| 1. |
- Lindeberg, Tony, 1964-
(författare)
-
On the behaviour in scale-space of local extrema and blobs
- 1991
-
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)
-
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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| 4. |
- 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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| 5. |
- 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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| 6. |
- Lindeberg, Tony, 1964-
(författare)
-
Scale-Space Theory : A Basic Tool for Analysing Structures at Different Scales
- 1994
-
Ingår i: Journal of Applied Statistics. - : Informa UK Limited. - 0266-4763 .- 1360-0532. ; 21, s. 225-270
-
Tidskriftsartikel (refereegranskat)abstract
- An inherent property of objects in the world is that they only exist as meaningful entities over certain ranges of scale. If one aims at describing the structure of unknown real-world signals, then a multi-scale representation of data is of crucial importance.This article gives a tutorial review of a special type of multi-scale representation, linear scale-space representation, which has been developed by the computer vision community in order to handle image structures at different scales in a consistent manner. The basic idea is to embed the original signal into a one-parameter family of gradually smoothed signals, in which the fine scale details are successively suppressed.Under rather general conditions on the type of computations that are to performed at the first stages of visual processing, in what can be termed the visual front end, it can be shown that the Gaussian kernel and its derivatives are singled out as the only possible smoothing kernels. The conditions that specify the Gaussian kernel are, basically, linearity and shift-invariance combined with different ways of formalizing the notion that structures at coarse scales should correspond to simplifications of corresponding structures at fine scales --- they should not be accidental phenomena created by the smoothing method. Notably, several different ways of choosing scale-space axioms give rise to the same conclusion.The output from the scale-space representation can be used for a variety of early visual tasks; operations like feature detection, feature classification and shape computation can be expressed directly in terms of (possibly non-linear) combinations of Gaussian derivatives at multiple scales. In this sense, the scale-space representation can serve as a basis for early vision.During the last few decades a number of other approaches to multi-scale representations have been developed, which are more or less related to scale-space theory, notably the theories of pyramids, wavelets and multi-grid methods. Despite their qualitative differences, the increasing popularity of each of these approaches indicates that the crucial notion of scaleis increasingly appreciated by the computer vision community and by researchers in other related fields.An interesting similarity with biological vision is that the scale-space operators closely resemble receptive field profiles registered in neurophysiological studies of the mammalian retina and visual cortex.
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| 7. |
- Lindeberg, Tony, 1964-
(författare)
-
Scale-Space Theory in Computer Vision
- 1993
-
Bok (övrigt vetenskapligt/konstnärligt)abstract
- A basic problem when deriving information from measured data, such as images, originates from the fact that objects in the world, and hence image structures, exist as meaningful entities only over certain ranges of scale. "Scale-Space Theory in Computer Vision" describes a formal theory for representing the notion of scale in image data, and shows how this theory applies to essential problems in computer vision such as computation of image features and cues to surface shape. The subjects range from the mathematical foundation to practical computational techniques. The power of the methodology is illustrated by a rich set of examples.This book is the first monograph on scale-space theory. It is intended as an introduction, reference, and inspiration for researchers, students, and system designers in computer vision as well as related fields such as image processing, photogrammetry, medical image analysis, and signal processing in general.The presentation starts with a philosophical discussion about computer vision in general. The aim is to put the scope of the book into its wider context, and to emphasize why the notion of scaleis crucial when dealing with measured signals, such as image data. An overview of different approaches to multi-scale representation is presented, and a number special properties of scale-space are pointed out.Then, it is shown how a mathematical theory can be formulated for describing image structures at different scales. By starting from a set of axioms imposed on the first stages of processing, it is possible to derive a set of canonical operators, which turn out to be derivatives of Gaussian kernels at different scales.The problem of applying this theory computationally is extensively treated. A scale-space theory is formulated for discrete signals, and it demonstrated how this representation can be used as a basis for expressing a large number of visual operations. Examples are smoothed derivatives in general, as well as different types of detectors for image features, such as edges, blobs, and junctions. In fact, the resulting scheme for feature detection induced by the presented theory is very simple, both conceptually and in terms of practical implementations.Typically, an object contains structures at many different scales, but locally it is not unusual that some of these "stand out" and seem to be more significant than others. A problem that we give special attention to concerns how to find such locally stable scales, or rather how to generate hypotheses about interesting structures for further processing. It is shown how the scale-space theory, based on a representation called the scale-space primal sketch, allows us to extract regions of interest from an image without prior information about what the image can be expected to contain. Such regions, combined with knowledge about the scales at which they occur constitute qualitative information, which can be used for guiding and simplifying other low-level processes.Experiments on different types of real and synthetic images demonstrate how the suggested approach can be used for different visual tasks, such as image segmentation, edge detection, junction detection, and focus-of-attention. This work is complemented by a mathematical treatment showing how the behaviour of different types of image structures in scale-space can be analysed theoretically.It is also demonstrated how the suggested scale-space framework can be used for computing direct cues to three-dimensional surface structure, using in principle only the same types of visual front-end operations that underlie the computation of image features.Although the treatment is concerned with the analysis of visual data, the general notion of scale-space representation is of much wider generality and arises in several contexts where measured data are to be analyzed and interpreted automatically.
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| 8. |
- Brunnström, Kjell, et al.
(författare)
-
Active detection and classification of junctions by foveation with a head-eye system guided by the scale-space primal sketch
- 1992
-
Ingår i: Computer Vision — ECCV'92. - Berlin, Heidelberg : Springer Berlin/Heidelberg. - 9783540554264 ; , s. 701-709
-
Konferensbidrag (refereegranskat)abstract
- We consider how junction detection and classification can be performed in an active visual system. This is to exemplify that feature detection and classification in general can be done by both simple and robust methods, if the vision system is allowed to look at the world rather than at prerecorded images. We address issues on how to attract the attention to salient local image structures, as well as on how to characterize those.
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| 9. |
- Gårding, Jonas, et al.
(författare)
-
Direct estimation of local surface shape in a fixating binocular vision system
- 1994
-
Ingår i: Computer Vision — ECCV '94. - Berlin, Heidelberg : Springer Berlin/Heidelberg. - 9783540579564 ; , s. 365-376
-
Konferensbidrag (refereegranskat)abstract
- This paper addresses the problem of computing cues to the three-dimensional structure of surfaces in the world directly from the local structure of the brightness pattern of a binocular image pair. The geometric information content of the gradient of binocular disparity is analyzed for the general case of a fixating vision system with symmetric or asymmetric vergence, and with either known or unknown viewing geometry. A computationally inexpensive technique which exploits this analysis is proposed. This technique allows a local estimate of surface orientation to be computed directly from the local statistics of the left and right image brightness gradients, without iterations or search. The viability of the approach is demonstrated with experimental results for both synthetic and natural gray-level images.
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| 10. |
- 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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