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  1. Article

    Open Access

    Discrete Approximations of Gaussian Smoothing and Gaussian Derivatives

    This paper develops an in-depth treatment concerning the problem of approximating the Gaussian smoothing and the Gaussian derivative computations in scale-space theory for application on discrete data. With cl...

    Tony Lindeberg in Journal of Mathematical Imaging and Vision (2024)

  2. Article

    Open Access

    Scale-Invariant Scale-Channel Networks: Deep Networks That Generalise to Previously Unseen Scales

    The ability to handle large scale variations is crucial for many real-world visual tasks. A straightforward approach for handling scale in a deep network is to process an image at several scales simultaneously...

    Ylva Jansson, Tony Lindeberg in Journal of Mathematical Imaging and Vision (2022)

  3. Article

    Open Access

    Scale-Covariant and Scale-Invariant Gaussian Derivative Networks

    This paper presents a hybrid approach between scale-space theory and deep learning, where a deep learning architecture is constructed by coupling parameterized scale-space operations in cascade. By sharing the...

    Tony Lindeberg in Journal of Mathematical Imaging and Vision (2022)

  4. Article

    Open Access

    Provably Scale-Covariant Continuous Hierarchical Networks Based on Scale-Normalized Differential Expressions Coupled in Cascade

    This article presents a theory for constructing hierarchical networks in such a way that the networks are guaranteed to be provably scale covariant. We first present a general sufficiency argument for obtainin...

    Tony Lindeberg in Journal of Mathematical Imaging and Vision (2020)

  5. Article

    Open Access

    Dynamic Texture Recognition Using Time-Causal and Time-Recursive Spatio-Temporal Receptive Fields

    This work presents a first evaluation of using spatio-temporal receptive fields from a recently proposed time-causal spatio-temporal scale-space framework as primitives for video analysis. We propose a new fam...

    Ylva Jansson, Tony Lindeberg in Journal of Mathematical Imaging and Vision (2018)

  6. Article

    Open Access

    Spatio-Temporal Scale Selection in Video Data

    This work presents a theory and methodology for simultaneous detection of local spatial and temporal scales in video data. The underlying idea is that if we process video data by spatio-temporal receptive fiel...

    Tony Lindeberg in Journal of Mathematical Imaging and Vision (2018)

  7. Article

    Open Access

    Temporal Scale Selection in Time-Causal Scale Space

    When designing and develo** scale selection mechanisms for generating hypotheses about characteristic scales in signals, it is essential that the selected scale levels reflect the extent of the underlying st...

    Tony Lindeberg in Journal of Mathematical Imaging and Vision (2017)

  8. Article

    Open Access

    Time-Causal and Time-Recursive Spatio-Temporal Receptive Fields

    We present an improved model and theory for time-causal and time-recursive spatio-temporal receptive fields, obtained by a combination of Gaussian receptive fields over the spatial domain and first-order integ...

    Tony Lindeberg in Journal of Mathematical Imaging and Vision (2016)

  9. Article

    Open Access

    Image Matching Using Generalized Scale-Space Interest Points

    The performance of matching and object recognition methods based on interest points depends on both the properties of the underlying interest points and the choice of associated image descriptors. This paper d...

    Tony Lindeberg in Journal of Mathematical Imaging and Vision (2015)

  10. Article

    Open Access

    Scale Selection Properties of Generalized Scale-Space Interest Point Detectors

    Scale-invariant interest points have found several highly successful applications in computer vision, in particular for image-based matching and recognition.

    Tony Lindeberg in Journal of Mathematical Imaging and Vision (2013)

  11. No Access

    Article

    Generalized Gaussian Scale-Space Axiomatics Comprising Linear Scale-Space, Affine Scale-Space and Spatio-Temporal Scale-Space

    This paper describes a generalized axiomatic scale-space theory that makes it possible to derive the notions of linear scale-space, affine Gaussian scale-space and linear spatio-temporal scale-space using a si...

    Tony Lindeberg in Journal of Mathematical Imaging and Vision (2011)

  12. No Access

    Article

    Discrete derivative approximations with scale-space properties: A basis for low-level feature extraction

    This article shows how discrete derivative approximations can be defined so thatscale-space properties hold exactly also in the discrete domain. Starting from a set of natural requirements on the first processing...

    Tony Lindeberg in Journal of Mathematical Imaging and Vision (1993)

  13. No Access

    Article

    Scale-space behaviour of local extrema and blobs

    Elementary techniques from real analysis, and singularity theory are applied to derive analytical results for the behaviour in scale-space of critical points and related entities. The main results of the treat...

    Tony Lindeberg in Journal of Mathematical Imaging and Vision (1992)