| 1. |
- Lindeberg, Tony, 1964-
(författare)
-
On the behaviour in scale-space of local extrema and blobs
- 1991
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Ingår i: Theory and Applications of Image Analysis. - : World Scientific. ; , s. 38-47, s. 8-17
-
Bokkapitel (refereegranskat)abstract
- We apply elementary techniques from real analysis and singularity theory to derive analytical results for the behaviour in scale-space of critical points and related entities. The main results of the treatment comprise: a description of the general nature of trajectories of critical points in scale-space. an estimation of the drift velocity of critical points and edges. an analysis of the qualitative behaviour of critical points in bifurcation situations. a classification of what types of blob bifurcations are possible.
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| 2. |
- Lindeberg, Tony, 1964-, et al.
(författare)
-
Linear Scale-Space II : Early visual operations
- 1994
-
Ingår i: Geometry-Driven Diffusion in Vision. - : Kluwer Academic Publishers. ; , s. 43-77
-
Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- Vision deals with the problem of deriving information about the world from the light reflected from it. Although the active and task-oriented nature of vision is only implicit in this formulation, this view captures several of the essential aspects of vision. As Marr (1982) phrased it in his book Vision, vision is an information processing task, in which an internal representation of information is of utmost importance. Only by representation information can be captured and made available to decision processes. The purpose of a representation is to make certain aspects of the information content explicit, that is, immediately accessible without any need for additional processing.This introductory chapter deals with a fundamental aspect of early image representation---the notion of scale. As Koenderink (1984) emphasizes, the problem of scale must be faced in any imaging situation. An inherent property of objects in the world and details in images is that they only exist as meaningful entities over certain ranges of scale. A simple example of this is the concept of a branch of a tree, which makes sense only at a scale from, say, a few centimeters to at most a few meters. It is meaningless to discuss the tree concept at the nanometer or the kilometer level. At those scales it is more relevant to talk about the molecules that form the leaves of the tree, or the forest in which the tree grows. Consequently, a multi-scale representation is of crucial importance if one aims at describing the structure of the world, or more specifically the structure of projections of the three-dimensional world onto two-dimensional images.The need for multi-scale representation is well understood, for example, in cartography; maps are produced at different degrees of abstraction. A map of the world contains the largest countries and islands, and possibly, some of the major cities, whereas towns and smaller islands appear at first in a map of a country. In a city guide, the level of abstraction is changed considerably to include streets and buildings etc. In other words, maps constitute symbolic multi-scale representations of the world around us, although constructed manually and with very specific purposes in mind.To compute any type of representation from image data, it is necessary to extract information, and hence interact with the data using certain operators. Some of the most fundamental problems in low-level vision and image analysis concern: what operators to use, where to apply them, and how large they should be. If these problems are not appropriately addressed, the task of interpreting the output results can be very hard. Ultimately, the task of extracting information from real image data is severely influenced by the inherent measurement problem that real-world structures, in contrast to certain ideal mathematical entities, such as ``points'' or ``lines'', appear in different ways depending upon the scale of observation.Phrasing the problem in this way shows the intimate relation to physics. Any physical observation by necessity has to be done through some finite aperture, and the result will, in general, depend on the aperture of observation. This holds for any device that registers physical entities from the real world including a vision system based on brightness data. Whereas constant size aperture functions may be sufficient in many (controlled) physical applications, e.g., fixed measurement devices, and also the aperture functions of the basic sensors in a camera (or retina) may have to determined a priori because of practical design constraints, it is far from clear that registering data at a fixed level of resolution is sufficient. A vision system for handling objects of different sizes and at difference distances needs a way to control the scale(s) at which the world is observed.The goal of this chapter is to review some fundamental results concerning a framework known as scale-space that has been developed by the computer vision community for controlling the scale of observation and representing the multi-scale nature of image data. Starting from a set of basic constraints (axioms) on the first stages of visual processing it will be shown that under reasonable conditions it is possible to substantially restrict the class of possible operations and to derive a (unique) set of weighting profiles for the aperture functions. In fact, the operators that are obtained bear qualitative similarities to receptive fields at the very earliest stages of (human) visual processing (Koenderink 1992). We shall mainly be concerned with the operations that are performed directly on raw image data by the processing modules are collectively termed the visual front-end. The