Deformable kernels for early vision

Early vision algorithms often have a first stage of linear-filtering that `extracts' from the image information at multiple scales of resolution and multiple orientations. A common difficulty in the design and implementation of such schemes is that one feels compelled to discretize coarsely the space of scales and orientations in order to reduce computation and storage costs. A technique is presented that allows: 1) computing the best approximation of a given family using linear combinations of a small number of `basis' functions; and 2) describing all finite-dimensional families, i.e., the families of filters for which a finite dimensional representation is possible with no error. The technique is based on singular value decomposition and may be applied to generating filters in arbitrary dimensions and subject to arbitrary deformations. The relevant functional analysis results are reviewed and precise conditions for the decomposition to be feasible are stated. Experimental results are presented that demonstrate the applicability of the technique to generating multiorientation multi-scale 2D edge-detection kernels. The implementation issues are also discussed

Idealized computational models for auditory receptive fields

This paper presents a theory by which idealized models of auditory receptive fields can be derived in a principled axiomatic manner, from a set of structural properties to enable invariance of receptive field responses under natural sound transformations and ensure internal consistency between spectro-temporal receptive fields at different temporal and spectral scales. For defining a time-frequency transformation of a purely temporal sound signal, it is shown that the framework allows for a new way of deriving the Gabor and Gammatone filters as well as a novel family of generalized Gammatone filters, with additional degrees of freedom to obtain different trade-offs between the spectral selectivity and the temporal delay of time-causal temporal window functions. When applied to the definition of a second-layer of receptive fields from a spectrogram, it is shown that the framework leads to two canonical families of spectro-temporal receptive fields, in terms of spectro-temporal derivatives of either spectro-temporal Gaussian kernels for non-causal time or the combination of a time-causal generalized Gammatone filter over the temporal domain and a Gaussian filter over the logspectral domain. For each filter family, the spectro-temporal receptive fields can be either separable over the time-frequency domain or be adapted to local glissando transformations that represent variations in logarithmic frequencies over time. Within each domain of either non-causal or time-causal time, these receptive field families are derived by uniqueness from the assumptions. It is demonstrated how the presented framework allows for computation of basic auditory features for audio processing and that it leads to predictions about auditory receptive fields with good qualitative similarity to biological receptive fields measured in the inferior colliculus (ICC) and primary auditory cortex (A1) of mammals.Comment: 55 pages, 22 figures, 3 table

Discovery of 59ms Pulsations from 1RXS J141256.0+792204 (Calvera)

We report on a multi-wavelength study of the compact object candidate 1RXS J141256.0+792204 (Calvera). Calvera was observed in the X-rays with XMM/EPIC twice for a total exposure time of ~50 ks. The source spectrum is thermal and well reproduced by a two component model composed of either two hydrogen atmosphere models, or two blackbodies (kT_1~ 55/150 eV, kT_2~ 80/250 eV, respectively, as measured at infinity). Evidence was found for an absorption feature at ~0.65 keV; no power-law high-energy tail is statistically required. Using pn and MOS data we discovered pulsations in the X-ray emission at a period P=59.2 ms. The detection is highly significant (> 11 sigma), and unambiguously confirms the neutron star nature of Calvera. The pulse profile is nearly sinusoidal, with a pulsed fraction of ~18%. We looked for the timing signature of Calvera in the Fermi Large Area Telescope (LAT) database and found a significant (~5 sigma) pulsed signal at a period coincident with the X-ray value. The gamma-ray timing analysis yielded a tight upper limit on the period derivative, dP/dt < 5E-18 s/s (dE_rot/dt <1E33 erg/s, B<5E10 G for magneto- dipolar spin-down). Radio searches at 1.36 GHz with the 100-m Effelsberg radio telescope yielded negative results, with a deep upper limit on the pulsed flux of 0.05 mJy. Diffuse, soft (< 1 keV) X-ray emission about 13' west of the Calvera position is present both in our pointed observations and in archive ROSAT all-sky survey images, but is unlikely associated with the X-ray pulsar. Its spectrum is compatible with an old supernova remnant (SNR); no evidence for diffuse emission in the radio and optical bands was found. The most likely interpretations are that Calvera is either a central compact object escaped from a SNR or a mildly recycled pulsar; in both cases the source would be the first ever member of the class detected at gamma-ray energies.Comment: 20 pages, 15 figures and 4 tables. Accepted for publication in MNRA