Abstract. Hierarchical structures provide versatile and efficient solutions for representing, processing and analyzing images. In the framework of mathematical morphology, partial partition trees were proposed in order to model the grey-level images. The most popular are the component tree and the tree of shapes. Both trees are image models, i.e., they represent an image in a lossless, reversible way. Based on this property, they can be used for designing image processing operators. Indeed, by selecting some nodes of these trees and/or by modifying their associated grey-level values, one can define so-called connected operators, that act at the scale of flat zones instead of pixels, and thus avoid the generation of new contours. The definition of connected operators from the component tree has been the subject of an abundant literature. This is not the case of the tree of shapes, despite its high ability to model the topological and differential properties of grey-level images. In this article, we propose an algorithmic scheme to build consistent connected operators based on the tree of shapes. More precisely, the induced connected operators do not modify the differential properties of the image, and they also preserve the equivalence between any image and its tree of shapes. We prove that this algorithmic scheme presents an efficient time cost. We also demonstrate that it generalizes the previous approaches developed for connected operator design from morphological trees. Finally, we show how it opens the way to the development of connected versions of usual pixel-based, linear, and nonlinear operators. Codes freely available at https://github.com/jmendesf/ToSConOp .

Quasi-regularity has been proved to be a sufficient condition for simple-connectedness preservation during the digitization process of 2D continuous objects. The original definition of quasi-regularity relies on set-based morphological operations of erosion and dilation. With this definition, quasi-regularity is algorithmically difficult to assess. In this paper, we propose a tractable framework for quasi-regularity verification, especially designed for polygons. Our approach mainly relies on the computation and analysis of the medial axis of these objects, and determines their potential quasi-regularity, and thus their ability to undergo a digitization without alteration of their topological properties. The framework is applied in the context of topology-preserving rigid motions of digital objects.

Hierarchical image segmentation provides a region-oriented scale-space, i.e. a set of image segmentations at different detail levels in which the segmentations at finer levels are nested with respect to those at coarser levels. However, most image segmentation algorithms, among which a graph-based image segmentation method relying on a region merging criterion was proposed by Felzenszwalb–Huttenlocher in 2004, do not lead to a hierarchy. In order to cope with a demand for hierarchical segmentation, Guimarães et al. proposed in 2012 a method for hierarchizing the popular Felzenszwalb–Huttenlocher method, without providing an algorithm to compute the proposed hierarchy. This paper is devoted to providing a series of algorithms to compute the result of this hierarchical graph-based image segmentation method efficiently, based mainly on two ideas: optimal dissimilarity measuring and incremental update of the hierarchical structure. Experiments show that, for an image of size 321 × 481 pixels, the most efficient algorithm produces the result in half a second whereas the most naive one requires more than 4 h.

We propose an efficient algorithm that removes unimportant regions from a hierarchical partition tree, while preserving the hierarchical partition structure. Various experiments demonstrate that applying this algorithm on various classification or segmentation problems does indeed improve the results by a large margin. Code is available online at https://github.com/higra/Higra. B. Perret, G. Chierchia, J. Cousty, S.J. F. Guimarães, Y. Kenmochi, L. Najman, Higra: Hierarchical Graph Analysis, SoftwareX, 10, 1--6, ISSN 2019, 2352-7110, 10.1016/j.softx.2019.100335.

Volume data can be represented by voxels. In many applications of computer graphics (e.g. animation, simulation) and image processing (e.g. shape registration), such voxel data require manipulations. Among the simplest manipulations, we are interested in rigid motions, namely motions that do not change the shape of voxel objects but do change their position and orientation. Such motions are well-known as isometric transformations in continuous spaces. However, when they are applied on voxel data, some important properties of geometry and topology are generally lost. In this article, we discuss this issue, and we provide a method for rigid motions of voxel objects that preserves the global convexity properties of objects, with digital topology guarantees. This method is based on the standard notion of H-convexity, and a new notion of quasi-regularity.

We provide conditions under which 2D digital images preserve their topological properties under rigid transformations. We consider the two most common digital topology models, namely dual adjacency and well-composedness. This paper leads to the proposal of optimal preprocessing strategies that ensure the topological invariance of images under arbitrary rigid transformations. These results and methods are proved to be valid for various kinds of images (binary, gray-level, label), thus providing generic and efficient tools, which can be used in particular in the context of image registration and warping.

We study the conditions under which the topological properties of a 2D well-composed binary image are preserved under arbitrary rigid transformations. This work initiates a more global study of digital image topological properties under such transformations, which is a crucial but under-considered problem in the context of image processing, e.g., for image registration and warping.

Given a set of discrete points in a 2D digital image containing noise, we formulate our problem as robust digital line fitting. More precisely, we seek the maximum subset whose points are included in a digital line, called the optimal consensus. The paper presents an efficient method for exactly computing the optimal consensus by using the topological sweep, which provides us with the quadratic time complexity and the linear space complexity with respect to the number of input points.

