Representation and recognition of 3D curves

Proceedings 1998 International Conference on Image Processing. ICIP98 (Cat. No.98CB36269), 1998

; I general paradigm for recognizing 3D objects is offered, and applied to some geometric primitives [sphe,res, cylinders, cones, and tori). The assumption is that Q curve on the surface W Q S measured with high accuracy (for instance, by a sensory robot). Differential properties of curves and surfaces are used to recognize the surface. The motivation is t,wofold: the output of some devices is not surface range data, but such curves. So, surface invariants, which may be simpler in some cases, cannot Q~W Q Y S be obtained. Also, a consaderable speedup is obtained by using curve data, QS opposed to surface data which usually contains Q much higher number of points.

2009 IEEE International Conference on Acoustics, Speech and Signal Processing, 2009

We present a new similarity invariant signature for space curves. This signature is based on the information contained in the turning angles of both the tangent and the binormal vectors at each point on the curve. For an accurate comparison of these signatures, we define a Riemannian metric on the space of the invariant. We show through relevant examples that, unlike classical invariants, the one we define in this paper enjoys multiple important properties at the same time, namely, a high discrimination level, independence of any reference point, uniqueness property, as well as a good preservation of the correspondence between curves. Moreover, we illustrate how to match 3D objects by extracting and comparing the invariant signatures of their curved skeletons.

Image and Vision Computing, 2008

In this paper we present a new physically motivated curve/region descriptor based on the solution of Helmholtz's equation. The descriptor we propose satisfies the six principles set by MPEG-7: it has a good retrieval accuracy, it is compact, it can be applied in general contests, it has a reasonable computational complexity, it is rotation and scale invariant and provides an hierarchical representation of the curve from coarse to fine. In addition to these properties, the descriptor can be generalized in order to take into account also the intensity content of the image region defined by the curve. The construction of the descriptor can be coupled with a preprocessing step that enables us to describe a curve in an affine invariant fashion. The performance of our approach has been tested in the contest of affine invariant curve and region matching, both within a controlled experimental setup and also using real images. The experiments show that the proposed approach compares favorably to the state of the art curve/region descriptors.

2019

Characteristic curves play a fundamental role in the way a shape is perceived and illustrated. To address the curve recognition problem on surfaces, we adopt a generalisation of the Hough Transform (HT) which is able to deal with mathematical curves. In particular, we extend the set of curves so far adopted for curve recognition with the HT and propose a new dictionary of curves to be selected as templates. In addition, we introduce rules of composition and aggregation of curves into patterns, not limiting the recognition to a single curve at a time. Our method recognises various curves and patterns, possibly compound on a 3D surface. It selects the most suitable profile in a family of curves and, deriving from the HT, it is robust to noise and able to deal with data incompleteness. The system we have implemented is open and allows new additions of curves in the dictionary of functions already available. CCS Concepts • Computing methodologies → Shape modeling; Representation of mathematical objects;

Acta Applicandae Mathematicae, 2008

We propose a robust classification algorithm for curves in 2D and 3D, under special and full groups of affine transformations. To each plane or spatial curve we assign a plane signature curve. Curves, equivalent under an affine transformation, have the same signature. The signatures introduced in this paper are based on integral invariants, which behave much better on noisy images than classically known differential invariants. The comparison with other types of invariants is given in the introduction. Though the integral invariants for planar curves were known before, the affine integral invariants for spatial curves are proposed here for the first time. Using the inductive variation of the moving frame method we compute affine invariants in terms of Euclidean invariants. We present two types of signatures, the global signature and the local signature. Both signatures are independent of parameterization (curve sampling). The global signature depends on the choice of the initial point and does not allow us to compare fragments of curves, and is therefore sensitive to occlusions. The local signature, although is slightly more sensitive to noise, is independent of the choice of the initial point and is not sensitive to occlusions in an image. It helps establish local equivalence of curves. The robustness of these invariants and signatures in their application to the problem of classification of noisy spatial curves extracted from a 3D object is analyzed.

