is a combination of polygonal and curved arcs. Although there is not enough information to infer the true shape of the cross section here, it can be well approximated. This is a two step process and is depicted in Figure 15. Here again, the GC axis can be first recovered using a reasoning similar to that presented in section Next, at any given point, a plane perpendicular to the axis is defined. This plane intersects the surfaces in different points -true points, which are points on true edges and limb points, which are points on limb edges. Joining

7 consecutive true points gives us the polygonal part of the visible cross section. The remaining part of the cross section made up of smooth curves may then be approximated by using the best fitting circular or elliptical arc as shown in Figure 15. The cross section here is only an approximation near the limb edges. Limb edge True edge Surface axes (a) Three views of a wooden block and detected edges True Corresponding points of side 1 Limb edge Plane perpendicular to GC axis (b) Example of a matched group Limb (c) Labelled edges Corresponding points of side 2 Figure 15 Recovered GC axis Approximated cross section Approximating the cross section when no cross section is seen In Figure 9, we show an example on a real image. Three views of a block of wood are shown in (a). As seen in the views, this is a very non intuitive object to be described by GCs. Although the cross section changes in size and shape, our approach infers an description which is very close to the actual description. The groups with true edges generated a surface as can be seen in the reconstructed volume. The GC axis was computed and cross sections were approximated at regular intervals by taking planes perpendicular to axis, as explained above. The resulting reconstructed volume is shown in (d). The dark regions in the texture mapped image indicates areas where no texture is visible in the three views. 4 Description of more complex objects In the previous sections, a method to infer volumes from intensity images was proposed. It first extracts and matches groups in three images, labels the contours and hypothesizes surfaces depending on the group and the label of its contours. The surfaces are then used to infer the GC axis, the cross section and the volumes, using properties described in section 3.2. Certain objects cannot be immediately described in terms of GCs. An example in shown in Figure 17. A GC based description is not obvious here because it is difficult to extract reliable groups. Hence, not enough data is present to make use of the properties discussed in this paper and make volumetric inferences. At such times, when no volumetric inferences can be made, the descriptions are kept at the surface level. Three views of a Renault piece and the edge images used as input are shown in (a). Groups were detected and matched. There were 13 high level groups detected (d) reconstructed volume from different viewpoints - rendered (first three) and with texture (fourth) Figure 16 Three views of a wooden block (a), matched groups (b), labelled edges (c), reconstructed volume (d) in all the images and their contours labelled. Volumetric inferences could only be made for two parts. The remaining parts are shown as surfaces (c). The recovered description with texture mapped on the surfaces is shown from three different viewpoints in (b). Here the first two views are from the front. The third view is from behind the recovered object. As seen, the third view does not correspond to the expected view of the object because no volumetric inference could be made for the entire object. 5 Conclusion We have demonstrated inference procedures to generate segmented, volumetric descriptions of an object from three intensity images from close viewpoints. Volumetric representations have been achieved for moderately complex objects, where all surfaces of the object could not be seen in the images. The inference mechanisms have been demonstrated for all types of groups - with true edges, limb edges or a combination of both. Examples on real images show the viability of our approach. For objects which are not well described by GCs, not enough information is available to make an inference about the volumes comprising the object. In such case, the descriptions are left at a surface level. Our current work attempts to generate global volumetric descriptions in terms of GCs. This is so because we work with edge images and valuable intensity information is lost where edges don t show up. As a result, the generated cross sections still need to be locally

8 (a) Three views of a Renault piece and detected edges (b) Recovered volume and surface description shown from different viewpoints (c) Recovered parts - two are volumetric descriptions, three are surface level descriptions Figure 17 Decomposition of the Renault Piece fine tuned, although they are globally well approximated. This process should take into account intensity information available for each cross section in the intensity image and locally modify the cross section using stereo cues. Such a well constrained stereo problem can be solved by correlation along cross sections in two intensity views. Our future work aims to describes objects in terms of volumes which are not only globally correct but also locally well approximated. 6 Bibliography [1] I. Biederman. Recognition-by-Components: A Theory of Human Image Understanding. Psychological Review 1987, Vol. 94, No 2, [2] R. Cipolla and A. Blake. Surface Shape from the Deformation of Apparent Contours. International Journal of Computer Vision, 9:2, , [3] R. Deriche, Z. Zhang, Q.T. Luong, O. Faugeras. Robust recovery of the epipolar geometry for an uncalibrated stereo rig. In Proceeding of the European Conference on Computer Vision, pages , vol I, [4] S. Edelman and H.H. Bulthoff. Orientation Dependence in the Recognition of Familiar and Novel Views of 3-D Objects. Vision Research, 32, pages , [5] P. Havaldar and G. Medioni. Segmented Shape Descriptions from 3-view stereo. International Conference on Computer Vision. pages, Boston, 1995 [6] P. Havaldar, G. Medioni and F. Stein. Perceptual Grouping for Generic Recognition. International Journal of Computer Vision - to appear [7] P. Havaldar, G. Medioni and F. Stein.Extraction of groups for recognition. Proceedings of the European Conference on Computer Vision, volume I, pages , Stolkholm, [8] T. Joshi, N. Ahuja and J. Ponce. Structure and Motion Estimation from Dynamic Silhouettes. Technical Report UIUC-BI-AI-RCV [9] T. Kanade. Recovery of the three-dimensional shape of an object from a single view. Artificial Intelligence, 17: , [10] A.K.Mackworth, Interpreting Pictures of Polyhedral Scenes. Artificial Intelligence, 4: [11] R.Mohan and R. Nevatia. Using Perceptual Organization to Extract 3-D Structures, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 11, No. 11, November 1989, pages [12] R.Nevatia and Th. O. Binford - Description and recognition of curved objects. In Artificial Intelligence, 8(1):77-98, February [13] J. Ponce, D. Chelberg and W.B. Mann. Invariant Properties of Straight Homogeneous Generalized Cylinders and their Contours. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11(9): , [14] C. Tomasi and T. Kanade. Shape and motion from image streams under orthography: a factorization method. International Journal of Computer Vision, vol 9, No 2, Nov 1992, pages [15] F.Ulupinar and R. Nevatia, Perception of 3-D surfaces from 2-D contours, In IEEE Transactions on Pattern Analysis and Machine Intelligence, pages 3-18, Jan [16] R.Vaillant and O. D. Faugeras. Using Extremal Boundaries for 3-D Object Modelling. IEEE Transactions on Pattern Analysis and Machine Intelligence. Vol 14-2, pages , Feb [17] M. Zerroug and R. Nevatia, Quasi-invariant Properties and 3-D Shape Recovery of Non-Straight, Non- Constant Generalized Cylinders. In Proceedings of Computer Vision and Pattern Recognition, pages , 1993, New York. [18] M. Zerroug and R. Nevatia, Segmentation and Recovery of SHGCs from a Single Intensity Image. Proceedings of the European Conference on Computer Vision, pages , Stolkholm, [19] M. Zerroug and R. Nevatia, Segmentation and 3-D Recovery of Curved Axis Generalized Cylinders from an Intensity Image. In Proceedings of the International Conference on Pattern Recognition, 1994.