Even if facial expression analysis from 2D luminance images is the present mainstream, it has problems due to changes in facial pose and lighting. In this paper, we use 3D range images which do not maintain such problems for facial expression analysis. We first apply the subspace method to range and luminance images, and clarify their differences in image characteristics. Examining the validity of range images for facial expression analysis, we consider improvement in correct classification rates by integrating results from range and luminance images. We employ the linear combination for their integration and show experimental results.

The accuracy of optical flow estimation is much worth on the occluded and appeared objects. In this paper, we describe an extrapolation method for improving the accuracy of optical flow estimation based on the characteristics of constraint lines in the velocity space and the extraction of the occluded/appeared regions using cluster analysis.

This paper shows an extraction method of a symmetric object for eyeglass face analysis using an active contour model. A contour of eyeglasses hinders a face analysis and synthesis which treats contours of facial parts or partial regions of the face such as eyes, mouth, cheek, eyelid and so on. Methods of active contours extract object contour well. We show an active contour model which is adapted to extract a contour of symmetric object, especially we focus on extracting eyeglass frame using snakes. We study to obtain parameters of snakes by genetic algorithm. We show the good results of applying the snakes in an actual facial image, and synthesize an expressive face with eyeglasses as an application.

For image analysis of facial expressions, we deal with information which are not only the gray levels of pixels but also positions of feature points. We first obtain each result of facial expression identification by using each information and then show that there is the difference between their results. Due to their difference, we integrate both information to improve the results. We define integrated similarity measures by linear combination or belief integration using virtual belief space and show the experimental results of facial expression identification using the measure.

For estimation of optical flow, voting has been used in the process of detection of an intersection of constraint line in voting space. The intersections are often scattered because of the quantization of voting space, image noise, etc. The authors first analyze the intersection distribution, then they show a filtering of voting to converge the scattering by convolution with a weight function. Some experimental results of the method are also given.

This paper shows a picture quality evaluation model for JPEG coded color images. This methodology is obtained by a multi-variable analysis of picture distortion and it provides a numerical value of picture quality. The accuracy of the picture quality evaluation is dependent upon characteristics of the picture quality evaluation models. The error components e(x,y) are computed by subtracting color components (RGB, CIE L*a*b*, L*u*v*, etc.) of distorted compressed images from the original ones. The evaluation model is obtained by multi-variable analysis of distortion models. We then use regression methods to combine these picture quality evaluation models into a single number representative of the quality of a given image. We also evaluate the characteristics of picture quality evaluation models, because good picture quality evaluation models are indispensable to estimate the subjective mean opinion score (MOS) with a high accuracy. This model evaluates picture quality with high accuracy and estimates MOS well.

In the field of astronomy, there is a need for a method to get three-dimensional information of 'corona' from an X-ray solar image. From the observation satellite 'Yohkoh', we can obtain images from different view angles by the rotation of the sun. However, in the case of changing textures on the sun's surface, stereo images lose the stereoscopic effect. To display accurate stereoscopic images, we propose a method for making a correct correspondence between stereo image pairs which includes varying surface using morphological processing and affine transformation.

In this paper, we solve the topological problem of isosurfaces generated by the marching cubes method using the approach of combinatorial topology. For each marching cube, we examine the connectivity of polyhedral configuration in the sense of combinatorial topology. For the cubes where the connectivities are not considered, we modify the polyhedral configurations with the connectivity and construct polyhedral isosurfaces with the correct topologies.

This paper presents two methods for the analysis of facial individuality and expression; an eigenspace method based on class features (EMC) and multiple discriminant analysis (MDA). Those methods are used since they derive eigenvectors by which we may extract facial individuality or expression information from a given facial image. The facial individuality and expression analysis can be achieved by projecting the facial image onto the subspace spanned by a set of those eigenvectors. We apply EMC and MDA to the classification of facial images into 50 classes of individuals or into seven classes of facial expressions, and verify their effectiveness with some experimental results.

For facial image analysis, facial parts such as eyes, nose, and mouth are generally focused and used. When these facial parts are hindered by additional objects (eyeglasses, beard, injury, etc.), the feature extraction from facial image will not be accurate. In this paper, we focus on the eyeglass faces because they account for 40% of population in Japan, and present a method of the removal of eyeglass frame in facial images with eyeglasses using principal component analysts. Two approaches are discussed for removal of eyeglasses in facial image. The first method calculates basis vectors from many eyeglassless facial images and one eyeglass facial image, and reconstructs the facial image with the basis vectors which include no feature of eyeglass frame. The second method calculates basis vectors from a set of eyeglassless facial images, and reconstructs the facial image using the values of inner product of the basis vectors and an eyeglass facial image. The former obtains the images which restrain. The features of eyeglass frame while loses the facial individuality a little. The latter obtains a natural eyeglassless facial image.

This paper describes a reflection and transparency model of rose petals for photorealistic computer graphics. Our model for each rose petal is based on its microscopic scale structures, such as the dome-shaped and translucent cells. The model has some parameters whose values are estimated from measuring of reflected light's intensities on rose petals. The values of those parameters are adjusted for the faithful simulation of the optical phenomena on rose petals. Finally, images of a rose produced by using our model are shown.