Rotation recovery from spherical images without correspondences

This paper addresses the problem of rotation estimation directly from images defined on the sphere and without correspondence. The method is particularly useful for the alignment of large rotations and has potential impact on 3D shape alignment. The foundation of the method lies in the fact that the spherical harmonic coefficients undergo a unitary mapping when the original image is rotated. The correlation between two images is a function of rotations and we show that it has an SO(3)-Fourier transform equal to the pointwise product of spherical harmonic coefficients of the original images. The resolution of the rotation space depends on the bandwidth we choose for the harmonic expansion and the rotation estimate is found through a direct search in this 3D discretized space. A refinement of the rotation estimate can be obtained from the conservation of harmonic coefficients in the rotational shift theorem. A novel decoupling of the shift theorem with respect to the Euler angles is presented and exploited in an iterative scheme to refine the initial rotation estimates. Experiments show the suitability of the method for large rotations and the dependence of the method on bandwidth and the choice of the spherical harmonic coefficients.     

Learning SO(3) Equivariant Representations with Spherical CNNs

International Journal of Computer Vision - We address the problem of 3D rotation equivariance in convolutional neural networks. 3D rotations have been a challenging nuisance in 3D classification...     

Baselines for Image Annotation

Automatically assigning keywords to images is of great interest as it allows one to retrieve, index, organize and understand large collections of image data. Many techniques have been proposed for image annotation in the last decade that give reasonable performance on standard datasets. However, most of these works fail to compare their methods with simple baseline techniques to justify the need for complex models and subsequent training. In this work, we introduce a new and simple baseline technique for image annotation that treats annotation as a retrieval problem. The proposed technique utilizes global low-level image features and a simple combination of basic distance measures to find nearest neighbors of a given image. The keywords are then assigned using a greedy label transfer mechanism. The proposed baseline method outperforms the current state-of-the-art methods on two standard and one large Web dataset. We believe that such a baseline measure will provide a strong platform to compare and better understand future annotation techniques.     

Morphology of PI-PEO block copolymers for lithium batteries

Polyimide (PI)-polyethylene oxide (PEO) block copolymers have a wide variety of applications in microelectronics, since PI-PEO films exhibit a high degree of thermal and chemical stability. The polymers consist of short, rigid rod T-shaped PI segments, alternating with flexible, PEO coil segments. The highly incompatible PI rods and PEO coils should phase-separate, especially in the presence of lithium ions used as electrolytes for lithium polymer batteries. The rigid rod phase provides a high degree of dimensional stability. In this paper, we provide evidence by DSC that the self-assembled ordered structure of the PI-PEO molecules is formed from concentrated solution rather than the bulk state. Tapping mode AFM and X-ray diffraction are applied to observe the nanodomains in the phase separation of the PI and PEO before and after doping with lithium ions. In addition, we report evidence of the ion transport primary mechanism, in the amorphous phase of the lithium salt-doped PI-PEO block copolymers' multinuclear NMR linewidth, spin-lattice relaxation time, and pulsed field gradient diffusion measurements.     

Two new siloxanic proton conducting membranes: Part II. Proton conductivity mechanism and NMR study

