Non-flat Structuring Elements Research Articles

Robust Object Detection in Colour Images Using a Multivariate Percentage Occupancy Hit-or-Miss Transform

AbstractThe extension of Mathematical Morphology to colour and multivariate images is challenging due to the need to define a total ordering in the colour space. No one general way of ordering multivariate data exists and, therefore, there is no single, definitive way of performing morphological operations on colour images. In this paper, we propose an extension to mathematical morphology, based on reduced ordering, specifically the morphological Hit-or-Miss Transform which is used for object detection. The reduced ordering employed transforms multivariate observations to scalar comparisons allowing for an order to be derived and for both flat and non-flat structuring elements to be used. We also compare other definitions of the Hit-or-Miss Transform and test alternative colour ordering schemes presented in the literature. Our proposed method is shown to be intuitive and outperforms other approaches to multivariate Hit-or-Miss Transforms. Furthermore, methods of setting the parameters of the proposed Hit-or-Miss Transform are introduced in order to make the transform robust to noise and partial occlusion of objects and, finally, a set of design tools are presented in order to obtain optimal values for setting these parameters accordingly.

Effectiveness of morphological reconstruction operators in change detection for remote sensing images

Change detection (CD) in multi-temporal images aims at quantifying the temporal effects or changes in remote sensing images taken at different times of the same area of Earth. With huge constellations of satellites setup by various countries, monitoring the Earth's surface for changes helps us understand and respond to various natural phenomenon affecting the Earth's atmosphere. In this paper, we have used texture features along with the spectral features for CD. The texture features have been extracted after applying three different morphological reconstruction operators, namely, opening by reconstruction, closing by reconstruction and opening of closing by reconstruction. Also flat and non-flat structuring elements (SE) have been used for applying morphological reconstruction. The paper compares the impact of different types of morphological operators on the accuracy of the CD. It also presents the comparison between the effectiveness of flat and non-flat SEs on the accuracy.

Effectiveness of morphological reconstruction operators in change detection for remote sensing images

Change detection (CD) in multi-temporal images aims at quantifying the temporal effects or changes in remote sensing images taken at different times of the same area of Earth. With huge constellations of satellites setup by various countries, monitoring the Earth's surface for changes helps us understand and respond to various natural phenomenon affecting the Earth's atmosphere. In this paper, we have used texture features along with the spectral features for CD. The texture features have been extracted after applying three different morphological reconstruction operators, namely, opening by reconstruction, closing by reconstruction and opening of closing by reconstruction. Also flat and non-flat structuring elements (SE) have been used for applying morphological reconstruction. The paper compares the impact of different types of morphological operators on the accuracy of the CD. It also presents the comparison between the effectiveness of flat and non-flat SEs on the accuracy.

Perceptual color hit-or-miss transform: application to dermatological image processing

The hit-or-miss transform is a mathematical morphological processing designed to find objects in image. Its extension to grayscale domain is not unique, but Barat’s method is the most appropriate to find specific objects with bandwidth in space and color evolutions. This tolerance is possible with the use of non-flat structuring elements. In this paper, a color extension of the Barat’s method is presented. For this purpose, a new mathematical morphology method, based on the concept of convergence in the CIELAB space and where the definition of non-flat structuring elements is possible, is used. A comparison with the existing approaches in the literature is done. Results are given and commented on synthetic and real images.

Unsupervised morphological granulometric texture segmentation of digital mammograms

Segmentation via morphological granulometric features is based on fitting structuring elements into image topography from below and above. Each structuring element captures a specific texture content. This paper applies granulometric segmentation to digitized mammograms in an unsupervised framework. Granulometries based on a number of flat and nonflat structuring elements are computed, local size distributions are tabulated at each pixel, granulometric-moment features are derived from these size distributions to produce a feature vector at each pixel, the Karhunen–Loeve transform is applied for feature reduction, and Voronoi-based clustering is performed on the reduced Karhunen–Loeve feature set. Various algorithmic choices are considered, including window size and shape, number of clusters, and type of structuring elements. The algorithm is applied using only granulometric texture features, using gray-scale intensity along with the texture features, and on a compressed mammogram. Segmentation results are clinically evaluated to determine the algorithm structure that best accords to an expert radiologist’s view of a set of mammograms.

