In search of a general picture processing operator

Granlund, Gösta H.

doi:10.1016/0146-664x(78)90047-3

Cited by 230 publications

(90 citation statements)

References 8 publications

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“…, which defines the mapping 2 A employed later in (17) and (20). Let us make a minor digression at this point.…”

Section: Line Detection In Two-dimensional Imagesmentioning

confidence: 99%

“…From the analytical expressions of the derivators in (11) and (12) we retrieve θ as (19) We are now ready to formulate the derotation equation (20) for the 2D second derivative case. The response vector is called 2 f , since this is a second order variation.…”

Section: Line Detection In Two-dimensional Imagesmentioning

confidence: 99%

“…The matrix 2 A was defined in (12). In (20) there is one parameter β representing orientation, and one free parameter κ representing shape. The prototype response is a vector in the [ ] From (20) and (21) we find the following more explicit expression for the prototype vector.…”

Section: Line Detection In Two-dimensional Imagesmentioning

confidence: 99%

“…In (20) there is one parameter β representing orientation, and one free parameter κ representing shape. The prototype response is a vector in the [ ] From (20) and (21) we find the following more explicit expression for the prototype vector. The normalized prototype vector is residing on a semi-circle, a meridian, of the unit sphere in Figure 3, which goes from the top to bottom of the sphere while passing 21 b .…”

Section: Line Detection In Two-dimensional Imagesmentioning

confidence: 99%

See 3 more Smart Citations

Efficient Detection of Second-Degree Variations in 2D and 3D Images

Danielsson¹,

Lin²,

Ye³

2001

Journal of Visual Communication and Image Representation

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“…, which defines the mapping 2 A employed later in (17) and (20). Let us make a minor digression at this point.…”

Section: Line Detection In Two-dimensional Imagesmentioning

confidence: 99%

Section: Line Detection In Two-dimensional Imagesmentioning

confidence: 99%

Section: Line Detection In Two-dimensional Imagesmentioning

confidence: 99%

Section: Line Detection In Two-dimensional Imagesmentioning

confidence: 99%

See 2 more Smart Citations

Efficient Detection of Second-Degree Variations in 2D and 3D Images

Danielsson¹,

Lin²,

Ye³

2001

Journal of Visual Communication and Image Representation

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“…Subsampled low-pass filters give rise to resolution pyramids [12,13] and multi-resolution analysis. The complementing high-pass filters became very popular in terms of wavelets [14], where signals are decomposed based on a orthonormal basis.…”

Section: Introductionmentioning

confidence: 99%

Incremental Computation of Feature Hierarchies

Felsberg

2010

Lecture Notes in Computer Science

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Abstract. Feature hierarchies are essential to many visual object recognition systems and are well motivated by observations in biological systems. The present paper proposes an algorithm to incrementally compute feature hierarchies. The features are represented as estimated densities, using a variant of local soft histograms. The kernel functions used for this estimation in conjunction with their unitary extension establish a tight frame and results from framelet theory apply. Traversing the feature hierarchy requires resampling of the spatial and the feature bins. For the resampling, we derive a multi-resolution scheme for quadratic spline kernels and we derive an optimization algorithm for the upsampling. We complement the theoretic results by some illustrative experiments, consideration of convergence rate and computational efficiency.

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Representation and detection of multiscale, multiorientation fields using local differentiation filters

Shizawa¹,

Iso²

1996

Electron Comm Jpn Pt III

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A basic theory is proposed for detecting multiorientation fields from images that have multiple orientations at each point in the field. This theory, representing a multiorientation field by a single set of fundamental constraint equations, differs from conventional methods which use many filters tuned to different orientations. It is also different from the steerable filters proposed by Freeman and Adelson [12]. This theory renders implementation of a selection process of orientation-tuned filters with high-magmtude output unnsessary. It also makes it unnecessary to implement a search process for an extreme value output of steerable filters. This theory lets analytical solutions to be derived that explicitly compute multiple orientations. This theory is derived from the operational formalism of the principle of linear superposition. Conventional methods suffer from interference between component signals when multiorientation signal components fall in the tuning range of each filter. As a result, filters with a narrow tuning range are necessary in conventional methods. The algorithms derived from our theory are not negatively influenced by interference. By using these algorithms in multiscale image representation, characteristic image structures such as junctions can be extracted from low-order image derivatives. This theory is expected to provide a theoretical foundation for the image representation of multiple orientations of the hypercolumn structure in the primary visual cortex of the brain.

show abstract

In search of a general picture processing operator

Cited by 230 publications

References 8 publications

Efficient Detection of Second-Degree Variations in 2D and 3D Images

Efficient Detection of Second-Degree Variations in 2D and 3D Images

Incremental Computation of Feature Hierarchies

Representation and detection of multiscale, multiorientation fields using local differentiation filters

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