Laurent Mascarilla

The Color Monogenic Signal: Application to Color Edge Detection and Color Optical Flow

The aim of this paper is to define an extension of the analytic signal for a color image. We generalize the construction of the so-called monogenic signal to mappings with values in the vectorial part of the Clifford algebra ℝ5,0. Solving a Dirac equation in this context leads to a multiscale signal (relatively to the Poisson scale-space) which contains both structure and color information. The color monogenic signal can be used in a wide range of applications. Two examples are detailed: the first one concerns a multiscale geometric segmentation with respect to a given color; the second one is devoted to the extraction of the optical flow from moving objects of a given color.

Color Fourier-Mellin descriptors for image recognition

We propose new sets of Fourier-Mellin descriptors for color images. They are constructed using the Clifford Fourier transform of Batard et al. (2010) [4] and are an extension of the classical Fourier-Mellin descriptors for grayscale images. These are invariant under direct similarity transformations (translations, rotations, scale) and marginal treatment of colors images is avoided. An implementation of these features is given and the choice of the bivector (a distinguished color plane which parameterizes the Clifford Fourier transform) is discussed. The proposed formalism extends and clarifies the notion of direction of analysis as introduced for the quaternionic Fourier-Mellin moments (Guo and Zhu, 2011). Thus, another set of descriptors invariant under this parameter is defined. Our proposals are tested with the purpose of object recognition on well-known color image databases. Their retrieval rates are favorably compared to standard feature descriptors.

A k-order fuzzy OR operator for pattern classification with k -order ambiguity rejection

In pattern recognition, the membership of an object to classes is often measured by labels. This article mainly deals with the mathematical foundations of labels combination operators, built on t-norms, that extend previous ambiguity measures of objects by dealing not only with two classes ambiguities but also with k classes, k lying between 1 and the number of classes c. Mathematical properties of this family of combination operators are established and a weighted extension is proposed, allowing to give more or less importance to a given class. A classifier with reject options built on the proposed measure is presented and applied on synthetic data. A critical analysis of the results led to derivate some new operators by aggregating previous measures. A modified classifier is proposed and applied to synthetic data as well as to standard real data.

New geometric fourier descriptors for color image recognition

This article relies on two recent developments of well known methods which are a color Fourier transform using geometric algebra [1] and Generalized Fourier descriptors defined from the group M2 of the motion of the plane [2]. In this paper, new generalized color Fourier descriptors (GCFD) are proposed. They depend on the choice of a bivector B acting as an analysis plane in a colorimetric space. The relevance of proposed descriptors is discussed on several color image databases. In particular, the influence of parameter B is studied regarding the type of images. It appears that proposed descriptors are more compact with a lower complexity and better classification rate.

Color Object Recognition Based on a Clifford Fourier Transform

The aim of this chapter is to propose two different approaches for color object recognition, both using the recently defined color Clifford Fourier transform. The first one deals with so-called Generalized Fourier Descriptors, the definition of which relies on plane motion group actions. The proposed color extension leads to more compact descriptors, with lower complexity and better recognition rates, than the already existing descriptors based on the processing of the r, g and b channels separately. The second approach concerns color phase correlation for color images. The idea here is to generalize in the Clifford framework the usual means of measuring correlation from the well-known shift theorem. Both methods necessitate to choose a 2-blade B of ℝ4 which corresponds to an analysis plane in the color space. The relevance of proposed methods for classification purposes is discussed on several color image databases. In particular, the influence of parameter B is studied regarding the type of images.

Action recognition in videos using frequency analysis of critical point trajectories

This paper focuses on human action recognition in video sequences. A method based on the optical flow estimation is presented, where critical points of the flow field are extracted. Multi-scale trajectories are generated from those points and are characterized in the frequency domain. Finally, a sequence is described by fusing this frequency information with motion orientation and shape information. Experiments show that this method has recognition rates among the highest in the state of the art on the KTH dataset. Contrary to recent dense sampling strategies, the proposed method only requires critical points of motion flow field, thus permitting a lower computation time and a better sequence description. Results and perspectives are then discussed.

The Color Monogenic Signal: A new framework for color image processing. application to color optical flow

We use in this paper the formalism of Clifford algebras to define the so-called Color Monogenic Signal associated to a color image. It consists in a function with values in the Clifford algebra ℝ5,0 that codes color (RGB) and geometric structures information. Using geometric calculus, a notion of local color phase is introduced, generalizing the one for gray level image. As an example of application, a color optical flow robust against noise and brightness variation is provided. It extends the gray level CLG method to color images. The results we obtain on images from the Middleburry database show the relevance of the proposed approach.

An efficient and sparse approach for large scale human action recognition in videos

This paper focuses on human action recognition in video sequences. A method based on optical flow estimation is presented, where critical points of this flow field are extracted. Multi-scale trajectories are generated from those points and are characterized in the frequency domain. Finally, a sequence is described by fusing this frequency information with motion orientation and shape information. This method has been tested on video datasets with recognition rates among the highest in the state of the art. Contrary to recent dense sampling strategies, the proposed method only requires critical points of motion flow field, thus permitting a lower computational cost and a better sequence description. A cross-dataset generalization is performed to illustrate the robustness of the method to recognition dataset biases. Results, comparisons and prospects on complex action recognition datasets are finally discussed.

Un nouvel ensemble de descripteurs de Fourier Clifford pour les images couleur. Les GCFD3

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Un nouvel ensemble de descripteurs de Fourier Clifford pour les images couleur : les GCFD3 José Mennesson, Christophe Saint-Jean, Laurent Mascarilla

A Metric and Multiscale Color Segmentation Using the Color Monogenic Signal

In this paper, we use the formalism of Clifford algebras to extend the so-called Monogenic Signal to color images. This extension consists in a function with values in the Clifford algebra ?5,0 that encodes color as well as geometric structure information. Using geometric calculus, such a mathematical object can be used to extend classical concepts of signal processing (filtering, Fourier Transform...) to color images in a consistent manner. Regarding this paper, a local color phase is introduced, which generalizes the one for grayscale image. As an example of application, we provide a new method for color segmentation. Based on our phase definition and the multiscale aspect of the Color Monogenic Signal, we provide a metric approach using differential geometry which reveals relevant on the Berkeley Image Dataset.