purpose of this processing is to register the information on the retina, and to make important aspects of it explicit that are to be used in later stage processes. If the operations are to be local, they have to preserve the topology at the retina; for this reason the processing can be termed retinotopic processing.Early visual operationsAn obvious problem concerns what information should be extracted and what computations should be performed at these levels. Is any type of operation feasible? An axiomatic approach that has been adopted in order to restrict the space of possibilities is to assume that the very first stages of visual processing should be able to function without any direct knowledge about what can be expected to be in the scene. As a consequence, the first stages of visual processing should be as uncommitted and make as few irreversible decisions or choices as possible.The Euclidean nature of the world around us and the perspective mapping onto images impose natural constraints on a visual system. Objects move rigidly, the illumination varies, the size of objects at the retina changes with the depth from the eye, view directions may change etc. Hence, it is natural to require early visual operations to be unaffected by certain primitive transformations (e.g. translations, rotations, and grey-scale transformations). In other words, the visual system should extract properties that are invariant with respect to these transformations.As we shall see below, these constraints leads to operations that correspond to spatio-temporal derivatives which are then used for computing (differential) geometric descriptions of the incoming data flow. Based on the output of these operations, in turn, a large number of feature detectors can be expressed as well as modules for computing surface shape.The subject of this chapter is to present a tutorial overview on the historical and current insights of linear scale-space theories as a paradigm for describing the structure of scalar images and as a basis for early vision. For other introductory texts on scale-space; see the monographs by Lindeberg (1991, 1994) and Florack (1993) as well as the overview articles by ter Haar Romeny and Florack (1993) and Lindeberg (1994).
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| 3. |
- Brunnström, Kjell, et al.
(författare)
-
Scale and Resolution in Active Analysis of Local Image Structure
- 1990
-
Ingår i: Image and Vision Computing. - : Elsevier. ; 8:4, s. 289-296
-
Tidskriftsartikel (refereegranskat)abstract
- Focus-of-attention is extremely important in human visual perception. If computer vision systems are to perform tasks in a complex, dynamic world they will have to be able to control processing in a way that is analogous to visual attention in humans. Problems connected to foveation (examination of selected regions of the world at high resolution) are examined. In particular, the problem of finding and classifying junctions from this aspect is considered. It is shown that foveation as simulated by controlled, active zooming in conjunction with scale-space techniques allows for robust detection and classification of junctions.
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| 4. |
- Lindeberg, Tony, 1964-
(författare)
-
Scale-space for discrete signals
- 1990
-
Ingår i: IEEE Transactions on Pattern Analysis and Machine Intelligence. - : IEEE Computer Society. - 0162-8828 .- 1939-3539. ; 12:3, s. 234-254
-
Tidskriftsartikel (refereegranskat)abstract
- This article addresses the formulation of a scale-space theory for discrete signals. In one dimension it is possible to characterize the smoothing transformations completely and an exhaustive treatment is given, answering the following two main questions:Which linear transformations remove structure in the sense that the number of local extrema (or zero-crossings) in the output signal does not exceed the number of local extrema (or zero-crossings) in the original signal?How should one create a multi-resolution family of representations with the property that a signal at a coarser level of scale never contains more structure than a signal at a finer level of scale?It is proposed that there is only one reasonable way to define a scale-space for 1D discrete signals comprising a continuous scale parameter, namely by (discrete) convolution with the family of kernels T(n; t) = e^{-t} I_n(t), where I_n are the modified Bessel functions of integer order. Similar arguments applied in the continuous case uniquely lead to the Gaussian kernel.Some obvious discretizations of the continuous scale-space theory are discussed in view of the results presented. It is shown that the kernel T(n; t) arises naturally in the solution of a discretized version of the diffusion equation. The commonly adapted technique with a sampled Gaussian can lead to undesirable effects since scale-space violations might occur in the corresponding representation. The result exemplifies the fact that properties derived in the continuous case might be violated after discretization.A two-dimensional theory, showing how the scale-space should be constructed for images, is given based on the requirement that local extrema must not be enhanced, when the scale parameter is increased continuously. In the separable case the resulting scale-space representation can be calculated by separated convolution with the kernel T(n; t).The presented discrete theory has computational advantages compared to a scale-space implementation based on the sampled Gaussian, for instance concerning the Laplacian of the Gaussian. The main reason is that the discrete nature of the implementation has been taken into account already in the theoretical formulation of the scale-space representation.
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| 5. |
- Lindeberg, Tony, 1964-, et al.
