K. Arbter, W. Snyder, H. Burkhardt, and G. Hirzinger. Application of Affine-Invariant Fourier Descriptors to Recognition of 3d Objects. IEEE Trans. on Pattern Analysis and Machine Intelligence, 12, 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....where a similarity measure is sought between two shapes. An usual approach in shape matching is to compute a signature of a shape and then comparing it with the signature of the other shape. Different quantities such as curvature distribution [3, 32] wavelet coefficients [19] Fourier descriptors [2], geometric statistics [4, 33] spin image [20] and shape distribution [24] have been suggested for shape signatures; see survey articles [1, 7, 23, 34] for more details. Another prevalent approach is to segment a shape into its salient features and then match the shapes based on the features and ....

K. Arbter, W. E. Snyder, H. Burkhardt and G. Hirzinger. Application of affine-invariant fourier descriptors to recognition of 3-d objects. IEEE Trans. Pattern Analysis Machine Intelligence, 12 (1990), 640--

....have been proposed to describe the shape of an object undergoing a general affine transform. The following classes of invariants have been studied in the literature: affine area moment invariants [2] 4] affine curve moment invariants [5] cross weighted moments [6] and Fourier descriptors [7], among others. Most of the aforementioned invariants are global, i.e. the whole object must be visible and accessible to calculate them. However, this implies significant limitations when recognizing occluded or locally distorted objects. To overcome this, Yang and Cohen [1] proposed local ....

K. Arbter, W. E. Snyder, H. Burkhardt, and G. Hirzinger, "Application of affine-invariant Fourier descriptors to recognition of 3-D objects," IEEE Trans. Pattern Anal. Machine Intell., vol. 12, pp. 640--647, Aug. 1990.

....is more general than the simple similarity transformation. When a planar object is imaged from multiple viewpoints, the image to image transformation is general projective and the conventional algorithms based on Euclidean and similarity frameworks will not work for them. Klaus Arbter et al. [1] formulated techniques for affine invariant recognition. Their emphasis was on choosing a suitable set of affine invariant features and then perform matching in an affine invariant space. In this paper, we try to analyse the properties of a collection of points, such as a planar object s contour, ....

K. Arbter, W. Snyder, H. Burkhardt, and G. Hirzinger. Application of Affine-Invariant Fourier Descriptors to Recognition of 3d Objects. IEEE Trans. on Pattern Analysis and Machine Intelligence, 12, 1990.

....algorithm for indexing 3D shapes. One problem for indexing 3D surfaces is boundary parameterization. Although the 1D boundary contours of 2D shapes have a natural arc length parameterization, 3D surfaces of arbitrary genus do not. As a result, common shape descriptors for 2D contours (e.g. [7, 8, 47, 52, 90, 96]) cannot be extended to 3D surfaces, and computationally efficient matching algorithms based on dynamic programming (e.g. 85, 88] cannot be applied to 3D objects. Another problem is the higher dimensionality of 3D data, which makes registration, finding feature correspondences, and fitting ....

....Matching hand drawn sketches to projected silhouettes of 3D models poses another problem. Although we prompt users with example sketches containing clean boundary contours, user input is often made up of fragmented sketch marks. Thus, we cannot use efficient contour matching algorithms (e.g. [7, 8, 90]) Instead, we compare sketches and rendered views with an image matching method. To handle deformations and geometric inaccuracies, we first apply the distance transform to both the sketch and rendered image. This helps make our method robust to small variations in the positions of lines, as in ....

Klaus Arbter, Wesley E. Snyder, Hans Burkhardt, and Gerd Hirzinger. Application of affineinvariant fourier descriptors to recognition of 3-D objects. IEEE Transactions on Pattern Analysis and Machine Intelligence, 12(7):640--647, July 1990.

....49, NO. 5, MAY 2001 nonuniqueness of the FD parameterization would lead to a degeneracy in the evaluation of the estimation performance. 3 This problem has been resolved by appropriate normalization with respect to the starting point of the curve in the case of complex FD s representation [33] [34]. This can be done by imposing the constraint in (12) Hence, the set of normalized FD coefficients has only real valued degrees of freedom (instead of for the original FD coefficients) once the ambiguity due to the starting point has been removed. Therefore, the parameter vector in (8) becomes . ....

K. Arbter, W. E. Snyder, H. Burkhardt, and C. Hirzinger, "Application of affine-invariant Fourier descriptors to recognition of 3-D objects," IEEE Trans. Pattern Anal. Machine Intelligence, pp. 640--647, July 1990.

