arXiv subjects

Olakunle S. Abawonse

Publications and source records attributed to Olakunle S. Abawonse.

3 recordsLinked to original sources

arXiv2026

Riemannian Shape Analysis of the Corpus Callosum in Kendall Space: Aging and Alzheimer's Disease

The corpus callosum (CC) is a major white-matter structure and a well-established marker of brain aging, but most studies quantify it using scalar summaries that discard its boundary geometry. We present a Riemannian shape-space framework \cite{fletcher2013geodesic-regression} for analyzing age-related morphological change in the midsagittal CC, applied to the OASIS-1 cohort. Each contour is represented by $128$ landmarks and embedded into Kendall shape space, where translation, rotation, and scale are removed. We derive a multivariate geodesic regression with exact Riemannian gradients and use the fitted age-velocity field to localize age-related deformation to five anatomical sub-regions. In the cognitively normal cohort ($n = 252$), geodesic regression outperforms the Euclidean linear benchmark ($R^2 = 0.1355$ vs.\ $0.1216$). Regional energy is anterior-dominant: the Genu carries $46.1\%$ and the Anterior Body $23.3\%$ of total age-related shape change, together accounting for $\sim 69\%$ despite comprising only $\sim 41\%$ of landmarks. Signed projections confirm the ordering (Genu $r = 0.562$; Anterior Body $r = 0.507$). In contrast, age explains less than $0.5\%$ of shape variance in Alzheimer's disease ($n = 88$), indicating that the disease disrupts the healthy aging trajectory. A tangent-space classifier achieves an age-group AUC of $0.791$ from the 2D contour alone, exceeding a recent volumetric benchmark ($0.67$).

cs.CV↗

arXiv2026

An Implemention of Two-Phase Image Segmentation using the Split Bregman Method

In this paper, we describe an implementation of the two-phase image segmentation algorithm proposed by Goldstein, Bresson, Osher in \cite{gold:bre}. This algorithm partitions the domain of a given 2d image into foreground and background regions, and each pixel of the image is assigned membership to one of these two regions. The underlying assumption for the segmentation model is that the pixel values of the input image can be summarized by two distinct average values, and that the region boundaries are smooth. Accordingly, the model is defined as an energy in which the variable is a region membership function to assign pixels to either region, originally proposed by Chan and Vese in \cite{chan:vese}. This energy is the sum of image data terms in the regions and a length penalty for region boundaries. Goldstein, Bresson, Osher modify the energy of Chan-Vese in \cite{gold:bre} so that their new energy can be minimized efficiently using the split Bregman method to produce an equivalent two-phase segmentation. We provide a detailed implementation of this method \cite{gold:bre}, and document its performance with several images over a range of algorithm parameters.

cs.CV↗

arXiv2025

Generalized Samorodnitsky noisy function inequalities, with applications to error-correcting codes

An inequality by Samorodnitsky states that if $f : \mathbb{F}_2^n \to \mathbb{R}$ is a nonnegative boolean function, and $S \subseteq [n]$ is chosen by randomly including each coordinate with probability a certain $λ= λ(q,ρ) < 1$, then \begin{equation} \log \|T_ρf\|_q \leq \mathbb{E}_{S} \log \|\mathbb{E}(f|S)\|_q\;. \end{equation} Samorodnitsky's inequality has several applications to the theory of error-correcting codes. Perhaps most notably, it can be used to show that \emph{any} binary linear code (with minimum distance $ω(\log n)$) that has vanishing decoding error probability on the BEC$(λ)$ (binary erasure channel) also has vanishing decoding error on \emph{all} memoryless symmetric channels with capacity above some $C = C(λ)$. Samorodnitsky determined the optimal $λ= λ(q,ρ)$ for his inequality in the case that $q \geq 2$ is an integer. In this work, we generalize the inequality to $f : Ω^n \to \mathbb{R}$ under any product probability distribution $μ^{\otimes n}$ on $Ω^n$; moreover, we determine the optimal value of $λ= λ(q,μ,ρ)$ for any real $q \in [2,\infty]$, $ρ\in [0,1]$, and distribution~$μ$. As one consequence, we obtain the aforementioned coding theory result for linear codes over \emph{any} finite alphabet.

cs.IT↗