Improved Fourier Mellin Invariant for Robust Rotation Estimation with Omni-cameras

Spectral methods such as the improved Fourier Mellin Invariant (iFMI) transform have proved faster, more robust and accurate than feature based methods on image registration. However, iFMI is restricted to work only when the camera moves in 2D space and has not been applied on omni-cameras images so far. In this work, we extend the iFMI method and apply a motion model to estimate an omni-camera's pose when it moves in 3D space. This is particularly useful in field robotics applications to get a rapid and comprehensive view of unstructured environments, and to estimate robustly the robot pose. In the experiment section, we compared the extended iFMI method against ORB and AKAZE feature based approaches on three datasets showing different type of environments: office, lawn and urban scenery (MPI-omni dataset). The results show that our method boosts the accuracy of the robot pose estimation two to four times with respect to the feature registration techniques, while offering lower processing times. Furthermore, the iFMI approach presents the best performance against motion blur typically present in mobile robotics.Comment: 5 pages, 4 figures, 1 tabl

Log-periodic route to fractal functions

Log-periodic oscillations have been found to decorate the usual power law behavior found to describe the approach to a critical point, when the continuous scale-invariance symmetry is partially broken into a discrete-scale invariance (DSI) symmetry. We classify the `Weierstrass-type'' solutions of the renormalization group equation F(x)= g(x)+(1/m)F(g x) into two classes characterized by the amplitudes A(n) of the power law series expansion. These two classes are separated by a novel ``critical'' point. Growth processes (DLA), rupture, earthquake and financial crashes seem to be characterized by oscillatory or bounded regular microscopic functions g(x) that lead to a slow power law decay of A(n), giving strong log-periodic amplitudes. In contrast, the regular function g(x) of statistical physics models with ``ferromagnetic''-type interactions at equibrium involves unbound logarithms of polynomials of the control variable that lead to a fast exponential decay of A(n) giving weak log-periodic amplitudes and smoothed observables. These two classes of behavior can be traced back to the existence or abscence of ``antiferromagnetic'' or ``dipolar''-type interactions which, when present, make the Green functions non-monotonous oscillatory and favor spatial modulated patterns.Comment: Latex document of 29 pages + 20 ps figures, addition of a new demonstration of the source of strong log-periodicity and of a justification of the general offered classification, update of reference lis

Barcode Annotations for Medical Image Retrieval: A Preliminary Investigation

This paper proposes to generate and to use barcodes to annotate medical images and/or their regions of interest such as organs, tumors and tissue types. A multitude of efficient feature-based image retrieval methods already exist that can assign a query image to a certain image class. Visual annotations may help to increase the retrieval accuracy if combined with existing feature-based classification paradigms. Whereas with annotations we usually mean textual descriptions, in this paper barcode annotations are proposed. In particular, Radon barcodes (RBC) are introduced. As well, local binary patterns (LBP) and local Radon binary patterns (LRBP) are implemented as barcodes. The IRMA x-ray dataset with 12,677 training images and 1,733 test images is used to verify how barcodes could facilitate image retrieval.Comment: To be published in proceedings of The IEEE International Conference on Image Processing (ICIP 2015), September 27-30, 2015, Quebec City, Canad

Discrete scale invariance and complex dimensions

We discuss the concept of discrete scale invariance and how it leads to complex critical exponents (or dimensions), i.e. to the log-periodic corrections to scaling. After their initial suggestion as formal solutions of renormalization group equations in the seventies, complex exponents have been studied in the eighties in relation to various problems of physics embedded in hierarchical systems. Only recently has it been realized that discrete scale invariance and its associated complex exponents may appear ``spontaneously'' in euclidean systems, i.e. without the need for a pre-existing hierarchy. Examples are diffusion-limited-aggregation clusters, rupture in heterogeneous systems, earthquakes, animals (a generalization of percolation) among many other systems. We review the known mechanisms for the spontaneous generation of discrete scale invariance and provide an extensive list of situations where complex exponents have been found. This is done in order to provide a basis for a better fundamental understanding of discrete scale invariance. The main motivation to study discrete scale invariance and its signatures is that it provides new insights in the underlying mechanisms of scale invariance. It may also be very interesting for prediction purposes.Comment: significantly extended version (Oct. 27, 1998) with new examples in several domains of the review paper with the same title published in Physics Reports 297, 239-270 (1998