improc ass4: Added report with derivatives of f(x, y).

improc/ass4/report/report.tex

+\documentclass[10pt,a4paper]{article}
+
+\usepackage[english]{babel}
+\usepackage[utf8]{inputenc}
+\usepackage{amsmath,hyperref,graphicx,booktabs,float}
+
+% Paragraph indentation
+\setlength{\parindent}{0pt}
+\setlength{\parskip}{1ex plus 0.5ex minus 0.2ex}
+
+\title{Image processing 4: Local Structure}
+\author{Sander van Veen \& Tadde\"us Kroes \\ 6167969 \& 6054129}
+
+\begin{document}
+
+\maketitle
+
+\section{Analytical Local Structure}
+
+\subsection{Derivatives}
+
+We have been given the following function:
+$$f(x, y) = A sin(Vx) + B cos(Wy)$$
+
+The partial derivatives $f_x, f_y, f_{xx}, f_{xy}$ and $f_{yy}$ can be derived as follows:
+\begin{table}[H]
+	\begin{tabular}{rl}
+		$f_x$    & $= A \frac{\delta}{\delta x} sin(Vx) + B \frac{\delta}{\delta x} cos(Wy)$ \\
+	    	     & $= A cos(Vx) \times V + B \times 0$ \\
+	    	     & $= AV cos(Vx)$ \\
+	    	     & \\
+		$f_y$    & $= A \frac{\delta}{\delta y} sin(Vx) + B \frac{\delta}{\delta y} cos(Wy)$ \\
+	    	     & $= A \times 0 - B sin(Wy) \times W$ \\
+	    	     & $= -BW sin(Wy)$ \\
+	    	     & \\
+		$f_{xx}$ & $= AV \frac{\delta}{\delta x} cos(Vx)$ \\
+		         & $= -AV^2 sin(Vx)$ \\
+	    	     & \\
+		$f_{xy}$ & $= AV \frac{\delta}{\delta y} cos(Vx) = 0$ \\
+	    	     & \\
+		$f_{yy}$ & $= -BW \frac{\delta}{\delta y} sin(Wy)$ \\
+		         & $= -BW^2 cos(Wy)$ \\
+	\end{tabular}
+\end{table}
+
+\end{document}
\ No newline at end of file