[CT404]: Add Lab 2

year4/semester1/CT404: Graphics & Image Processing/assignments/lab2/code/hog.m

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+close all;
+clear all;
+clc;
+
+% Load necessary package
+pkg load image;
+
+% Load and preprocess the image
+img = imread('truck.jpg'); % Replace with the path to your image
+if size(img, 3) == 3
+    img = rgb2gray(img); % Convert to grayscale if the image is in color
+end
+
+% Resize the image to 128x64 for standardization
+img = imresize(img, [128, 64]);
+
+% Gamma normalization
+gamma = 0.9; % Example gamma value
+img = im2double(img) .^ gamma; % Convert to double and apply gamma normalization
+
+figure;
+imshow(img);
+title('Gamma-normalized Image');
+
+% Parameters for HOG
+cell_size = 4;         % Size of each cell (4x4 pixels)
+block_size = 2;        % Number of cells per block (2x2 cells)
+num_bins = 9;          % Number of orientation bins (0° to 180°)
+bin_size = 180 / num_bins;
+
+% Compute gradients using Sobel operator on the entire image
+Gx = imfilter(double(img), [-1 0 1; -2 0 2; -1 0 1], 'conv'); % Horizontal gradient
+Gy = imfilter(double(img), [-1 -2 -1; 0 0 0; 1 2 1], 'conv'); % Vertical gradient
+
+% Compute gradient magnitude and orientation
+magnitude = sqrt(Gx.^2 + Gy.^2);
+orientation = atan2d(Gy, Gx);
+orientation(orientation < 0) += 180; % Convert orientation to [0, 180] range
+
+% Display gradient magnitude and orientation
+figure;
+imshow(magnitude, []);
+title('Gradient Magnitude of the Image');
+
+% Display gradient orientation using quiver
+figure;
+imshow(img); % Show original image as background
+hold on;
+
+% Downsample the quiver plot for better visualization, e.g., every 4th pixel
+step = 4; % Adjust the step to make the plot less dense if needed
+
+% Plot gradient orientations using Gx and Gy as the vector components
+[x, y] = meshgrid(1:step:size(Gx, 2), 1:step:size(Gy, 1));
+quiver(x, y, Gx(1:step:end, 1:step:end), Gy(1:step:end, 1:step:end), 'color', 'r', 'LineWidth', 0.5);
+
+title('Gradient Orientation Visualization Using Quiver');
+hold off;
+
+% Calculate number of cells in each direction
+num_cells_row = floor(size(img, 1) / cell_size);
+num_cells_col = floor(size(img, 2) / cell_size);
+
+% Preallocate the HOG feature array
+hog_features = zeros(1, num_cells_row * num_cells_col * num_bins);
+
+% Calculate HOG features for each cell
+counter = 1;
+for row = 1:cell_size:(size(img, 1) - cell_size + 1)
+    for col = 1:cell_size:(size(img, 2) - cell_size + 1)
+        % Extract cell gradient magnitudes and orientations
+        cell_magnitude = magnitude(row:row+cell_size-1, col:col+cell_size-1);
+        cell_orientation = orientation(row:row+cell_size-1, col:col+cell_size-1);
+
+        % Calculate histogram for the cell manually
+        cell_histogram = zeros(1, num_bins);
+        for bin = 1:num_bins
+            % Define the orientation range for the bin
+            angle_min = (bin - 1) * bin_size;
+            angle_max = bin * bin_size;
+
+            % Find pixels within the bin range
+            mask = (cell_orientation >= angle_min) & (cell_orientation < angle_max);
+
+            % Sum the magnitudes of pixels within the current orientation bin
+            cell_histogram(bin) = sum(cell_magnitude(mask));
+        end
+
+        % Store cell histogram in hog_features
+        hog_features(counter:counter+num_bins-1) = cell_histogram;
+        counter = counter + num_bins;
+    end
+end
+
+% Block normalization: Divide the HOG features into blocks of 2x2 cells and normalize
+block_histograms = [];
+for row = 1:num_cells_row - block_size + 1
+    for col = 1:num_cells_col - block_size + 1
+        % Compute the index in hog_features for the current block
+        start_index = ((row - 1) * num_cells_col + col - 1) * num_bins + 1;
+        end_index = start_index + block_size * block_size * num_bins - 1;
+
+        % Extract the block of HOG features
+        block = hog_features(start_index:end_index);
+
+        % Normalize the block histogram