The synthesis and structural characterization of two types of membranes with formulas {Si(CH₃)₃O[Si(CH₃)HO]_21.26-[Si(CH₃)((CH₂)₃SO₃H)O]_1.8-[Si(CH₃)((CH₂)₃Si(CH₃)₂O-)-O]₁₄-Si(CH₃)₃}_n (A) and {Si(CH₃)₃O[Si(CH₃)HO]_21.26-[Si(CH₃)((CH₂)₃SO₃H)O]_1.8-[Si(CH₃)((CH₂)₃(Si(CH₃)₂O-w₎)-Ov_][Si(CH₃)((CH₂)₃Si(CH₃)₂O-)-O_]14−vSi(CH₃)₃}_n (B), (w=20.31), were previously proposed.The ac electrical response of A and B was fully characterized in the 40 Hz-2 MHz frequency region by studying the impedance spectra in the medium and low frequency regions by equivalent circuits and complex dielectric spectra at high frequency in terms of dielectric relaxation modes. Results demonstrated that A and B conduct ionically by means of a proton exchange event which occurs via a vehicular mechanism between neighboring water clusters formed by water molecules aggregated around each sulfonic acid group of the siloxane side chains. The proton conductivities at 115 °C of ca. 1.9 × 10⁻³ and 1.8 × 10⁻⁴ S cm⁻¹ of fully hydrated membranes A and B, respectively, classify these silicone networks as good proton conductors.Membrane B was chosen for a closer investigation using NMR spectroscopy. Solid state ²⁹Si MAS NMR experiments gave further insight about the three-dimensional structure. Proton diffusion measurements provided some encouraging results about proton dynamics of this membrane signaling the great potential of siloxanic based proton conductors.     

Correspondence-free Structure from Motion

We present a novel approach for the estimation of 3D-motion directly from two images using the Radon transform. The feasibility of any camera motion is computed by integrating over all feature pairs that satisfy the epipolar constraint. This integration is equivalent to taking the inner product of a similarity function on feature pairs with a Dirac function embedding the epipolar constraint. The maxima in this five dimensional motion space will correspond to compatible rigid motions. The main novelty is in the realization that the Radon transform is a filtering operator: If we assume that the similarity and Dirac functions are defined on spheres and the epipolar constraint is a group action of rotations on spheres, then the Radon transform is a correlation integral. We propose a new algorithm to compute this integral from the spherical Fourier transform of the similarity and Dirac functions. Generating the similarity function now becomes a preprocessing step which reduces the complexity of the Radon computation by a factor equal to the number of feature pairs processed. The strength of the algorithm is in avoiding a commitment to correspondences, thus being robust to erroneous feature detection, outliers, and multiple motions. The authors are grateful for support through the following grants: NSF-IIS-0083209, NSF-IIS-0121293, NSF-EIA-0324977, NSF-CNS-0423891, NSF-IIS-0431070, and ARO/MURI DAAD19-02-1-0383. The author is grateful for the generous support of the ARO MURI program (DAAD-19-02-1-0383) while at U. C. Berkeley.     

Optimisation of machining parameters for turning operations based on response surface methodology

Design of experiments has been used to study the effect of the main turning parameters such as feed rate, tool nose radius, cutting speed and depth of cut on the surface roughness of AISI 410 steel. A mathematical prediction model of the surface roughness has been developed in terms of above parameters. The effect of these parameters on the surface roughness has been investigated by using Response Surface Methodology (RSM). Response surface contours were constructed for determining the optimum conditions for a required surface roughness. The developed prediction equation shows that the feed rate is the main factor followed by tool nose radius influences the surface roughness. The surface roughness was found to increase with the increase in the feed and it decreased with increase in the tool nose radius. The verification experiment is carried out to check the validity of the developed model that predicted surface roughness within 6% error.     

Spherical Correlation of Visual Representations for 3D Model Retrieval

In recent years we have seen a tremendous growth in the amount of freely available 3D content, in part due to breakthroughs for 3D model design and acquisition. For example, advances in range sensor technology and design software have dramatically reduced the manual labor required to construct 3D models. As collections of 3D content continue to grow rapidly, the ability to perform fast and accurate retrieval from a database of models has become a necessity. At the core of this retrieval task is the fundamental challenge of defining and evaluating similarity between 3D shapes. Some effective methods dealing with this challenge consider similarity measures based on the visual appearance of models. While collections of rendered images are discriminative for retrieval tasks, such representations come with a few inherent limitations such as restrictions in the image viewpoint sampling and high computational costs. In this paper we present a novel algorithm for model similarity that addresses these issues. Our proposed method exploits techniques from spherical signal processing to efficiently evaluate a visual similarity measure between models. Extensive evaluations on multiple datasets are provided.