The Marr Conjecture and Uniqueness of Wavelet Transforms

The inverse question of identifying a function from the nodes (zeroes) of its wavelet transform arises in a number of fields. These include whether the nodes of a heat or hypoelliptic equation solution determine its initial conditions, and in mathematical vision theory the Marr conjecture, on whether an image is mathematically determined by its edge information. We prove a general version of this conjecture by reducing it to the moment problem, using a basis dual to the Taylor monomial basis $x^\alpha$ on $\mathbb {R}^n$.Comment: 52 pages, 4 figure

Contour Detection from Deep Patch-level Boundary Prediction

In this paper, we present a novel approach for contour detection with Convolutional Neural Networks. A multi-scale CNN learning framework is designed to automatically learn the most relevant features for contour patch detection. Our method uses patch-level measurements to create contour maps with overlapping patches. We show the proposed CNN is able to to detect large-scale contours in an image efficienly. We further propose a guided filtering method to refine the contour maps produced from large-scale contours. Experimental results on the major contour benchmark databases demonstrate the effectiveness of the proposed technique. We show our method can achieve good detection of both fine-scale and large-scale contours.Comment: IEEE International Conference on Signal and Image Processing 201

Reconstructive Sparse Code Transfer for Contour Detection and Semantic Labeling

We frame the task of predicting a semantic labeling as a sparse reconstruction procedure that applies a target-specific learned transfer function to a generic deep sparse code representation of an image. This strategy partitions training into two distinct stages. First, in an unsupervised manner, we learn a set of generic dictionaries optimized for sparse coding of image patches. We train a multilayer representation via recursive sparse dictionary learning on pooled codes output by earlier layers. Second, we encode all training images with the generic dictionaries and learn a transfer function that optimizes reconstruction of patches extracted from annotated ground-truth given the sparse codes of their corresponding image patches. At test time, we encode a novel image using the generic dictionaries and then reconstruct using the transfer function. The output reconstruction is a semantic labeling of the test image. Applying this strategy to the task of contour detection, we demonstrate performance competitive with state-of-the-art systems. Unlike almost all prior work, our approach obviates the need for any form of hand-designed features or filters. To illustrate general applicability, we also show initial results on semantic part labeling of human faces. The effectiveness of our approach opens new avenues for research on deep sparse representations. Our classifiers utilize this representation in a novel manner. Rather than acting on nodes in the deepest layer, they attach to nodes along a slice through multiple layers of the network in order to make predictions about local patches. Our flexible combination of a generatively learned sparse representation with discriminatively trained transfer classifiers extends the notion of sparse reconstruction to encompass arbitrary semantic labeling tasks.Comment: to appear in Asian Conference on Computer Vision (ACCV), 201

A Case for Renewed Activity in the Giant Radio Galaxy J0116-473

We present ATCA radio observations of the giant radio galaxy J0116-473 at 12 and 22 cm wavelengths in total intensity and polarization. The images clearly reveal a bright inner-double structure within more extended edge-brightened lobe emission. The lack of hotspots at the ends of the outer lobes, the strong core and the inner-double structure with its edge-brightened morphology lead us to suggest that this giant radio galaxy is undergoing a renewed nuclear activity: J0116-473 appears to be a striking example of a radio galaxy where a young double source is evolving within older lobe material. We also report the detection of a Mpc-long linear feature which is oriented perpendicular to the radio axis and has a high fractional polarization.Comment: 25 pages, 10 figures, appeared in 2002 ApJ, 565, 25

Boundary, Brightness, and Depth Interactions During Preattentive Representation and Attentive Recognition of Figure and Ground

This article applies a recent theory of 3-D biological vision, called FACADE Theory, to explain several percepts which Kanizsa pioneered. These include 3-D pop-out of an occluding form in front of an occluded form, leading to completion and recognition of the occluded form; 3-D transparent and opaque percepts of Kanizsa squares, with and without Varin wedges; and interactions between percepts of illusory contours, brightness, and depth in response to 2-D Kanizsa images. These explanations clarify how a partially occluded object representation can be completed for purposes of object recognition, without the completed part of the representation necessarily being seen. The theory traces these percepts to neural mechanisms that compensate for measurement uncertainty and complementarity at individual cortical processing stages by using parallel and hierarchical interactions among several cortical processing stages. These interactions are modelled by a Boundary Contour System (BCS) that generates emergent boundary segmentations and a complementary Feature Contour System (FCS) that fills-in surface representations of brightness, color, and depth. The BCS and FCS interact reciprocally with an Object Recognition System (ORS) that binds BCS boundary and FCS surface representations into attentive object representations. The BCS models the parvocellular LGN→Interblob→Interstripe→V4 cortical processing stream, the FCS models the parvocellular LGN→Blob→Thin Stripe→V4 cortical processing stream, and the ORS models inferotemporal cortex.Air Force Office of Scientific Research (F49620-92-J-0499); Defense Advanced Research Projects Agency (N00014-92-J-4015); Office of Naval Research (N00014-91-J-4100

Ordered magnetic fields around radio galaxies: evidence for interaction with the environment

We present detailed imaging of Faraday rotation and depolarization for the radio galaxies 0206+35, 3C 270, 3C 353 and M 84, based on Very Large Array observations at multiple frequencies in the range 1365 to 8440 MHz. This work suggests a more complex picture of the magneto-ionic environments of radio galaxies than was apparent from earlier work. All of the sources show spectacular banded rotation measure (RM) structures with contours of constant RM perpendicular to the major axes of their radio lobes. We give a comprehensive description of the banded RM phenomenon and present an initial attempt to interpret it as a consequence of interactions between the sources and their surroundings. We show that the material responsible for the Faraday rotation is in front of the radio emission and that the bands are likely to be caused by magnetized plasma which has been compressed by the expanding radio lobes. A two-dimensional magnetic structure in which the field lines are a family of ellipses draped around the leading edge of the lobe can produce RM bands in the correct orientation for any source orientation. We also report the first detections of rims of high depolarization at the edges of the inner radio lobes of M 84 and 3C 270. These are spatially coincident with shells of enhanced X-ray surface brightness, in which both the field strength and the thermal gas density are likely to be increased by compression.Comment: 21 pages, 15 figures, accepted for publication in MNRAS. Full resolution paper available at http://www.ira.inaf.it/~guidetti/bands/ Subjects: Astrophysics (astro-ph