+        norm_block = block / sqrt(sum(block .^ 2) + 1e-6);
+
+        % Append the normalized block to block_histograms
+        block_histograms = [block_histograms, norm_block];
+    end
+end
+
+% Final HOG descriptor for the entire image
+hog_descriptor = block_histograms;
+
+% Display results
+disp("HOG Descriptor for the entire image:");
+disp(size(hog_descriptor));
+disp("Length of HOG descriptor vector:");
+disp(length(hog_descriptor));
+
+% Visualization of HOG Features on a Blank Canvas
+figure;
+imshow(ones(size(img)), []); % Blank figure with same size as image
+hold on;
+
+% Visualize dominant gradient direction per cell
+for row = 1:cell_size:(size(img, 1) - cell_size + 1)
+    for col = 1:cell_size:(size(img, 2) - cell_size + 1)
+        % Get cell gradient data
+        cell_magnitude = magnitude(row:row+cell_size-1, col:col+cell_size-1);
+        cell_orientation = orientation(row:row+cell_size-1, col:col+cell_size-1);
+
+        % Calculate histogram for the cell manually
+        cell_histogram = zeros(1, num_bins);
+        for bin = 1:num_bins
+            % Define the orientation range for the bin
+            angle_min = (bin - 1) * bin_size;
+            angle_max = bin * bin_size;
+
+            % Find pixels within the bin range
+            mask = (cell_orientation >= angle_min) & (cell_orientation < angle_max);
+
+            % Sum the magnitudes of pixels within the current orientation bin
+            cell_histogram(bin) = sum(cell_magnitude(mask));
+        end
+
+        % Find the dominant orientation
+        [max_value, dominant_bin] = max(cell_histogram);
+        dominant_orientation = (dominant_bin - 1) * bin_size + bin_size / 2; % Center of the bin
+
+        % Convert the orientation to radians for plotting
+        angle_rad = deg2rad(dominant_orientation);
+
+        % Plot the dominant gradient direction using quiver
+        scale_factor = 0.3;
+        quiver(col + cell_size / 2, row + cell_size / 2, ...
+               scale_factor * max_value * cos(angle_rad), ...
+               scale_factor * max_value * sin(angle_rad), ...
+               'color', 'w', 'LineWidth', 1);
+    end
+end
+
+title('HOG Features Visualization for Dominant Orientation per Cell');
+hold off;
+

year4/semester1/CT404: Graphics & Image Processing/assignments/lab2/latex/assignment.tex

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+%! TeX program = lualatex
+\documentclass[a4paper]{article} 
+
+% packages
+\usepackage{microtype}      % Slightly tweak font spacing for aesthetics
+\usepackage[english]{babel} % Language hyphenation and typographical rules
+\usepackage[final, colorlinks = true, urlcolor = black, linkcolor = black]{hyperref} 
+\usepackage{changepage}     % adjust margins on the fly
+
+\usepackage{fontspec}
+\setmainfont{EB Garamond}
+\setmonofont[Scale=MatchLowercase]{Deja Vu Sans Mono}
+
+\usepackage{minted}
+\usemintedstyle{algol_nu}
+\usepackage{xcolor}
+
+\usepackage{pgfplots}
+\pgfplotsset{width=\textwidth,compat=1.9}
+
+\usepackage{caption}
+\newenvironment{code}{\captionsetup{type=listing}}{}
+\captionsetup[listing]{skip=0pt}
+\setlength{\abovecaptionskip}{5pt}
+\setlength{\belowcaptionskip}{5pt}
+
+\usepackage[yyyymmdd]{datetime}
+\renewcommand{\dateseparator}{--}
+
+\usepackage{titlesec}
+% \titleformat{\section}{\LARGE\bfseries}{}{}{}[\titlerule]
+% \titleformat{\subsection}{\Large\bfseries}{}{0em}{}
+% \titlespacing{\subsection}{0em}{-0.7em}{0em}
+%
+% \titleformat{\subsubsection}{\large\bfseries}{}{0em}{$\bullet$ }
+% \titlespacing{\subsubsection}{1em}{-0.7em}{0em}
+
+% margins
+\addtolength{\hoffset}{-2.25cm}
+\addtolength{\textwidth}{4.5cm}
+\addtolength{\voffset}{-3.25cm}
+\addtolength{\textheight}{5cm}
+\setlength{\parskip}{0pt}
+\setlength{\parindent}{0in}
+% \setcounter{secnumdepth}{0}
+
+\begin{document}
+\hrule \medskip
+\begin{minipage}{0.295\textwidth} 
+    \raggedright
+    \footnotesize 
+    \begin{tabular}{@{}l l} % Define a two-column table with left alignment
+        Name: & Andrew Hayes \\
