&lt;title&gt;Statistical dependence between orientation filter outputs used in a human-vision-based image code&lt;/title&gt;

Wegmann, Bernhard; Zetzsche, Christoph

doi:10.1117/12.24279

Cited by 44 publications

(36 citation statements)

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“…In particular, we are motivated by two observations: The first is that although the prior over the coefficients in sparse coding models is typically factorial, the actual joint distribution of coefficients, even after learning, exhibits strong statistical dependencies in response to natural images. One particularly prevalent form of dependency is a circularly symmetric, yet kurtotic, distribution found among pairs of coefficients with basis functions at nearby spatial positions, scales, or orientations (Wegmann & Zetzsche, 1990). Such a circularly symmetric distribution strongly suggests that these pairs of coefficients are better described in polar coordinates rather than Cartesian coordinates-that is, in terms of amplitude and phase.…”

Section: First Layer: Sparse and Temporally Persistent Representationmentioning

confidence: 99%

“…A number of researchers have pointed out the dependencies of nearby linear filters among groups substantially larger than two, such as in the variances of nearby filters (Simoncelli, 1997;Schwartz & Simoncelli, 2001;Lyu & Simoncelli, 2009) or in the circular joint distributions of neighboring filters (Wegmann & Zetzsche, 1990). Extensions of ICA also model dependencies among cliques of filters, as in topographic ICA (Hyvärinen, Hoyer, & Inki, 2001), or among large groups of filters, as in independent subspace analysis (Hyvärinen & Hoyer, 2000).…”

Section: Amplitude Componentsmentioning

confidence: 99%

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Learning Intermediate-Level Representations of Form and Motion from Natural Movies

Cadieu

Olshausen

2012

Neural Computation

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We present a model of intermediate-level visual representation that is based on learning invariances from movies of the natural environment.The model is composed of two stages of processing: an early feature representation layer and a second layer in which invariances are explicitly represented. Invariances are learned as the result of factoring apart the temporally stable and dynamic components embedded in the early feature representation. The structure contained in these components is made explicit in the activities of second-layer units that capture invariances in both form and motion. When trained on natural movies, the first layer produces a factorization, or separation, of image content into a temporally persistent part representing local edge structure and a dynamic part representing local motion structure, consistent with known response properties in early visual cortex (area V1). This factorization linearizes statistical dependencies among the first-layer units, making them learnable by the second layer. The second-layer units are split into two populations according to the factorization in the first layer. The form-selective units receive their input from the temporally persistent part (local edge structure) and after training result in a diverse set of higher-order shape features consisting of extended contours, multiscale edges, textures, and texture boundaries. The motion-selective units receive their input from the dynamic part (local motion structure) and after training result in a representation of image translation over different spatial scales and directions, in addition to more complex deformations. These representations provide a rich description of dynamic natural images and testable hypotheses regarding intermediate-level representation in visual cortex.

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Section: First Layer: Sparse and Temporally Persistent Representationmentioning

confidence: 99%

Section: Amplitude Componentsmentioning

confidence: 99%

Learning Intermediate-Level Representations of Form and Motion from Natural Movies

Cadieu

Olshausen

2012

Neural Computation

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“…Zetzsche and his colleagues also investigated the distribution of local image structures in [41]. They analyzed the multi-dimensional hyperspace which was constructed from all the percentages we have provided above) and visualize clusters of the structures for a few orientation pairs.…”

Section: Statistics Of Intrinsic Dimensionalitymentioning

confidence: 99%

“…That leads to the decision areas for i0D, i1D and i2D as seen in figure 1(d). We would like to note that the bary-centric coordinates are only one possibly way to distinguish the different structures (see, e.g., [41]). …”

Section: Intrinsic Dimensionalitymentioning

confidence: 99%

Local image structures and optic flow estimation

Kalkan

Calow

Wörgötter

et al. 2005

Network: Computation in Neural Systems

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Abstract.Different kinds of local image structures (such as homogeneous, edge-like and junctionlike patches) can be distinguished by the intrinsic dimensionality of the local signals. Intrinsic dimensionality makes use of variance from a point and a line in spectral representation of the signal in order to classify it as homogeneous, edge-like or junction-like. The concept of intrinsic dimensionality has been mostly exercised using discrete formulations; however, a recent work [23,11] has introduced a continuous definition. The current study analyzes the distribution of local patches in natural images according to this continuous understanding of intrinsic dimensionality. This distribution reveals specific patterns than can be also associated to local image structures established in computer vision and which can be related to orientation and optic flow features. In particular, we link quantitative and qualitative properties of opticflow error estimates to these patterns. In this way, we also introduce a new tool for better analysis of optic flow algorithms.

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“…For typical natural images, empirical observations of a single linear filter activation reveal a highly kurtotic (e.g., sparse) distribution (Field, 1987). Groups of linear filters (coordinated across parameters such as orientation, frequency, phase, or spatial position) exhibit a striking form of statistical dependency (Wegmann & Zetzsche, 1990;Zetzsche, Wegmann, & Barth, 1993;Simoncelli, 1997), which can be characterized in terms of the variance (Simoncelli, 1997;Buccigrossi & Simoncelli, 1999;Schwartz & Simoncelli, 2001). The importance of variance statistics had been suggested earlier in pixel space (Lee, 1980) and has been addressed in other domains such as speech (Brehm & Stammler, 1987) and even finance (Bollerslev, Engle, & Nelson, 1994).…”

Section: Introductionmentioning

confidence: 99%

Soft Mixer Assignment in a Hierarchical Generative Model of Natural Scene Statistics

2006

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Gaussian scale mixture models offer a top-down description of signal generation that captures key bottom-up statistical characteristics of filter responses to images. However, the pattern of dependence among the filters for this class of models is prespecified. We propose a novel extension to the gaussian scale mixture model that learns the pattern of dependence from observed inputs and thereby induces a hierarchical representation of these inputs. Specifically, we propose that inputs are generated by gaussian variables (modeling local filter structure), multiplied by a mixer variable that is assigned probabilistically to each input from a set of possible mixers. We demonstrate inference of both components of the generative model, for synthesized data and for different classes of natural images, such as a generic ensemble and faces. For natural images, the mixer variable assignments show invariances resembling those of complex cells in visual cortex; the statistics of the gaussian components of the model are in accord with the outputs of divisive normalization models. We also show how our model helps interrelate a wide range of models of image statistics and cortical processing.

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<title>Statistical dependence between orientation filter outputs used in a human-vision-based image code</title>

Cited by 44 publications

References 0 publications

Learning Intermediate-Level Representations of Form and Motion from Natural Movies

Learning Intermediate-Level Representations of Form and Motion from Natural Movies

Local image structures and optic flow estimation

Soft Mixer Assignment in a Hierarchical Generative Model of Natural Scene Statistics

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