Mathematical morphology on l-images

In most applications, morphological operations are considered as unary operations, each associated with a structuring element. Due to the problem of grey-level overflow, the associated structuring elements of morphological operations on grey-level images (functions from R n or Z n to [0, m ], where m is a fixed positive number) are limited to ‘flat’ or ‘non-flat’ structuring elements. However, neither flat nor non-flat structuring elements are grey-level images. In this paper, we propose the notion of l -images, based on a clc-monoid (complete lattice-ordered commutative monoid), as a unified representation of binary images (functions from R n or Z n to {0, 1}, signals (functions from R n or Z n to the set of extended real numbers R ∗ ) and grey-level images. Then we generalize morphological operations to l -images such that the associated structuring elements can be arbitrary l -images. As consequences, we obtain several concrete expressions for dilations and erosions on grey-level images such that the associated structuring elements are also grey-level images. Therefore, the grey-level overflow problem is solved with no limitations on structuring elements. Furthermore, we show that the duality property of dilations and erosions on l -images holds if the underlying clc-monoid is self-dual. In den meisten Anwendungen werden morphologische Operationen als einzelne Operationen betrachtet, von denen jede mit strukturierenden Elementen verknüpft ist. In Verbindung mit dem Problem der Grauwert-Übersteuerung sind die morphologischen Operationen für Grauwertbilder (Funktionen von R n oder Z n bis [0, m ], wobei m eine feste positive Zahl ist) begrenzt auf ‘flache’ oder ‘nicht flache’ Strukturelemente. Jedoch sind weder flache noch nicht flache Strukturelemente Grauwertbilder. Wir schlagen in dieser Arbeit die Idee der l -Bilder vor, die auf einem clc-Monoid (‘complete lattice-ordered commutative monoid’) basieren, als eine einheitliche Darstellung binärer Bilder (Funktionen von R n oder Z n bis {0, 1}, Signale (Funktionen von R n oder Z n bis zur Menge der erweiterten reellen Zahlen R ∗ ) und Grauwerbilder. Dann verallgemeinern wir die morphologischen Operationen auf l -Bilder und zwar so, daβ die zugehörigen strukturierenden Elemente beliebige l -Bilder sein können. Dadurch erhalten wir einige konkrete Ausdrücke für die Dilationen und Erosionen von Grauwertbildern, so daβ die zugehörigen Strukturelemente auch Graubilder darstellen. Damit wird das Problem der Grauwert-Übersteuerung ohne Begrenzung der Strukturelemente gelöst. Weiterhin zeigen wir, daβ die Dualitäts-Eigenschaft von Dilation und Erosion für l -Bilder bestehen bleibt, wenn das zugrundeliegende clc-Monoid selbst dual ist. Lorsqu'elles sont appliquées à des images à niveaux de gris bornées (appelées dans la suite images discrètes), les opérations morphologiques sont habituellement définies à partir d'un élément structurant. Cependant, qu'ils soient plans ou non, les éléments structurants ne sont pas des images discrètes eux-mêmes. Dans ce papier, la notion de l -image est proposée pour unifier images binaires et numériques, discrètes ou non et éléments structurants. La structure sous-jacente est celle de monoïde clc, c'est-à-dire de monoïde commutatif ordonné sur un treillis complet. Les opérations morphologiques sont alors généralisées à ces monoïdes clc. Ceci permet alors d'obtenir différentes expressions concrètes pour dilatation et érosion, de telle sorte que ces opérations soient binaires, c'est-à-dire prennent deux images discrètes comme paramètres. Plus précisément, lorsque dilatation et érosion sont regardées comme des opérations unaires, les éléments structurants associés sont également des images discrètes. De plus, nous prouvons que la dualité entre dilation et érosion est valide sur des l -image si le monoïde clc sous-jacent est auto-dual.

Theoretical aspects of gray-level morphology

After a brief discussion of the extension of mathematical morphology to complete lattices, the space of gray-level functions is considered and the concept of a threshold set is introduced. It is shown how one can use binary morphological operators and thresholding techniques to build a large class of gray-level morphological operators. Particular attention is given to the class of so-called flat operators, i.e. operators which commute with thresholding. It is also shown how to define dilations and erosions with nonflat structuring elements if the gray-level set is finite. It is reported that mere truncation yields wrong results.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>