+        Student ID: & 21321503 \\
+    \end{tabular}
+\end{minipage}
+\begin{minipage}{0.4\textwidth} 
+    \centering 
+    \vspace{0.4em}
+    \LARGE 
+    \textsc{ct404} \\ 
+\end{minipage}
+\begin{minipage}{0.295\textwidth} 
+    \raggedleft
+    \footnotesize 
+    \begin{tabular}{@{}l l} % Define a two-column table with left alignment
+        Name: & Brian Moyles \\
+        Student ID: & 21333461\\
+    \end{tabular}
+\end{minipage}
+\smallskip
+\hrule 
+\begin{center}
+    \normalsize
+    Lab Assignment 2: HOG
+\end{center}
+\hrule
+
+\section{HOG Feature Extraction on Your Own Image (\mintinline{matlab}{cell_size=4}, \mintinline{matlab}{block_size=2})}
+\noindent
+\begin{minipage}{0.49\textwidth}
+\begin{figure}[H]
+    \centering
+    \includegraphics[width=0.6\textwidth]{./images/1_gamma-normalised.png}
+    \caption{Gamma-normalised image}
+\end{figure}
+\end{minipage}
+\hfill
+\begin{minipage}{0.49\textwidth}
+\begin{figure}[H]
+    \centering
+    \includegraphics[width=0.6\textwidth]{./images/1_gradient_magnitude.png}
+    \caption{Gradient magnitude of the image}
+\end{figure}
+\end{minipage}
+
+\begin{minipage}{0.49\textwidth}
+\begin{figure}[H]
+    \centering
+    \includegraphics[width=0.6\textwidth]{./images/1_gradient_orientation.png}
+    \caption{Gradient orientation visualisation using Quiver}
+\end{figure}
+\end{minipage}
+\hfill
+\begin{minipage}{0.49\textwidth}
+\begin{figure}[H]
+    \centering
+    \includegraphics[width=0.6\textwidth]{./images/1_hog_features.png}
+    \caption{HOG features visualisation for the dominant orientation per cell}
+\end{figure}
+\end{minipage}
+
+\section{Experiment with HOG Parameters}
+\subsection{\mintinline{matlab}{cell_size = 8}, \mintinline{matlab}{block_size=2}}
+\noindent
+\begin{minipage}{0.49\textwidth}
+\begin{figure}[H]
+    \centering
+    \includegraphics[width=0.6\textwidth]{./images/2_1_gamma-normalised.png}
+    \caption{Gamma-normalised image}
+\end{figure}
+\end{minipage}
+\hfill
+\begin{minipage}{0.49\textwidth}
+\begin{figure}[H]
+    \centering
+    \includegraphics[width=0.6\textwidth]{./images/2_1_gradient_magnitude.png}
+    \caption{Gradient magnitude of the image}
+\end{figure}
+\end{minipage}
+
+\begin{minipage}{0.49\textwidth}
+\begin{figure}[H]
+    \centering
+    \includegraphics[width=0.6\textwidth]{./images/2_1_gradient_orientation.png}
+    \caption{Gradient orientation visualisation using Quiver}
+\end{figure}
+\end{minipage}
+\hfill
+\begin{minipage}{0.49\textwidth}
+\begin{figure}[H]
+    \centering
+    \includegraphics[width=0.6\textwidth]{./images/2_1_hog_features.png}
+    \caption{HOG features visualisation for the dominant orientation per cell}
+\end{figure}
+\end{minipage}
+
+\subsection{\mintinline{matlab}{cell_size = 16}, \mintinline{matlab}{block_size=4}}
+\noindent
+\begin{minipage}{0.49\textwidth}
+\begin{figure}[H]
+    \centering
+    \includegraphics[width=0.6\textwidth]{./images/2_2_gamma-normalised.png}
+    \caption{Gamma-normalised image}
+\end{figure}
+\end{minipage}
+\hfill
+\begin{minipage}{0.49\textwidth}
+\begin{figure}[H]
+    \centering
+    \includegraphics[width=0.6\textwidth]{./images/2_2_gradient_magnitude.png}
+    \caption{Gradient magnitude of the image}
+\end{figure}
+\end{minipage}
+
+\begin{minipage}{0.49\textwidth}
+\begin{figure}[H]
+    \centering
+    \includegraphics[width=0.6\textwidth]{./images/2_2_gradient_orientation.png}
+    \caption{Gradient orientation visualisation using Quiver}
+\end{figure}
+\end{minipage}
+\hfill
+\begin{minipage}{0.49\textwidth}
+\begin{figure}[H]
+    \centering
+    \includegraphics[width=0.6\textwidth]{./images/2_2_hog_features.png}
+    \caption{HOG features visualisation for the dominant orientation per cell}
+\end{figure}
+\end{minipage}
+
+\subsection{How does changing the cell size \& block size affect the HOG visualisation?}
+A smaller cell size captures finer details \& small-scale gradients in the image, resulting in more local features and a dense \& detailed visualisation.
