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+*.tif filter=lfs diff=lfs merge=lfs -text
+*.png filter=lfs diff=lfs merge=lfs -text
+manuscript/manuscriptImages/*.* filter=lfs diff=lfs merge=lfs -text

manuscript/.gitignore

+archive*/*
+*.aux
+*.bcf
+*.fdb*
+*.fls
+*.xml
+*.gz
+*.log
+*.out

manuscript/RSF.tex

+%\documentclass[12pt]{article}
+%\usepackage{amsmath,amstext,amsthm,amssymb,epsf}
+\documentclass[draftcls,onecolumn,12pt]{IEEEtran}
+% \documentclass[twocolumn,twoside]{IEEEtran}
+%\documentclass[12pt]{article}
+\usepackage[]{authblk}
+\usepackage{amsmath,amstext,amsthm,amssymb,epsf}
+\usepackage{latexsym} 
+\usepackage[pdftex]{graphicx}
+\graphicspath{ {./manuscriptImages}}
+\usepackage{setspace} 
+\usepackage{float}
+\usepackage[section]{placeins}
+\usepackage[]{hyperref}
+\usepackage{caption} % hypcap is true by default so [hypcap=true] is optional in \usepackage[hypcap=true]{caption}
+\usepackage{xcolor}
+\usepackage{subcaption}
+\usepackage[]{soul}
+\usepackage[bibstyle=nature,citestyle=nature]{biblatex}
+% \addbibresource{ssfClustering.bib}
+\hypersetup{
+    colorlinks=true,
+    linkcolor={blue},
+    citecolor={blue!50!black}, 
+    urlcolor={blue!80!black}
+}
+\sloppy  
+\numberwithin{equation}{section} % in amsmath
+
+%\setlength{\topmargin}{-0.6in}
+%\setlength{\textwidth}{6.4in}
+%\setlength{\oddsidemargin}{0.1in}
+%\setlength{\evensidemargin}{0.1in}
+%\setlength{\textheight}{9.4in}
+
+
+\newtheorem{theorem}{\sc Theorem}
+\newtheorem{proposition}{\sc Proposition}
+\newtheorem{lemma}{\sc Lemma}
+\newtheorem{coro}{\sc Corollary}
+\newtheorem{req}{\sc Requirement}
+\newtheorem{nota}{\sc Notation}
+\newtheorem{defin}{\sc Definition}
+\newtheorem{rem}{\sc Remark}
+\newtheorem{cla}{\sc Claim}
+\newtheorem{ex}{\sc Example}
+\newenvironment{comment}{\begin{small}\begin{quotation}\hspace{-0.23in}\rm}{\end{quotation}\end{small}}
+%\newenvironment{proof}{\par \sc Proof.\rm}{\hspace*{\fill}$\Box$\vspace{1ex}}
+\newenvironment{remark}{\begin{rem}}{\hspace*{\fill}$\Diamond$\end{rem}}
+\newenvironment{example}{\begin{ex}}{\hspace*{\fill}$\diamondsuit$\end{ex}}
+\newenvironment{claim}{\begin{cla}}{\end{cla}}
+\newenvironment{corollary}{\begin{coro}}{\end{coro}}
+\newenvironment{requirement}{\begin{req}}{\end{req}}
+\newenvironment{definition}{\begin{defin}}{\end{defin}}
+\renewcommand{\emptyset}{\varnothing}
+\newcommand{\bin}{\rm bin}
+
+\DeclareMathOperator*{\argmax}{argmax} % no space, limits underneath in displays
+
+\begin{document}
+
+\title{A spatial structure function with metric embedding kernel for retinal OCT}
+
+\author[]{author order TBD}
+\author[1]{Loan Huynh}
+\author[2,3]{Ronald Zambrano}
+\author[1]{Layton Aho}
+\author[2]{Gadi Wollstein}
+\author[2,3]{Joel S. Schuman}
+\author[1]{Andrew R. Cohen}
+
+\affil[1]{Electrical and Computer Engineering, Drexel University, USA}
+\affil[2]{Wills Eye Hospital, Philadelphia, USA}
+\affil[3]{Biomedical Engineering, Drexel University, USA}
+% \affil[3]{Epic?}
+% \affil[*]{correspondence to andrew.r.cohen@drexel.edu}
+\maketitle
+
+\section{???}
+\begin{list}{}{}  
+  \item{ possible submission : \href{https://datacompressionconference.org/program/}{IEEE Data Compression Conference? } }
+  \item { ???visualization aspect ratio??? any strong feelings on stretching images for visualization?}
+  
+\end{list}
+
+\section{The retinal structure function}
+
+We build on these technologies:
+
+0. \href{https://pure.uva.nl/ws/files/4346395/68110\_297537.pdf}{Normalized information distance (NID)}. 
+
+and 
+
+\href{https://doi.org/10.1109/tpami.2023.3264690}{Kolmogorov structure functions}
+
+1. Semi-supervised spectral learning as in \href{https://dl.acm.org/doi/10.5555/1630659.1630742}{Kamvar et al., 2003} [Cohen, et al. 2008]. Key advantage of RKHS [RKHS primer].
+
+2. \href{https://doi.org/10.1093/bioinformatics/btz523}{Hydra Image Processor (HIP)} : The HIP provides 3-D multi-scale structure enhancing filters applied here for retinal OCT stacks []. The HIP allows an efficient plate-enhancement based on 3-D LoG. The HIP also gives us a 3-D non-local means denoising filter. See figure 1. Preliminary experiments with a HIP plate-enhancing non-local means via anisotropic kernel is a promising area for future study. See figure 2.   
+
+observation: Inherent anisotropy of retinal OCT implements optically a plate-enhancing filter, as in \href{https://dspace.library.uu.nl/bitstream/1874/377/18/c2.pdf}{Frangi }.  
+