....to 3D model matching. The main problem is boundary parameterization. Although the 1D boundary contours of 2D shapes have a natural arc length parameterization, 3D surfaces of arbitrary genus do not. As a result, common representations of 2D contours for shape matching, such as Fourier descriptors [5], turning functions [6] bending energy functions [60] arch height functions [40] and size functions [55, 56] have no analogs for 3D models. Shape matching has also been well studied for 3D objects. For instance, representations for registering and matching 3D surfaces include Extended Gaussian ....

K. Arbter, W. E. Snyder, H. Burkhardt, and G. Hirzinger. Application of affine-invariant fourier descriptors to recognition of 3-d objects. IEEE Transactions on Pattern Analysis and Machine Intelligence, 12(7):640--647, July 1990.

....Shape is one of important features for describing an object of interest. Even though it is easy to understand the concept of 2D shape, it is very difficult to represent, define and describe it. There are many different methods proposed in the literature such as the Fourier Descriptors [1 2], the moments [3] the Bspline shape representation [4 7] the autoregressive models [2, 8] the Hough Transform [9] the Fractal geometry methods [10] and the Wavelet Transform Zero Crossing Representation [11] Moments have been used extensively for curve recognition and classification. ....

....For shape indexing and recognition, it is necessary that the descriptors obtained from shape representation can be made invariant under affine transform such as translation, rotation, scaling, and different camera orientations. Arbter et al. proposed the AffineInvariant Fourier Descriptors [1]. As mentioned earlier, the Fourier Descriptors cannot be used in the case of occlusion shape. To overcome this problem, Huang and Cohen proposed invariant affine transform of B spline curve representation using weighted curve moments [4] Most shape representations are obtained from objects in ....

[Article contains additional citation context not shown here]

K. Arbter, W. E. Snyder, H. Burkhardt, and G. Hirzinger, "Application of affine-invariant Fourier descriptors to recognition of 3-D objects," IEEE Trans. PAMI, vol. 12, pp. 640-647, July 1990.

....coordinate system is used here to make the representation translation invariant. 3.1. 2 Fourier based shape description In the area of shape analysis and classification, several shape feature representation schemes based on autoregressive (AR) models [7, 25] and Fourier descriptors [1, 21, 35] of contours have been proposed. Recently, an experimental comparison of shape classification methods based on these two principles has been carried out in [12] which indicates that Fourierbased methods provide better performance than AR based approaches, especially for noisy images. For this ....

Arbter K, Snyder WE, Burkhardt H, Hirzinger G (1990) Application of affine-invariant Fourier descriptors to recognition of 3D objects. IEEE Trans Pattern Anal Machine Intell 12: 640--647

....scheme. 3.3 Fourier Descriptors Fourier descriptors are used for the representation of the boundary of two dimensional shapes. The basic idea is to represent a closed curve by a periodic function of a continuous parameter, or alternatively, by a set of Fourier coefficients of this function [2]. Starting with an arbitrary point, coordinate pairs (x 0 ; y 0 ) x 1 ; y 1 ) x n ; y n ) are recorded while traversing the boundary in clockwise direction. The boundary can be represented as a sequence of complex numbers s(k) x k i y k , k = 0; 1; n. Applying the discrete ....

K. Arbter, W. E. Snyder, H. Burkhardt, and G. Hirzinger. Application of affine-invariant fourier descriptors to the recognition of 3-d objects. IEEE Trans. on PAMI, 12(7):640--647, July 1990.

....to 3D model matching. The main problem is boundary parameterization. Although the 1D boundary contours of 2D shapes have a natural arc length parameterization, 3D surfaces of arbitrary genus do not. As a result, common representations of 2D contours for shape matching, such as Fourier descriptors [5], turning functions [6] circular autoregressive models [36] bending energy functions [59] arch height functions [40] and size functions [55] have no analogs for 3D models. Shape matching has also been well studied for 3D objects. For instance, representations for registering and matching 3D ....

Klaus Arbter, Wesley E. Snyder, Hans Burkhardt, and Gerd Hirzinger. Application of affine-invariant fourier descriptors to recognition of 3-d objects. IEEE Transactions on Pattern Analysis and Machine Intelligence, 12(7):640--647, July 1990.

....edges and corners are often used. If two images are the 15 CHAPTER 3. BACKGROUND 16 same, these point sets must be the same. These points can be viewed as invariants under 2 D translation and rotation. Invariants under affine transformation have been studied by [7] using Hough based methods, by [8, 9] using Fourier descriptors, and by [10] using wavelets. The idea of the Hough transformation is to transform points in the spatial feature space into a parameter space, and a specified shape is detected by finding the peaks in the parameter space. In this way, a global evidence accumulation ....

