TY - JOUR AB - We present a new technique for passive and markerless facial performance capture based on anchor frames. Our method starts with high resolution per-frame geometry acquisition using state-of-theart stereo reconstruction, and proceeds to establish a single triangle mesh that is propagated through the entire performance. Leveraging the fact that facial performances often contain repetitive subsequences, we identify anchor frames as those which contain similar facial expressions to a manually chosen reference expression. Anchor frames are automatically computed over one or even multiple performances. We introduce a robust image-space tracking method that computes pixel matches directly from the reference frame to all anchor frames, and thereby to the remaining frames in the sequence via sequential matching. This allows us to propagate one reconstructed frame to an entire sequence in parallel, in contrast to previous sequential methods. Our anchored reconstruction approach also limits tracker drift and robustly handles occlusions and motion blur. The parallel tracking and mesh propagation offer low computation times. Our technique will even automatically match anchor frames across different sequences captured on different occasions, propagating a single mesh to all performances. AU - Beeler, Thabo AU - Hahn, Fabian AU - Bradley, Derek J AU - Bernd Bickel AU - Beardsley, Paul A AU - Gotsman, Craig AU - Sumner, Robert W AU - Groß, Markus S ID - 2099 IS - 4 JF - ACM Transactions on Graphics TI - High-quality passive facial performance capture using anchor frames VL - 30 ER - TY - CHAP AB - This chapter presents a method for real-time animation of highly detailed facial expressions based on sparse motion captures data and a limited set of static example poses. The method for real-time animation of highly detailed facial expressions decomposes geometry into large-scale motion and fine-scale details, such as expression wrinkles. Both large- and fine-scale deformation algorithms run entirely on the GPU, and our implementation based on CUDA achieves an overall performance of about 30 fps. The face conveys the most relevant visual characteristics of human identity and expression. Hence, realistic facial animations or interactions with virtual avatars are important for storytelling and gameplay. However, current approaches are either computationally expensive, require very specialized capture hardware, or are extremely labor intensive. At runtime, given an arbitrary facial expression, the algorithm computes the skin strain from the relative distance between marker points and derives fine-scale corrections for the largescale deformation. During gameplay only the sparse set of marker-point positions is transmitted to the GPU. The face animation is entirely computed on the GPU where the resulting mesh can directly be used as input for the rendering stages. This data can be easily obtained by traditional capture hardware. The proposed in-game algorithm is fast. It also is easy to implement and maps well onto programmable GPUs. AU - Bernd Bickel AU - Lang, Manuel ID - 2098 T2 - GPU Computing Gems Emerald Edition TI - From sparse mocap to highly detailed facial animation ER - TY - CONF AB - Acquiring panoramic images using stitching takes a lot of time and moving objects may cause ghosting. It is also difficult to obtain a full spherical panorama, because the downward picture cannot be captured while the camera is mounted on the tripod. AU - Pfeil, Jonas AU - Hildebrand, Kristian AU - Gremzow, Carsten AU - Bernd Bickel AU - Alexa, Marc ID - 2100 TI - Throwable panoramic ball camera ER - TY - CHAP AB - Let P be the Ornstein-Uhlenbeck semigroup associated with the stochastic Cauchy problem dU(t)=AU(t)dt+dWH(t), where A is the generator of a C 0-semigroup S on a Banach space E, H is a Hilbert subspace of E, and W H is an H-cylindrical Brownian motion. Assuming that S restricts to a C 0-semigroup on H, we obtain L p -bounds for D H P(t). We show that if P is analytic, then the invariance assumption is fulfilled. As an application we determine the L p -domain of the generator of P explicitly in the case where S restricts to a C 0-semigroup on H which is similar to an analytic contraction semigroup. The results are applied to the 1D stochastic heat equation driven by additive space-time white noise. AU - Jan Maas AU - Van Neerven, Jan ID - 2116 T2 - Parabolic Problems TI - Gradient estimates and domain identification for analytic Ornstein-Uhlenbeck operators VL - 80 ER - TY - JOUR AB - We study, in L1(R̃n; γ) with respect to the gaussian measure, non- tangential maximal functions and conical square functions associ- ated with the Ornstein-Uhlenbeck operator by developing a set of techniques which allow us, to some extent, to compensate for the non-doubling character of the gaussian measure. The main result asserts that conical square functions can be controlled in L1-norm by non-tangential maximal functions. Along the way we prove a change of aperture result for the latter. This complements recent results on gaussian Hardy spaces due to Mauceri and Meda. AU - Jan Maas AU - van Neerven, Jan M AU - Portal, Pierre ID - 2122 IS - 2 JF - Publicacions Matemàtiques TI - Conical square functions and non-tangential maximal functions with