+3. Free lossless image format (FLIF) 3.3D lossless image compression []. A maniac entropy encoder represents spatial voxel patterns using decision trees. Images that are more similar provide more improvement when compressed together than would images that are less similar. After we encode \emph{a priori} shape knowledge via the structure function radii, the FLIF compression approximates relative Kolmogorov complexity between image pairs to measure spatiotemporal patterns of change.
+
+\section{Using $NCD(OCT_1,OCT_2)$ to predict $|VFMD_1 -VFMD_2|$}
+key results mostly done. 
+
+open source code in progress (?). 
+
+open source image data? what can we release? maybe a small sample, e.g. $\sim 100$ stacks?
+
+Deep learning state of the art in estimating VFMD from retinal OCT achieves RMSE $\lessapprox 2.5$.  We pose the question differently, looking instead to predict 
+$|\Delta VFMD|$ given the normalized compression distance between image pairs. Training a single-layer single-node regression network with sigmoid activation yields cross-validation RMSE $\sim 0.8$.  A second single-layer 10-node regression network with input including one of the two VFMD values (from either image date) achieves cross-validation RMSE $\sim 0.7$. 
+
+\section{Why metric embedding?}
+tl;dr RKHS make subsequent optimization learning easier to implement and more likely to generalize better [primer]. 
+
+
+\section{Retinal OCT and VFMD} 
+related literature -- background on metadata, imaging physics. Key recent deep learning papers [Schuman et al.]. Other learning approaches [NNMF].
+
+
+\section{Future work}
+Anisotropic denoising on the GPU with HIP.
+
+Clustering by compression: e.g. M vs. F, OD vs. OS, zip code?
+
+RKHS combinations: macula + ONH simultaneously, multi-resolution by channel vs. dimensionality reduction, metadata w/ bzip,...?
+
+
+  \begin{figure*}[!ht]
+    {\includegraphics[page=1,width=1.0\textwidth]{figureX.pdf}}
+    \centering
+    \caption[]{\textbf{The retinal structure function (RSF) computes at each image voxel how ‘plate-like’ is the 3-D intensity configuration of the surrounding voxels}. The input image (a, single slice shown) is denoised using non-local means (c,d), and then processed with a Laplacian of Gaussian (LoG) convolution kernel (b, single slice shown). The LoG positive response (red) represents dark structure against a bright background, the negative response (green) represents bright structure against a dark background. The 2-D regional maxima weighted by the LoG, with the interior of each dot scaled by filter response, are shown for illustration (e). The 3-D regional maxima weighted by the LoG (f), are the representation used as input to the normalized compression distance (NCD). Top row (a-d) shows optic nerve OCT using LoG of size $[0.5,10,10]$ voxels, the bottom row (e-h, same captions as a-d) is macula OCT with LoG of size $[0.35,7,7]$ voxels. The goal of the RSF is to extract a local measure of the voxel structure so the NCD best captures patterns of similarity between image pairs. See also supplementary movie (\href[]{https://bioimage.coe.drexel.edu/media/andy/regional_max_pt5_20.mp4}{1}) and 
+    (\href[]{https://bioimage.coe.drexel.edu/media/andy/rsf_pt5_pt35_P10053_Macular Cube 200x200_6-17-2019_13-16-17_OD_sn1677_cube_raw.mp4}{2}).
+
+    }
+    \label{fig:figure1}
+  \end{figure*}  
+
+  \begin{figure*}[!ht]
+    {\includegraphics[page=1,width=1.0\textwidth]{P10010_ONH_NLM.pdf}}
+    \centering
+    \caption[]{\textbf{Inherent resolution anisotropy in retinal OCT enables novel denoising approaches}. The input image (a, single slice shown) is denoised using a 3-D non-local means (b) with an isotropic pattern ($[3,3,3]$ voxels) and search radius ($[25,25,25]$ voxels). With a 'plate-enhancing' anisotropy in both pattern ($[1,5,5]$)) and search ($[5,50,50]$), the orientation of the smoothing direction can be clearly seen along the vertical axis, while along the horizontal or low-res direction (c). The optimal image processing pipeline will be chosen to maximize the retinal structure function, as measured from characteristics of both the embedded and the kernel space. TODO -- add arrows indicating axes...Good figure for a grant, not ready for manuscript? }
+  \end{figure*}
+
+  \begin{figure*}[!ht]
+    {\includegraphics[page=1,width=1.0\textwidth]{P10010_sn0975_z100.pdf}}
+    \centering
+    \caption[]{\textbf{Comparison to Iowa segmentation}. The Iowa segmentation is generally gorgeous and does a great job at capturing the 2-D structure. \href{https://iibi.uiowa.edu/sites/iibi.uiowa.edu/files/2022-08/OCTExplorer_UserManual.pdf}{OCT Explorer} fabulous UI! but the algorithms do not appear to be open-source? Need to confirm. Loan -- re-render the ground truth panel (let's call this the 'Iowa reference algorithm' [Ronald -- refs here]) over the denoised background maybe?}
+  \end{figure*}
+
+\end{document}