K. Arbter, W. Snyder, H. Burkhardt, and G. Hirzinger, "Application of affineinvariant Fourier descriptors to recognition of 3D objects", IEEE Trans. Pattern Analysis and Machine Intelligence, V.12, pp. 640-647, 1990.

....are recognition of objects in the scene against a database, template matching, etc. Much effort has been spent to find invariants to imaging geometry, particularly to linear and projective transformations. Moment invariants [8] 1] 18] 19] 3] 9] 5] Fourier domain invariants [12] [2], differential invariants [20] 15] 21] and point sets invariants [13] 17] 11] 14] are the most popular groups of them. On the other hand, only few invariants to convolution have been described in the literature. A consistent theory has been published recently in [6] where two sets of ....

K. Arbter, W. E. Snyder, H. Burkhardt, and G. Hirzinger. Application of affine-invariant Fourier descriptors to recognition of 3-D objects. IEEE Trans. Pattern Analysis and Machine Intelligence, 12:640--647, 1990.

....will not be indexed correctly for many viewing directions, but we can easily determine which objects are flat or nearly flat prior to recognition time. For such objects we can either reduce the probability threshold or use special case techniques for flat [Lamdan et al. 1988] or nearly flat [Arbter et al. 1990] objects. Contrasting probabilistic indexing to grouping techniques [Ahuja and Tuceryan, 1989, Huttenlocher and Wayner, 1992, Lowe, 1985, Mohan and Nevatia, 1992] may be useful. Grouping techniques determine sets of image features that are likely to come from the same object. These techniques ....

K. Arbter, W. E. Snyder, H. Burkhardt, and G. Hirzinger. Application of affine-invariant Fourier descriptors to recognition of 3-d objects. IEEE Transactions on Pattern Analysis and Machine Intelligence, 12(7):640--647, July 1990.

....0 1 2 3 4 5 6 7 8 9 10 0 0.5 1 spline bases of order 2 0 1 2 3 4 5 6 7 8 9 10 0 0.5 1 spline bases of order 3 0 1 2 3 4 5 6 7 8 9 10 0 0.5 1 spline bases of order 4 (a) b) c) Figure 1: a) Wavelet, b) short time Fourier analysis, and (c) b spline bases showing two orthogonal dimensions. by [1, 30] using Fourier descriptors, and by [43] using wavelets. In these cases, affine invariants were used to recognize planar objects in 3D space. Orthographic projection was used to approximate perspective projection, and the shear effect in affine transformations modeled perspective distortion. ....

....because of its simplicity. Intrinsic arc length transforms linearly under any linear transformation. Translation and rotation do not affect the arc length, and scaling only scales the parameter accordingly. However, under affine transformation, the arc length parameter is nonlinearly transformed [1]. A more suitable parameterization is thus required. We describe two parameterizations which are linear under an affine transformation. The first, called affine arc length, is defined [14] as: Z b a 3 p xy Gamma x y dt where x; y are the first and x; y are the second derivatives ....

[Article contains additional citation context not shown here]

K. Arbter, W. E. Snyder, H. Burkhardt, and G. Hirzinger. Application of Affine-Invariant Fourier Descriptors to Recognition of 3-D Objects. IEEE Trans. Pattern Analy. Machine Intell., 12:640--647, 1990.

.... techniques can be found in the literature relating to this issue: B splines (Jain, 1989) autoregressive models (Jain, 1989; Kauppinen et al. 1995) Fourier descriptors (Zahn and Roskies, 1972; Richard and Hemami, 1974; Persoon and Fu, 1977; Wallace and Wintz, 1980; Proffitt, 1982; Jain, 1989; Arbter et al. 1990; Jia and Nixon, 1995; Kauppinen et al. 1995; Rothe et al. 1996; etc. In general, the Fourier based methods using different models for boundary representation provide superior performance in most cases (Kauppinen et al. 1995) The algorithm to be presented in this paper is also based on the ....

....degree of dissimilarity caused by different map scales, the computed Fourier descriptors have to be normalized prior to cross correlation. Unlike the normalization algorithms proposed in the literature (Zahn and Roskies, 1972; Richard and Hemami, 1974; Wallace and Wintz, 1980; Proffitt, 1982; Arbter et al. 1990; Jia and Nixon, 1995; Rothe et al. 1996) only the removals of transla tion and scale factors are considered. The fact for this study is that maps are usually in two dimensional coordinate system with aspect ratio close to one and without shear effect in one direction. The conformal ....