respect to the Gaussian measure VL - 55 ER - TY - JOUR AB - We prove a Trotter product formula for gradient flows in metric spaces. This result is applied to establish convergence in the L 2-Wasserstein metric of the splitting method for some Fokker-Planck equations and porous medium type equations perturbed by a potential. AU - Clément, Philippe AU - Maas, Jan ID - 2123 IS - 2 JF - Journal of Evolution Equations TI - A Trotter product formula for gradient flows in metric spaces VL - 11 ER - TY - JOUR AB - Let K be an irreducible and reversible Markov kernel on a finite set X. We construct a metric W on the set of probability measures on X and show that with respect to this metric, the law of the continuous time Markov chain evolves as the gradient flow of the entropy. This result is a discrete counterpart of the Wasserstein gradient flow interpretation of the heat flow in Rn by Jordan, Kinderlehrer and Otto (1998). The metric W is similar to, but different from, the L2-Wasserstein metric, and is defined via a discrete variant of the Benamou–Brenier formula. AU - Jan Maas ID - 2126 IS - 8 JF - Journal of Functional Analysis TI - Gradient flows of the entropy for finite Markov chains VL - 261 ER - TY - GEN AB - A (diatomic) shape resonance is a metastable state of a pair of colliding atoms quasi-bound by the centrifugal barrier imposed by the angular momentum involved in the collision. The temporary trapping of the atoms' scattering wavefunction corresponds to an enhanced atom pair density at low interatomic separations. This leads to larger overlap of the wavefunctions involved in a molecule formation process such as photoassociation, rendering the process more efficient. However, for an ensemble of atoms, the atom pair density will only be enhanced if the energy of the resonance comes close to the temperature of the atomic ensemble. Herein we explore the possibility of controlling the energy of a shape resonance by shifting it toward the temperature of atoms confined in a trap. The shifts are imparted by the interaction of non-resonant light with the anisotropic polarizability of the atom pair, which affects both the centrifugal barrier and the pair's rotational and vibrational levels. We find that at laser intensities of up to 5×109 W/cm2 the pair density is increased by one order of magnitude for 87Rb atoms at 100μK and by two orders of magnitude for 88Sr atoms at 20μK. AU - Ağanoğlu, Ruzin AU - Mikhail Lemeshko AU - Friedrich, Břetislav AU - González-Férez, Rosario AU - Koch, Christiane P ID - 2138 T2 - Unknown TI - Controlling a diatomic shape resonance with non-resonant light ER - TY - JOUR AB - We made use of supersymmetric (SUSY) quantum mechanics to find the condition under which the Stark effect problem for a polar and polarizable closed-shell diatomic molecule subjected to collinear electrostatic and nonresonant radiative fields becomes exactly solvable. The condition Δω = ω2/4(m+1)2 connects values of the dimensionless parameters ω and Δω that characterize the strengths of the permanent and induced dipole interactions of the molecule with the respective fields. The exact solutions are obtained for the \J̃ = m, m; ω, Δω) family of 'stretched' states. The field-free and strong-field limits of the combined-fields problem were found to exhibit supersymmetry and shape invariance, which is indeed the reason why they are analytically solvable. By making use of the analytic form of the \J̃ = m,m; ω, Δω) wavefunctions, we obtained simple formulae for the expectation values of the space-fixed electric dipole moment, the alignment cosine and the angular momentum squared, and derived a 'sum rule' that combines the above expectation values into a formula for the eigenenergy. The analytic expressions for the characteristics of the strongly oriented and aligned states provide direct access to the values of the interaction parameters required for creating such states in the laboratory. AU - Mikhail Lemeshko AU - Mustafa, Mustafa K AU - Kais, Sabre AU - Friedrich, Břetislav ID - 2200 JF - New Journal of Physics TI - Supersymmetry identifies molecular Stark states whose eigenproperties can be obtained analytically VL - 13 ER - TY - JOUR AB - By invoking supersymmetry, we found a condition under which the Stark-effect problem for a polar and polarizable molecule subject to nonresonant electric fields becomes exactly solvable for the family of stretched states. The analytic expressions for the wave function and eigenenergy and other expectation values allow one to readily reverse-engineer the problem of finding the values of the interaction parameters required for creating quantum states with preordained characteristics. The method also allows the construction of families of isospectral potentials, realizable with combined fields. AU - Mikhail Lemeshko AU - Mustafa, Mustafa K AU - Kais, Sabre AU - Friedrich, Břetislav ID - 2199 IS - 4 JF - Physical Review A - Atomic, Molecular, and Optical Physics TI - Supersymmetric factorization yields exact solutions to the molecular Stark-effect problem for "stretched" states VL - 83 ER - TY - JOUR AB - We show that dressing polar molecules with a far-off-resonant optical field leads to new types of intermolecular potentials, which undergo a crossover from the inverse power to oscillating