Affine Curvature Scale Space with Affine Length Parametrisation

The maxima of Curvature Scale Space (CSS) image have been used to represent 2D shapes under affine transforms. The CSS image is expected to be in the MPEG-7 package of standards. Since the CSS image employs the arc length parametrisation which is not affine invariant, we expect some deviations in the maxima of the CSS image under general affine transforms. Affine length and affine curvature have already been introduced and used as alternatives to arc length and conventional curvature in affine transformed environments. The utility of using these parameters to enrich the CSS representation is addressed in this paper. We use arc length to parametrise the curve prior to computing its CSS image. The parametrisation has been proven to be invariant under affine transformation and has been used in many affine invariant shape recognition methods. Since the organisation of the CSS image is based on curvature zero crossings of the curve, in this paper, we also investigate the advantages and shortcomings of using affine curvature in computation of the CSS image. The enriched CSS representations are then used to find similar shapes from a very large prototype database, and also a small classified database, both consisting of original as well as affine transformed shapes. An improvement is observed over the conventional CSS image.     

Parametric estimation of affine deformations of planar shapes

We consider the estimation of affine transformations aligning a known 2D shape and its distorted observation. The classical way to solve this registration problem is to find correspondences between the shapes and then compute the transformation parameters from these landmarks. Here we propose a novel approach where the exact transformation is obtained as the solution of a polynomial system of equations. The method has been tested on synthetic as well as on real images and its robustness in the presence of segmentation errors and additive geometric noise has also been demonstrated. We have successfully applied the method for the registration of hip prosthesis X-ray images. The advantage of the proposed solution is that it is fast, easy to implement, has linear time complexity, works without established correspondences and provides an exact solution regardless of the magnitude of transformation.     

Silhouette-based isolated object recognition through curvaturescale space

A complete, fast and practical isolated object recognition system has been developed which is very robust with respect to scale, position and orientation changes of the objects as well as noise and local deformations of shape (due to perspective projection, segmentation errors and non-rigid material used in some objects). The system has been tested on a wide variety of three-dimensional objects with different shapes and material and surface properties. A light-box setup is used to obtain silhouette images which are segmented to obtain the physical boundaries of the objects which are classified as either convex or concave. Convex curves are recognized using their four high-scale curvature extrema points. Curvature scale space (CSS) representations are computed for concave curves. The CSS representation is a multi-scale organization of the natural, invariant features of a curve (curvature zero-crossings or extrema) and useful for very reliable recognition of the correct model since it places no constraints on the shape of objects. A three-stage, coarse-to-fine matching algorithm prunes the search space in stage one by applying the CSS aspect ratio test. The maxima of contours in CSS representations of the surviving models are used for fast CSS matching in stage two. Finally, stage three verifies the best match and resolves any ambiguities by determining the distance between the image and model curves. Transformation parameter optimization is then used to find the best fit of the input object to the correct model     

A subspace approach for matching 2D shapes under affine distortions

This paper presents a subspace approach to matching a pair of 2D shapes, and estimating the affine transformation that aligns the two 2D shapes. In the proposed method, by considering each shape as a 2D signal, one shape is projected onto the subspace spanned by the other, and the affine transformation is estimated by minimizing the projection error in the subspace. The proposed method is fast, easy to implement, and with a clear physical interpretation. Furthermore, it is robust to noise due to the merit of the subspace method. The proposed approach has been tested for registration accuracy, computation time, and robustness to noise. Its performance on synthetic and real images is compared with the state-of-the-art reference algorithms. The experimental results show that our approach compares favorably to the reference methods, in terms of registration accuracy, computation speed, and robustness.     

Structural feature indexing for retrieval of partially visible shapes

Efficient and robust information retrieval from large image databases is an essential functionality for the reuse, manipulation, and editing of multimedia documents. Structural feature indexing is a potential approach to efficient shape retrieval from large image databases, but the indexing is sensitive to noise, scales of observation, and local shape deformations. It has now been confirmed that efficiency of classification and robustness against noise and local shape transformations can be improved by the feature indexing approach incorporating shape feature generation techniques (Nishida, Comput. Vision Image Understanding 73 (1) (1999) 121-136). In this paper, based on this approach, an efficient, robust method is presented for retrieval of model shapes that have parts similar to the query shape presented to the image database. The effectiveness is confirmed by experimental trials with a large database of boundary contours obtained from real images, and is validated by systematically designed experiments with a large number of synthetic data.     

2D affine-invariant contour matching using B-spline model

This paper presents a new affine-invariant matching algorithm based on B-Spline modeling, which solves the problem of the non-uniqueness of B-Spline in curve matching. This method first smoothes the B-Spline curve by increasing the degree of the curve. It is followed by a reduction of the curve degree using the Least Square Error (LSE) approach to construct the Curvature Scale Space (CSS) image. CSS matching is then carried out. Our method combines the advantages of B-Spline that are continuous curve representation and the robustness of CSS matching with respect to noise and affine transformation. It avoids the need for other matching algorithms that have to use the re-sampled points on the curve. Thus, the curve matching error is reduced. The proposed algorithm has been tested by matching similar shapes from a prototype database. The experimental results showed the robustness and accuracy of the proposed method in B-Spline curve matching.     

基于几何不变量的图像特征识别

图像的特征识别是图像处理和识别中的一个重要问题，几何不变量作为特征的特征值在很多领域已经得到了广泛的应用。实际中，普遍采用在仿射变换及射影变换下保持不变的仿射、射影不变量作为特征值。本文根据具体图像的特点，利用4类仿射和射影不变量构成特征的特征值空间，依据4步识别策略来识别图像中的特征点，从而完成识别任务。实验表明，这4类不变量能够较好地识别出实际图像中的特征。     

An application of wavelet-based affine-invariant representation

Recently, a novel technique used to construct an affine-invariant representation based on the dyadic wavelet transform was proposed and tested on synthesised 2D contours (Tieng and Boles, 1994). In this paper, the performance of this representation with real objects under perspective transformation is considered. In comparison with a similarity invariant (curvature) representation, experimental results show that the proposed affine-invariant representation is the most appropriate one to represent and recognise objects under perspective transform.     

Robust image corner detection through curvature scale space

This paper describes a novel method for image corner detection based on the curvature scale-space (CSS) representation. The first step is to extract edges from the original image using a Canny detector (1986). The corner points of an image are defined as points where image edges have their maxima of absolute curvature. The corner points are detected at a high scale of the CSS and tracked through multiple lower scales to improve localization. This method is very robust to noise, and we believe that it performs better than the existing corner detectors An improvement to Canny edge detector's response to 45° and 135° edges is also proposed. Furthermore, the CSS detector can provide additional point features (curvature zero-crossings of image edge contours) in addition to the traditional corners     

Affine and projective active contour models

We investigate the evolution of active contours in terms of progressive modification of an initial contour following the chosen Lie group of object-to-image transformations. Because of non-fronto-parallel viewing of an object or due to relative motion between the camera and the object, the resultant image may undergo affine or projective object-to-image transformations. In a recent paper we have shown that in the case of object tracking, frame-to-frame deformations of an initial curve obtained through Euler-Lagrange descent equations of a curve functional can be used to enact a desired Lie group of plane transformations [A.-R. Mansouri, D.P. Mukherjee, S.T. Acton, Constraining active contour evolution via Lie groups of transformation, IEEE Trans. Image Process. 13 (2004) 853-863]. In this work, we propose an energy functional that encodes the Lie group transformation parameters, which in turn guide shape distortion due to oblique viewing. Additional constraints, such as transformation smoothness, are imposed on the active contour by modifying the energy functional. The functional is minimized using numerical schemes similar to the conjugate gradient technique, and the convergence properties are discussed. The success of the technique for affine and projective scenes is demonstrated with both synthetic and real image examples and compared with the related approaches.     

3D model retrieval using principal plane analysis and dynamic programming

Three dimensional models play an important role in many applications; the problem is how to select the appropriate models from a 3D database rapidly and accurately. In recent years, a variety of shape representations, statistical methods, and geometric algorithms have been proposed for matching 3D shapes or models. In this paper, we propose a 3D shape representation scheme based on a combination of principal plane analysis and dynamic programming. The proposed 3D shape representation scheme consists of three steps. First, a 3D model is transformed into a 2D image by projecting the vertices of the model onto its principal plane. Second, the convex hall of the 2D shape of the model is further segmented into multiple disjoint triangles using dynamic programming. Finally, for each triangle, a projection score histogram and moments are extracted as the feature vectors for similarity searching. Experimental results showed the robustness of the proposed scheme, which resists translation, rotation, scaling, noise, and destructive attacks. The proposed 3D model retrieval method performs fairly well in retrieving models having similar characteristics from a database of 3D models.     

Multiphase B-spline level set and incremental shape priors with applications to segmentation and tracking of left ventricle in cardiac MR images

This paper presents a new multiphase active contour model for object segmentation and tracking. The paper introduces an energy functional which incorporates image feature information to drive contours toward desired boundaries, and shape priors to constrain the evolution of the contours with respect to reference shapes. The shape priors, in the model, are constructed by performing the incremental principal component analysis (iPCA) on a set of training shapes and newly available shapes which are the resulted shapes derived from preceding segmented images. By performing iPCA, the shape priors are updated without repeatedly performing PCA on the entire training set including the existing shapes and the newly available shapes. In addition, by incrementally updating the resulted shape information of consecutive frames, the approach allows to encode shape priors even when the database of training shapes is not available. Moreover, in shape alignment steps, we exploit the shape normalization procedure, which takes into account the affine transformation, to directly calculate pose transformations instead of solving a set of coupled partial differential equations as in gradient descent-based approaches. Besides, we represent the level set functions as linear combinations of continuous basic functions expressed on B-spline basics for a fast convergence to the segmentation solution. The model is applied to simultaneously segment/track both the endocardium and epicardium of left ventricle from cardiac magnetic resonance (MR) images. Experimental results show the desired performances of the proposed model.     

Covariant-Conics Decomposition of Quartics for 2D Shape Recognition and Alignment

This paper outlines a new geometric parameterization of 2D curves where parameterization is in terms of geometric invariants and parameters that determine intrinsic coordinate systems. This new approach handles two fundamental problems: single-computation alignment, and recognition of 2D shapes under Euclidean or affine transformations. The approach is model-based: every shape is first fitted by a quartic represented by a fourth degree 2D polynomial. Based on the decomposition of this equation into three covariant conics, we are able, in both the Euclidean and the affine cases, to define a unique intrinsic coordinate system for non-singular bounded quartics that incorporates usable alignment information contained in the polynomial representation, a complete set of geometric invariants, and thus an associated canonical form for a quartic. This representation permits shape recognition based on 11 Euclidean invariants, or 8 affine invariants. This is illustrated in experiments with real data sets.     

基于仿射参数估计的迭代点匹配算法

本文提出了一种新的迭代点匹配算法。算法建立点集间仿射映射关系,把匹配问题转化为函数优化问题,通过点集间匹配对应关系和仿射变换参数的反复迭代最终求出问题的解。文中提出了构造虚拟点对和最小方差两种仿射参数估计方法,并利用改进最近点原则求解点集匹配关系,且证明了算法的收敛性。本文算法较好地解决了由仿射带来的非刚性形变点集匹配问题,且有很好的抗噪声和点性能。实验证明了算法的有效性和鲁棒性。     

A constraint-based approach to shape management in multimedia databases

Shape management is an important functionality in multimedia databases. Shape information can be used in both image acquisition and image retrieval. Several approaches have been proposed to deal with shape representation and matching. Among them, the data-driven approach supports searches for shapes based on indexing techniques. Unfortunately, efficient data-driven approaches are often defined only for specific types of shape. This is not sufficient in contexts in which arbitrary shapes should be represented. Constraint databases use mathematical theories to finitely represent infinite sets of relational tuples. They have been proved to be very useful in modeling spatial objects. In this paper, we apply constraint-based data models to the problem of shape management in multimedia databases. We first present the constraint model and some constraint languages. Then, we show how constraints can be used to model general shapes. The use of a constraint language as an internal specification and execution language for querying shapes is also discussed. Finally, we show how a constraint database system can be used to efficiently retrieve shapes, retaining the advantages of the already defined approaches.     

Segmentation based compression for graylevel images

This paper presents a segmentation based lossy image compression (SLIC) algorithm. The segmentation scheme (Biswas and Pal, Pattern Recog. Lett. 21 (2000)), entropy based and hierarchical in nature, provides sub-images of homogeneous regions. The compression algorithm encodes a graylevel image through global approximations of sub-images by 2-d Bezier-Bernstein polynomial along with corrections, if needed, over regions in sub-images by local approximation; contours by 1-d Bezier-Bernstein polynomial and texture, if present, by Huffman coding scheme using Hilbert scan on texture blocks. Order of the 2-d polynomials has been computed with the help of an image quality index (IQI). The proposed compression algorithm also examines the compression result by encoding contours through their approximation based on stretching of discrete circular arcs. Stretching is done by affine transformation. Compression results in both the cases have been compared with JPEG results. Attempts have been made to evaluate the quality of reconstructed images through a fidelity vector whose components are different objective measures.