Arbter, K., W.E. Snyder, H. Burkhardt, G. Hirzinger, 1990. Application of Affine-Invariant Fourier Descriptors to Recognition of 3-D Objects. IEEE Transactions on Pattern Analysis and Machine Intelligence, 12(7), pp. 640-647.

....is the search for invariants [42] Invariant features can be designed based on many different methods and made invariant to rigid motion, general affine transform, scene illumination, occlusion, and projection. For examples, popular image invariants have been designed based on Fourier transform [1] and moments [20, 34, 38] Many such invariant features are insensitive to changes in geometry induced by motion and change of viewpoint [1, 14, 20, 32, 34, 38, 41, 43] while others are immune to changes in illumination [13, 18, 19, 17, 22, 26, 27, 28, 36, 37, 40] and occlusion [3] Invariants ....

....general affine transform, scene illumination, occlusion, and projection. For examples, popular image invariants have been designed based on Fourier transform [1] and moments [20, 34, 38] Many such invariant features are insensitive to changes in geometry induced by motion and change of viewpoint [1, 14, 20, 32, 34, 38, 41, 43], while others are immune to changes in illumination [13, 18, 19, 17, 22, 26, 27, 28, 36, 37, 40] and occlusion [3] Invariants can be computed either Originally submitted on February 7th, revised on March 21st globally, such is the case in moment invariants, or based on local properties ....

[Article contains additional citation context not shown here]

K. Arbter, W. E. Snyder, H. Burkhardt, and G. Hirzinger. Application of Affine-Invariant Fourier Descriptors to Recognition of 3-D Objects. IEEE Trans. Pattern Analy. Machine Intell., 12:640--647, 1990.

....to most object recognition systems including the human visual system. Two methods that could help alleviate this problem are to continue relaxing the parameters until most matches have been examined or using special case techniques for recognizing flat [Lamdan et al. 1988] or nearly flat objects [Arbter et al. 1990]. 9 Conclusions We have presented techniques that greatly reduce the number of matches that must be examined in the alignment method through use of the probabilistic peaking effect and error criteria, thus greatly increasing the speed at which objects can be recognized. Experimental results ....

K. Arbter, W. E. Snyder, H. Burkhardt, and G. Hirzinger. Application of affine-invariant Fourier descriptors to recognition of 3-d objects. IEEE Transactions on Pattern Analysis and Machine Intelligence, 12(7):640--647, July 1990.

No context found.

K. Arbter, W. Snyder, H. Burkhardt, and G. Hirzinger. Application of Affine-Invariant Fourier Descriptors to Recognition of 3d Objects. IEEE Trans. on Pattern Analysis and Machine Intelligence, 12, 1990.

No context found.

H. B. Klaus Arbter, Wesley Snyder and G. Hirzinger. Application of Affine-Invariant Fourier Descriptors to Recognition of 3D Objects. IEEE Trans. on Pattern Analysis and Machine Intelligence, 12, 1990.

No context found.

K. Arbter, W. Snyder, H. Burkhardt, G. Hirzinger, Application of affine-invariant Fourier descriptors to recognition of 3D objects, IEEE Transactions on Pattern Analysis and Machine Intelligence 12 (1990) 640 -- 647.

No context found.

K. Arbter, W.E. Synder, H. Burkhardt, and G. Hirzinger, "Application of Affine-Invariant Fourier Descriptors to Recognition 3-D Objects," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 12, no. 7, pp. 640-647, July 1990.

No context found.

K. Arbter, W. E. Snyder, H. Burkhardt, and G. Hirzinger, "Application of affine-invariant fourier descriptors to recognition of 3-d objects," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 12, no. 7, 1990.

No context found.

Arbter, K., Snyder, W.E., Burkhardt, H. and Hirzinger, G., Applications of Affine Invariant Fourier Descriptors to Recognition of 3D Objects, PAMI-12, No. 7, p.640-647, 1990.

No context found.

K. Arbter, W.E. Snyder, H. Burkhardt, and G. Hirzinger, "Application of AffineInvariant Fourier Descriptors to Recognition of 3D Objects," IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. 12, no. 7, pp. 452-459, July 1990. 4 We did not encounter such a phenomenon in our experiments. 23

No context found.

Arbter,K., Syder,W., Burkhardt,H., Hirzinger,G.: Application of affine-invariant Fourier descriptors to recognition of 3D objects. IEEE Trans. PAMI-12 (1990) pp. 640-647

First 50 documents

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC