On making nD images well-composed by a self-dual local interpolation

International audienceNatural and synthetic discrete images are generally not well-composed, leading to many topological issues: connectivities in binary images are not equivalent, the Jordan Separation theorem is not true anymore, and so on. Conversely, making images well-composed solves those problems and then gives access to many powerful tools already known in mathematical morphology as the Tree of Shapes which is of our principal interest. In this paper, we present two main results: a characterization of 3D well-composed gray-valued images; and a counter-example showing that no local self-dual interpolation satisfying a classical set of properties makes well-composed images with one subdivision in 3D, as soon as we choose the mean operator to interpolate in 1D. Then, we briefly discuss various constraints that could be interesting to change to make the problem solvable in nD

Encoding Specific 3D Polyhedral Complexes Using 3D Binary Images

We build upon the work developed in [4] in which we presented a method to “locally repair” the cubical complex Q(I) associated to a 3D binary image I, to obtain a “well-composed” polyhedral complex P(I), homotopy equivalent to Q(I). There, we developed a new codification system for P(I), called ExtendedCubeMap (ECM) representation, that encodes: (1) the (geometric) information of the cells of P(I) (i.e., which cells are presented and where), under the form of a 3D grayscale image gP ; (2) the boundary face relations between the cells of P(I), under the form of a set BP of structuring elements. In this paper, we simplify ECM representations, proving that geometric and topological information of cells can be encoded using just a 3D binary image, without the need of using colors or sets of structuring elements. We also outline a possible application in which well-composed polyhedral complexes can be useful.Junta de Andalucía FQM-369Ministerio de Economía y Competitividad MTM2012-32706Ministerio de Economía y Competitividad MTM2015-67072-

Strong Euler well-composedness

In this paper, we define a new flavour of well-composedness, called strong Euler well composedness. In the general setting of regular cell complexes, a regular cell complex of dimension n is strongly Euler well-composed if the Euler characteristic of the link of each boundary cell is 1, which is the Euler characteristic of an (n−1)-dimensional ball. Working in the particular setting of cubical complexes canonically associated with nD pictures, we formally prove in this paper that strong Euler well-composedness implies digital well-composedness in any dimension n ≥ 2 and that the converse is not true when n ≥ 4Ministerio de Ciencia, Innovación y Universidades PID2019-107339GB-I00Junta de Andalucía P20_0114

Computationally efficient locally adaptive demosaicing of color filter array images using the dual-tree complex wavelet packet transform

Most digital cameras use an array of alternating color filters to capture the varied colors in a scene with a single sensor chip. Reconstruction of a full color image from such a color mosaic is what constitutes demosaicing. In this paper, a technique is proposed that performs this demosaicing in a way that incurs a very low computational cost. This is done through a (dual-tree complex) wavelet interpretation of the demosaicing problem. By using a novel locally adaptive approach for demosaicing (complex) wavelet coefficients, we show that many of the common demosaicing artifacts can be avoided in an efficient way. Results demonstrate that the proposed method is competitive with respect to the current state of the art, but incurs a lower computational cost. The wavelet approach also allows for computationally effective denoising or deblurring approaches

A survey of real-time crowd rendering

In this survey we review, classify and compare existing approaches for real-time crowd rendering. We first overview character animation techniques, as they are highly tied to crowd rendering performance, and then we analyze the state of the art in crowd rendering. We discuss different representations for level-of-detail (LoD) rendering of animated characters, including polygon-based, point-based, and image-based techniques, and review different criteria for runtime LoD selection. Besides LoD approaches, we review classic acceleration schemes, such as frustum culling and occlusion culling, and describe how they can be adapted to handle crowds of animated characters. We also discuss specific acceleration techniques for crowd rendering, such as primitive pseudo-instancing, palette skinning, and dynamic key-pose caching, which benefit from current graphics hardware. We also address other factors affecting performance and realism of crowds such as lighting, shadowing, clothing and variability. Finally we provide an exhaustive comparison of the most relevant approaches in the field.Peer ReviewedPostprint (author's final draft

Workshop on Advanced Technologies for Planetary Instruments, part 1

This meeting was conceived in response to new challenges facing NASA's robotic solar system exploration program. This volume contains papers presented at the Workshop on Advanced Technologies for Planetary Instruments on 28-30 Apr. 1993. This meeting was conceived in response to new challenges facing NASA's robotic solar system exploration program. Over the past several years, SDIO has sponsored a significant technology development program aimed, in part, at the production of instruments with these characteristics. This workshop provided an opportunity for specialists from the planetary science and DoD communities to establish contacts, to explore common technical ground in an open forum, and more specifically, to discuss the applicability of SDIO's technology base to planetary science instruments

Tropospheric Phase Calibration in Millimeter Interferometry

We review millimeter interferometric phase variations caused by variations in the precipitable water vapor content of the troposphere, and we discuss techniques proposed to correct for these variations. We present observations with the Very Large Array at 22 GHz and 43 GHz designed to test these techniques. We find that both the Fast Switching and Paired Array calibration techniques are effective at reducing tropospheric phase noise for radio interferometers. In both cases, the residual rms phase fluctuations after correction are independent of baseline length for b > b_{eff}. These techniques allow for diffraction limited imaging of faint sources on arbitrarily long baselines at mm wavelengths. We consider the technique of tropospheric phase correction using a measurement of the precipitable water vapor content of the troposphere via a radiometric measurement of the brightness temperature of the atmosphere. Required sensitivities range from 20 mK at 90 GHz to 1 K at 185 GHz for the MMA, and 120 mK for the VLA at 22 GHz. The minimum gain stability requirement is 200 at 185 GHz at the MMA assuming that the astronomical receivers are used for radiometry. This increases to 2000 for an uncooled system. The stability requirement is 450 for the cooled system at the VLA at 22 GHz. To perform absolute radiometric phase corrections also requires knowledge of the tropospheric parameters and models to an accuracy of a few percent. It may be possible to perform an `empirically calibrated' radiometric phase correction, in which the relationship between fluctuations in brightness temperature differences with fluctuations in interferometric phases is calibrated by observing a celestial calibrator at regular intervals.Comment: AAS LATEX preprint format. to appear in Radio Science 199

System Characterizations and Optimized Reconstruction Methods for Novel X-ray Imaging

In the past decade there have been many new emerging X-ray based imaging technologies developed for different diagnostic purposes or imaging tasks. However, there exist one or more specific problems that prevent them from being effectively or efficiently employed. In this dissertation, four different novel X-ray based imaging technologies are discussed, including propagation-based phase-contrast (PB-XPC) tomosynthesis, differential X-ray phase-contrast tomography (D-XPCT), projection-based dual-energy computed radiography (DECR), and tetrahedron beam computed tomography (TBCT). System characteristics are analyzed or optimized reconstruction methods are proposed for these imaging modalities. In the first part, we investigated the unique properties of propagation-based phase-contrast imaging technique when combined with the X-ray tomosynthesis. Fourier slice theorem implies that the high frequency components collected in the tomosynthesis data can be more reliably reconstructed. It is observed that the fringes or boundary enhancement introduced by the phase-contrast effects can serve as an accurate indicator of the true depth position in the tomosynthesis in-plane image. In the second part, we derived a sub-space framework to reconstruct images from few-view D-XPCT data set. By introducing a proper mask, the high frequency contents of the image can be theoretically preserved in a certain region of interest. A two-step reconstruction strategy is developed to mitigate the risk of subtle structures being oversmoothed when the commonly used total-variation regularization is employed in the conventional iterative framework. In the thirt part, we proposed a practical method to improve the quantitative accuracy of the projection-based dual-energy material decomposition. It is demonstrated that applying a total-projection-length constraint along with the dual-energy measurements can achieve a stabilized numerical solution of the decomposition problem, thus overcoming the disadvantages of the conventional approach that was extremely sensitive to noise corruption. In the final part, we described the modified filtered backprojection and iterative image reconstruction algorithms specifically developed for TBCT. Special parallelization strategies are designed to facilitate the use of GPU computing, showing demonstrated capability of producing high quality reconstructed volumetric images with a super fast computational speed. For all the investigations mentioned above, both simulation and experimental studies have been conducted to demonstrate the feasibility and effectiveness of the proposed methodologies