(författare)
-
Foveal scale-space and the linear increase of receptive field size as a function of eccentricity
- 1994
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- This paper addresses the formulation of a foveal scale-space and its relation to the scaling property of receptive field sizes with eccentricity. It is shown how the notion of a fovea can be incorporated into conventional scale-space theory leading to a foveal log-polar scale-space. Natural assumptions about uniform treatment of structures over scales and finite processing capacity imply a linear increase of minimum receptive field size as a function of eccentricity. These assumptions are similar to the ones used for deriving linear scale-space theory and the Gaussian receptive field model for an idealized visual front-end.
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| 6. |
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| 7. |
- Lindeberg, Tony, 1964-, et al.
(författare)
-
Shape from Texture from a Multi-Scale Perspective
- 1993
-
Ingår i: Fourth International Conference on Computer Vision, 1993. Proceedings. - : IEEE conference proceedings. - 0818638702 ; , s. 683-691
-
Konferensbidrag (refereegranskat)abstract
- The problem of scale in shape from texture is addressed. The need for (at least) two scale parameters is emphasized; a local scale describing the amount of smoothing used for suppressing noise and irrelevant details when computing primitive texture descriptors from image data, and an integration scale describing the size of the region in space over which the statistics of the local descriptors is accumulated.A novel mechanism for automatic scale selection is used, based on normalized derivatives. It is used for adaptive determination of the two scale parameters in a multi-scale texture descriptor, thewindowed second moment matrix, which is defined in terms of Gaussian smoothing, first order derivatives, and non-linear pointwise combinations of these. The same scale-selection method can be used for multi-scale blob detection without any tuning parameters or thresholding.The resulting texture description can be combined with various assumptions about surface texture in order to estimate local surface orientation. Two specific assumptions, ``weak isotropy'' and ``constant area'', are explored in more detail. Experiments on real and synthetic reference data with known geometry demonstrate the viability of the approach.
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| 8. |
- Lindeberg, Tony, 1964-, et al.
(författare)
-
Analysis of aerosol images using the scale-space primal sketch
- 1991
-
Ingår i: Machine Vision and Applications. - 0932-8092 .- 1432-1769. ; 4:3, s. 135-144
-
Tidskriftsartikel (refereegranskat)abstract
- We outline a method to analyze aerosol images using the scale-space representation. The pictures, which are photographs of an aerosol generated by a fuel injector, contain phenomena that by a human observer are perceived as periodic or oscillatory structures. The presence of these structures is not immediately apparent since the periodicity manifests itself at a coarse level of scale while the dominating objects inthe images are small dark blobs, that is, fine scale objects. Experimentally, we illustrate that the scale-space theory provides an objective method to bring out these events. However, in this form the method still relies on a subjective observer in order to extract and verify the existence of the periodic phenomena.Then we extend the analysis by adding a recently developed image analysis concept called the scale-space primal sketch. With this tool, we are able to extract significant structures from a grey-level image automatically without any strong a priori assumptions about either the shape or the scale (size) of the primitives. Experiments demonstrate that the periodic drop clusters we perceived in the image are detected by the algorithm as significant image structures. These results provide objective evidence verifying the existence of oscillatory phenomena.
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| 9. |
- Brunnström, Kjell, et al.
(författare)
-
On Scale and Resolution in the Analysis of Local Image Structure
- 1990
-
Ingår i: Proc. 1st European Conf. on Computer Vision. ; , s. 3-12
-
Konferensbidrag (refereegranskat)abstract
- Focus-of-attention is extremely important in human visual perception. If computer vision systems are to perform tasks in a complex, dynamic world they will have to be able to control processing in a way that is analogous to visual attention in humans.In this paper we will investigate problems in connection with foveation, that is examining selected regions of the world at high resolution. We will especially consider the problem of finding and classifying junctions from this aspect. We will show that foveation as simulated by controlled, active zooming in conjunction with scale-space techniques allows robust detection and classification of junctions.
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| 10. |
- Lindeberg, Tony, 1964-, et al.
