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Riku Klén

Publications and source records attributed to Riku Klén.

At least 19 recordsLinked to original sources
arXiv2025

Quantitative evaluation of unsupervised clustering algorithms for dynamic total-body PET image analysis

Background. Recently, dynamic total-body positron emission tomography (PET) imaging has become possible due to new scanner devices. While clustering algorithms have been proposed for PET analysis already earlier, there is still little research systematically evaluating these algorithms for processing of dynamic total-body PET images. Materials and methods. Here, we compare the performance of 15 unsupervised clustering methods, including K-means either by itself or after principal component analysis (PCA) or independent component analysis (ICA), Gaussian mixture model (GMM), fuzzy c-means (FCM), agglomerative clustering, spectral clustering, and several newer clustering algorithms, for classifying time activity curves (TACs) in dynamic PET images. We use dynamic total-body $^{15}$O-water PET images collected from 30 patients with suspected or confirmed coronary artery disease. To evaluate the clustering algorithms in a quantitative way, we use them to classify 5000 TACs from each image based on whether the curve is taken from brain, right heart ventricle, right kidney, lower right lung lobe, or urinary bladder. Results. According to our results, the best methods are GMM, FCM, and ICA combined with mini batch K-means, which classified the TACs with a median accuracies of 89\%, 83\%, and 81\%, respectively, in a processing time of half a second or less on average for each image. Conclusion. GMM, FCM, and ICA with mini batch K-means show promise for dynamic total-body PET analysis.

stat.AP↗
arXiv2024

AI for the prediction of early stages of Alzheimer's disease from neuroimaging biomarkers -- A narrative review of a growing field

Objectives: The objectives of this narrative review are to summarize the current state of AI applications in neuroimaging for early Alzheimer's disease (AD) prediction and to highlight the potential of AI techniques in improving early AD diagnosis, prognosis, and management. Methods: We conducted a narrative review of studies using AI techniques applied to neuroimaging data for early AD prediction. We examined single-modality studies using structural MRI and PET imaging, as well as multi-modality studies integrating multiple neuroimaging techniques and biomarkers. Furthermore, they reviewed longitudinal studies that model AD progression and identify individuals at risk of rapid decline. Results: Single-modality studies using structural MRI and PET imaging have demonstrated high accuracy in classifying AD and predicting progression from mild cognitive impairment (MCI) to AD. Multi-modality studies, integrating multiple neuroimaging techniques and biomarkers, have shown improved performance and robustness compared to single-modality approaches. Longitudinal studies have highlighted the value of AI in modeling AD progression and identifying individuals at risk of rapid decline. However, challenges remain in data standardization, model interpretability, generalizability, clinical integration, and ethical considerations. Conclusion: AI techniques applied to neuroimaging data have the potential to improve early AD diagnosis, prognosis, and management. Addressing challenges related to data standardization, model interpretability, generalizability, clinical integration, and ethical considerations is crucial for realizing the full potential of AI in AD research and clinical practice. Collaborative efforts among researchers, clinicians, and regulatory agencies are needed to develop reliable, robust, and ethical AI tools that can benefit AD patients and society.

cs.LG↗
arXiv2023

Image augmentation with conformal mappings for a convolutional neural network

For augmentation of the square-shaped image data of a convolutional neural network (CNN), we introduce a new method, in which the original images are mapped onto a disk with a conformal mapping, rotated around the center of this disk and mapped under such a Möbius transformation that preserves the disk, and then mapped back onto their original square shape. This process does not result the loss of information caused by removing areas from near the edges of the original images unlike the typical transformations used in the data augmentation for a CNN. We offer here the formulas of all the mappings needed together with detailed instructions how to write a code for transforming the images. The new method is also tested with simulated data and, according the results, using this method to augment the training data of 10 images into 40 images decreases the amount of the error in the predictions by a CNN for a test set of 160 images in a statistically significant way (p-value=0.0360).

cs.CV↗
arXiv2020

Ptolemy constant and uniformity

We study Ptolemy constant and uniformity constant in various plane domains including triangles, quadrilaterals and ellipses.

math.MG↗
arXiv2017

Local convexity of metric balls

We study local convexity properties of the triangular ratio metric balls in proper subdomains of the real coordinate space. We also study inclusion properties of the visual angle metric balls and related hyperbolic type metric balls in the complement of the origin and the upper half space.

math.MG↗
arXiv2017

Volume growth of quasihyperbolic balls

The purpose of this paper is to study the notion of the quasihyperbolic volume and to find growth estimates for the quasihyperbolic volume of balls in a domain $G \subset {\mathbb R}^n\,$ in terms of the radii.

math.MG↗
arXiv2017

Geometric properties of $φ$-uniform domains

We consider proper subdomains $G$ of $\mathbb{R}^n$ and their images $G'=f(G)$ under quasiconformal mappings $f$ of $\mathbb{R}^n$. We compare the distance ratio metrics of $G$ and $G'$; as an application we show that $φ$-uniform domains are preserved under quasiconformal mappings of $\mathbb{R}^n$. A sufficient condition for $φ$-uniformity is obtained in terms of the quasi-symmetry condition. We give a geometric condition for uniformity: If $G\subset\mathbb{R}^n$ is $ϕ$-uniform and satisfies the twisted cone condition, then it is uniform. We also construct a planar $ϕ$-uniform domain whose complement is not $ψ$-uniform for any $ψ$.