IEEE Transactions on Pattern Analysis and Machine Intelligence, 2011

The 3D-shape matching problem plays a crucial role in many applications such as indexing or modeling by example. Here, we present a novel approach to match 3D-objects in presence of non-rigid transformation and partially similar models. In this paper, we use the representation of surfaces by 3D-curves extracted around feature points. Indeed, surfaces are represented with a collection of closed curves and tools from shape analysis of curves are applied to analyze and to compare curves. The belief functions are used to define a global distance between 3D-objects. The experimental results obtained on the TOSCA and the SHREC07 datasets show that the system efficiently performs in retrieving similar 3D-models.

2011

Shape descriptors are used to identify objects in the same way that human fingerprints are used to identify people. Features of an object are extracted by applying functions to the digital representation of the object. These features are structured as a vector which is known as the shape descriptor (feature vector) of that object. The objective when constructing a shape descriptor is to find functions that will yield shape descriptors that can be used to uniquely identify or at least classify an object. A measure of similarity is required to identify or classify an object. The similarity between two objects is computed by applying a distance function to the shape descriptors of the two objects. The objective of this paper is to examine two of the possible techniques in three-dimensional shape descriptor construction based on Fourier analysis, and to find a descriptor that is able to not only classify, but also identify objects.

Pattern Recognition, 2018

Feature curves are largely adopted to highlight shape features, such as sharp lines, or to divide surfaces into meaningful segments, like convex or concave regions. Extracting these curves is not sufficient to convey prominent and meaningful information about a shape. We have first to separate the curves belonging to features from those caused by noise and then to select the lines, which describe non-trivial portions of a surface. The automatic detection of such features is crucial for the identification and/or annotation of relevant parts of a given shape. To do this, the Hough transform (HT) is a feature extraction technique widely used in image analysis, computer vision and digital image processing, while, for 3D shapes, the extraction of salient feature curves is still an open problem. Thanks to algebraic geometry concepts, the HT technique has been recently extended to include a vast class of algebraic curves, thus proving to be a competitive tool for yielding an explicit representation of the diverse feature lines equations. In the paper, for the first time we apply this novel extension of the HT technique to the realm of 3D shapes in order to identify and localize semantic features like patterns, decorations or anatomical details on 3D objects (both complete and fragments), even in the case of features partially damaged or incomplete. The method recognizes various features, possibly compound, and it selects the most suitable feature profiles among families of algebraic curves.

Bag-of-feature technique is a popular approach in areas of computer vision and pattern recognition. Recently, it plays an important role in shape analysis community and especially in 3D-model retrieval. We present our approach for partial 3D-model retrieval using this technique based on closed curves. We define an invariant scalar function on the surface based on the commute-time distance. Our mapping function respects important properties in order to compute robust closed curves. Each scale of our scalar function detects a small region. The form of these regions are encoded in the form of the closed curves. We generate a collection of closed curves from a source point detected automatically. Based on the collection of all closed curves extracted, we construct our bag-of-features. Then we cluster the bag-of-features in the sense in accurate categorization. The centres of classes are defined as keyshapes. This method is particularly interesting in the sense of quantifying the 3D-model by its keyshapes that are accumulated into an histogram. The results shows the robustness of our method (BOF) compared to a method based on indexed closed curves (ICC) on various 3D-models with different poses.

Procedings of the British Machine Vision Conference 2004, 2004

In this paper we present a new physically motivated curve descriptor based on the solution of Helmholtz's equation. The descriptor satisfies the six principles set by MPEG-7: it has a good retrieval accuracy, it is compact, it can be applied in general contexts, it has a reasonable computational complexity, it is robust and provides an hierarchical representation of the curve from coarse to fine. Moreover this descriptor generalizes straightforwardly to three dimensional surfaces. We tested the performance of the descriptor in the context of affine invariant curve matching using the multiview curve dataset (MCD), which consists of 40 curves (extracted from the MPEG-7 shape dataset) imaged under 14 different points of view. The results we obtained show that the proposed descriptor satisfies the MPEG-7 requirements and presents some advantages over some of the commonly used curve descriptors.