behavior depending on the intermolecular distance, and whose parameters can be tuned by varying the laser intensity and wavelength. We present analytic expressions for the potential energy surfaces, thereby providing direct access to the parameters of an optical field required to design intermolecular interactions experimentally. AU - Mikhail Lemeshko ID - 2198 IS - 5 JF - Physical Review A - Atomic, Molecular, and Optical Physics TI - Shaping interactions between polar molecules with far-off-resonant light VL - 83 ER - TY - GEN AB - Soon, the genetic basis of most human Mendelian diseases will be solved. The next challenge will be to leverage this information to uncover basic mechanisms of disease and develop new therapies. To understand how this transformation is already beginning to unfold, we focus on the ciliopathies, a class of multi-organ diseases caused by disruption of the primary cilium. Through a convergence of data involving mutant gene discovery, proteomics, and cell biology, more than a dozen phenotypically distinguishable conditions are now united as ciliopathies. Sitting at the interface between simple and complex genetic conditions, these diseases provide clues to the future direction of human genetics. AU - Gaia Novarino AU - Akizu, Naiara AU - Gleeson, Joseph G ID - 2312 IS - 1 T2 - Cell TI - Modeling human disease in humans: The ciliopathies VL - 147 ER - TY - CONF AB - The binding of polarons, or its absence, is an old and subtle topic. After defining the model we state some recent theorems of ours. First, the transition from many-body collapse to the existence of a thermodynamic limit for N polarons occurs precisely at U = 2α, where U is the electronic Coulomb repulsion and α is the polaron coupling constant. Second, if U is large enough, there is no multi-polaron binding of any kind. We also discuss the Pekar-Tomasevich approximation to the ground state energy, which is valid for large α. Finally, we derive exact results, not reported before, about the one-dimensional toy model introduced by E. P. Gross. AU - Frank, Rupert L AU - Lieb, Élliott H AU - Robert Seiringer AU - Thomas, Lawrence E ID - 2320 TI - Binding, stability, and non-binding of multi-polaron systems ER - TY - CONF AB - We derive a sharp bound on the location of non-positive eigenvalues of Schrödinger operators on the half-line with complex-valued potentials. AU - Frank, Rupert L AU - Laptev, Ari AU - Robert Seiringer ID - 2321 TI - A sharp bound on eigenvalues of Schrödinger operators on the halfline with complex-valued potentials VL - 214 ER - TY - JOUR AB - For an irreducible polynomial in at most two variables the problem of representing power-free integers is investigated. AU - Timothy Browning ID - 233 IS - 2 JF - Archiv der Mathematik TI - Power-free values of polynomials VL - 96 ER - TY - JOUR AB - We investigate the average order of the divisor function at values of binary cubic forms that are reducible over Q and discuss some applications. AU - Timothy Browning ID - 234 IS - 3 JF - Journal de Theorie des Nombres de Bordeaux TI - The divisor problem for binary cubic forms VL - 23 ER - TY - JOUR AB - For given positive integers m and n, we consider the frequency of representations of m/n as a sum of unit fractions. AU - Browning, Timothy D AU - Elsholtz, Christian ID - 235 IS - 2 JF - Illinois Journal of Mathematics TI - The number of representations of rationals as a sum of unit fractions VL - 55 ER - TY - JOUR AB - An asymptotic formula is established for the number of Q-rational points of bounded height on a nonsingular quartic Del Pezzo surface with a conic bundle structure. AU - de la Bretèche, Régis AU - Timothy Browning ID - 236 IS - 1 JF - Duke Mathematical Journal TI - Manin's conjecture for quartic Del Pezzo surfaces with a conic fibration VL - 160 ER - TY - JOUR AB - We resolve several longstanding problems concerning the stability and the absence of multi-particle binding for N≥2 polarons. Fröhlich's 1937 polaron model describes non-relativistic particles interacting with a scalar quantized field with coupling √α, and with each other by Coulomb repulsion of strength U. We prove the following: (i) While there is a known thermodynamic instability for U<2α, stability of matter does hold for U>2α, that is, the ground state energy per particle has a finite limit as N→∞. (ii) There is no binding of any kind if U exceeds a critical value that depends on α but not on N. The same results are shown to hold for the Pekar-Tomasevich model. AU - Frank, Rupert L AU - Lieb, Élliott H AU - Robert Seiringer AU - Thomas, Lawrence E ID - 2390 IS - 1 JF - Publications Mathematiques de l Institut des Hautes Etudes Scientifiques TI - Stability and absence of binding for multi-polaron systems VL - 113 ER - TY - JOUR AB - The change in energy of an ideal Fermi gas when a local one-body potential is inserted into the system, or when the density is changed locally, are important quantities in condensed matter physics. We show that they can be rigorously bounded from below by a universal constant times the value given by the semiclassical approximation. AU - Frank, Rupert L AU - Lewin, Mathieu AU - Lieb, Élliott H AU - Robert Seiringer ID - 2391 IS - 15 JF - Physical Review Letters TI - Energy cost to make a hole in the fermi sea VL - 106 ER -