math.MG↗
arXiv2016

Hyperbolic type distances in starlike domains

We study the growth of hyperbolic type distances in starlike domains. We derive estimates for various hyperbolic type distances and consider the asymptotic sharpness of the estimates.

math.MG↗
arXiv2015

Geometric properties of the Cassinian metric

In this paper we prove a sharp distortion property of the Cassinian metric under Möbius transformations of a punctured ball onto another punctured ball. The paper also deals with discussion on local convexity properties of the Cassinian metric balls in some specific subdomains of $\mathbb{R}^n$. Inclusion properties of the Cassinian metric balls with other hyperbolic-type metric balls are also investigated. In particular, several conjectures are also stated in response to sharpness of the inclusion relations.

math.MG↗
arXiv2015

Balls in the triangular ratio metric

We consider the triangular ratio metric and estimate the radius of convexity for balls in some special domains and prove the inclusion relations of metric balls defined by the triangular ratio metric, the quasihyperbolic metric and the $j$-metric.

math.MG↗
arXiv2015

Lipschitz conditions, triangular ratio metric, and quasiconformal maps

The triangular ratio metric is studied in subdomains of the complex plane and Euclidean $n$-space. Various inequalities are proven for it. The main results deal with the behavior of this metric under quasiconformal maps. We also study the smoothness of metric disks with small radii.

math.CA↗
arXiv2015

New trigonometric and hyperbolic inequalities

The aim of this paper is to prove new trigonometric and hyperbolic inequalities, which constitute among others refinements or analogs of famous Cusa-Huygens, Wu-Srivastava, and related inequalities. In most cases, the obtained results are sharp.

math.CA↗
arXiv2015

On isometries of conformally invariant metric

We prove that isometries in a conformally invariant metric of a general domain are quasiconformal. In the particular case of the punctured space, we prove that isometries in this metric are Mobius, thus resolving a conjecture of Ferrand, Martin and Vuorinen [FMV, p. 200] in this particular case.

math.CV↗
arXiv2014

On smoothness of quasihyperbolic balls

We investigate properties of quasihyperbolic balls and geodesics in Euclidean and Banach spaces. Our main result is that in uniformly smooth Banach spaces a quasihyperbolic ball of a convex domain is $C^1$-smooth. The question about the smoothness of quasihyperbolic balls is old, originating back to the discussions of F.W. Gehring and M. Vuorinen in 1970's. To our belief, the result is new also in the Euclidean setting. We also address some other issues involving the smoothness of quasihyperbolic balls. We introduce an interesting application of quasihyperbolic metrics to renormings of Banach spaces. To provide a useful tool for this approach we turn our attention to the variational stability of quasihyperbolic geodesics. Several examples and illustrations are provided.

math.FA↗
arXiv2014

Distortion and topology

For a self mapping $f:\mathbb{D}\to \mathbb{D}$ of the unit disk in $\mathbb{C}$ which has finite distortion, we give a separation condition on the components of the set where the distortion is large - say greater than a given constant - which implies that $f$ extends homeomorphically and quasisymetrically to the boundary $\mathbb{S}$ and thus $f$ shares its boundary values with a quasiconformal mapping whose distortion can be explicitly estimated in terms of the data. This result holds more generally. This condition, uniformly separated in modulus, allows the set where the distortion is large to accumulate densely on the boundary but does not allow a component to run out to the boundary. The lift of a Jordan domain in a Riemann surface to its universal cover $\mathbb{D}$ is always uniformly separated in modulus and this allows us to apply these results in the theory of Riemann surfaces to identify an interesting link between the support of the high distortion of a map and topology of the surface - again with explicit and good estimates. As part of our investigations we study mappings $φ:\mathbb{S}\to\mathbb{S}$ which are the germs of a conformal mapping and give good bounds on the distortion of a quasiconformal extension of $φ$. We extend these results to the germs of quasisymmetric mappings. These appear of independent interest and identify new geometric invariants.

math.CV↗
arXiv2013

Examples of fractals satisfying the quasihyperbolic boundary condition

In this paper we give explicit examples of bounded domains that satisfy the quasihyperbolic boundary condition and calculate the values for the constants. These domains are also John domains and we calculate John constants as well. The authors do not know any other paper where exact values of parameters has been estimated.

math.CA↗
arXiv2013

The visual angle metric and Möbius transformations

A new similarity invariant metric $v_G$ is introduced. The visual angle metric $v_G$ is defined on a domain $G\subsetneq\Rn$ whose boundary is not a proper subset of a line. We find sharp bounds for $v_G$ in terms of the hyperbolic metric in the particular case when the domain is either the unit ball $\Bn$ or the upper half space $\Hn$. We also obtain the sharp Lipschitz constant for a Möbius transformation $f: G\rightarrow G'$ between domains $G$ and $G'$ in $\Rn$ with respect to the metrics $v_G$ and $v_{G'}$. For instance, in the case $G=G'=\Bn$ the result is sharp.

math.MG↗