(författare)
-
Linear Scale-Space I : Basic Theory
- 1994
-
Ingår i: Geometry-Driven Diffusion in Computer Vision. - : Kluwer Academic Publishers. ; , s. 1-41
-
Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- Vision deals with the problem of deriving information about the world from the light reflected from it. Although the active and task-oriented nature of vision is only implicit in this formulation, this view captures several of the essential aspects of vision. As Marr (1982) phrased it in his book Vision, vision is an information processing task, in which an internal representation of information is of utmost importance. Only by representation information can be captured and made available to decision processes. The purpose of a representation is to make certain aspects of the information content explicit, that is, immediately accessible without any need for additional processing.This introductory chapter deals with a fundamental aspect of early image representation---the notion of scale. As Koenderink (1984) emphasizes, the problem of scale must be faced in any imaging situation. An inherent property of objects in the world and details in images is that they only exist as meaningful entities over certain ranges of scale. A simple example of this is the concept of a branch of a tree, which makes sense only at a scale from, say, a few centimeters to at most a few meters. It is meaningless to discuss the tree concept at the nanometer or the kilometer level. At those scales it is more relevant to talk about the molecules that form the leaves of the tree, or the forest in which the tree grows. Consequently, a multi-scale representation is of crucial importance if one aims at describing the structure of the world, or more specifically the structure of projections of the three-dimensional world onto two-dimensional images.The need for multi-scale representation is well understood, for example, in cartography; maps are produced at different degrees of abstraction. A map of the world contains the largest countries and islands, and possibly, some of the major cities, whereas towns and smaller islands appear at first in a map of a country. In a city guide, the level of abstraction is changed considerably to include streets and buildings etc. In other words, maps constitute symbolic multi-scale representations of the world around us, although constructed manually and with very specific purposes in mind.To compute any type of representation from image data, it is necessary to extract information, and hence interact with the data using certain operators. Some of the most fundamental problems in low-level vision and image analysis concern: what operators to use, where to apply them, and how large they should be. If these problems are not appropriately addressed, the task of interpreting the output results can be very hard. Ultimately, the task of extracting information from real image data is severely influenced by the inherent measurement problem that real-world structures, in contrast to certain ideal mathematical entities, such as ``points'' or ``lines'', appear in different ways depending upon the scale of observation.Phrasing the problem in this way shows the intimate relation to physics. Any physical observation by necessity has to be done through some finite aperture, and the result will, in general, depend on the aperture of observation. This holds for any device that registers physical entities from the real world including a vision system based on brightness data. Whereas constant size aperture functions may be sufficient in many (controlled) physical applications, e.g., fixed measurement devices, and also the aperture functions of the basic sensors in a camera (or retina) may have to determined a priori because of practical design constraints, it is far from clear that registering data at a fixed level of resolution is sufficient. A vision system for handling objects of different sizes and at difference distances needs a way to control the scale(s) at which the world is observed.The goal of this chapter is to review some fundamental results concerning a framework known as scale-space that has been developed by the computer vision community for controlling the scale of observation and representing the multi-scale nature of image data. Starting from a set of basic constraints (axioms) on the first stages of visual processing it will be shown that under reasonable conditions it is possible to substantially restrict the class of possible operations and to derive a (unique) set of weighting profiles for the aperture functions. In fact, the operators that are obtained bear qualitative similarities to receptive fields at the very earliest stages of (human) visual processing (Koenderink 1992). We shall mainly be concerned with the operations that are performed directly on raw image data by the processing modules are collectively termed the visual front-end. The purpose of this processing is to register the information on the retina, and to make important aspects of it explicit that are to be used in later stage processes. If the operations are to be local, they have to preserve the topology at the retina; for this reason the processing can be termed retinotopic processing.Early visual operationsAn obvious problem concerns what information should be extracted and what computations should be performed at these levels. Is any type of operation feasible? An axiomatic approach that has been adopted in order to restrict the space of possibilities is to assume that the very first stages of visual processing should be able to function without any direct knowledge about what can be expected to be in the scene. As a consequence, the first stages of visual processing should be as uncommitted and make as few irreversible decisions or choices as possible.The Euclidean nature of the world around us and the perspective mapping onto images impose natural constraints on a visual system. Objects move rigidly, the illumination varies, the size of objects at the retina changes with the depth from the eye, view directions may change etc. Hence, it is natural to require early visual operations to be unaffected by certain primitive transformations (e.g. translations, rotations, and grey-scale transformations). In other words, the visual system should extract properties that are invariant with respect to these transformations.As we shall see below, these constraints leads to operations that correspond to spatio-temporal derivatives which are then used for computing (differential) geometric descriptions of the incoming data flow. Based on the output of these operations, in turn, a large number of feature detectors can be expressed as well as modules for computing surface shape.The subject of this chapter is to present a tutorial overview on the historical and current insights of linear scale-space theories as a paradigm for describing the structure of scalar images and as a basis for early vision. For other introductory texts on scale-space; see the monographs by Lindeberg (1991, 1994) and Florack (1993) as well as the overview articles by ter Haar Romeny and Florack (1993) and Lindeberg (1994).
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