+However, it's also more sensitive to noise, especially around the hair area where there are less prominent edges.
+A larger cell size, on the other hand, results in a coarser representation with reduced sensitivity to small details \& noise, but with potential to miss finer-detailed structures like ears, and an overall sparser \& less detailed visualisation.
+\\\\
+A smaller block size focuses on local normalisation of gradient features, maintaining fine details and ensuring that local contrast variations are accounted for which can improve robustness in areas with significant intensity variation, such as around the eyes.
+A larger block size averages features over a broader area, resulting in more ``global'' normalisation that can make it less sensitive to fine details \& noise.
+
+\subsection{Which cell size \& block size provide the most visually distinguishable features?}
+We would recommend the 8$\times$8 cell size with 2$\times$2 block size as it captures the important details \& overall structure of the face without introducing too much noise into the visualisation, without losing too much detail.
+The original results obtained with \mintinline{matlab}{cell_size = 4}, \mintinline{matlab}{block_size=2} had a lot of noise compared to results obtained with \mintinline{matlab}{cell_size = 8}, \mintinline{matlab}{block_size=2}.
+Furthermore, the results obtained with \mintinline{matlab}{cell_size = 16}, \mintinline{matlab}{block_size=4} were far too coarse to be visually distinguishable, and left out a lot of important details.
+
+\section{HOG Feature Extraction on a Car or Truck Image}
+\begin{figure}[H]
+    \centering
+    \includegraphics[width=0.6\textwidth]{../code/truck.jpg}
+    \caption{Original truck image}
+\end{figure}
+
+\noindent
+\begin{minipage}{0.49\textwidth}
+\begin{figure}[H]
+    \centering
+    \includegraphics[width=0.6\textwidth]{./images/3_gamma-normalised.png}
+    \caption{Gamma-normalised image}
+\end{figure}
+\end{minipage}
+\hfill
+\begin{minipage}{0.49\textwidth}
+\begin{figure}[H]
+    \centering
+    \includegraphics[width=0.6\textwidth]{./images/3_gradient_magnitude.png}
+    \caption{Gradient magnitude of the image}
+\end{figure}
+\end{minipage}
+
+\begin{minipage}{0.49\textwidth}
+\begin{figure}[H]
+    \centering
+    \includegraphics[width=0.6\textwidth]{./images/3_gradient_orientation.png}
+    \caption{Gradient orientation visualisation using Quiver}
+\end{figure}
+\end{minipage}
+\hfill
+\begin{minipage}{0.49\textwidth}
+\begin{figure}[H]
+    \centering
+    \includegraphics[width=0.6\textwidth]{./images/3_hog_features.png}
+    \caption{HOG features visualisation for the dominant orientation per cell}
+\end{figure}
+\end{minipage}
+
+\subsection{Differences in HOG Representation for Truck Image vs Face Image}
+\begin{minipage}{0.49\textwidth}
+\begin{figure}[H]
+    \centering
+    \includegraphics[width=0.6\textwidth]{./images/1_hog_features.png}
+    \caption{HOG features visualisation for the face image}
+\end{figure}
+\end{minipage}
+\hfill
+\begin{minipage}{0.49\textwidth}
+\begin{figure}[H]
+    \centering
+    \includegraphics[width=0.6\textwidth]{./images/3_hog_features.png}
+    \caption{HOG features visualisation for the truck image}
+\end{figure}
+\end{minipage}
+
+The truck image contains a more straight lines than the face image, as it is an inorganic, regular object while the face image has more curved lines due to organic facial structure.
+A large blank area can be seen in the HOG visualisation for the truck as the blank white side panel of the truck contains no edges or changes in intensity.
+There is significantly less noise in the HOG visualisation for the truck due to the comparatively simpler \& more regular shape \& colours of the truck image.
+
+\section{Conclusion}
+\subsection{What effect did changing the \mintinline{matlab}{cell_size} \& \mintinline{matlab}{block_size} parameters have on the HOG features?}
+Increasing the cell sizes \& block sizes reduced noise in the resulting HOG visualisations, but began to also remove important details \& features of the image as the cell size \& block size were further increased.
+
+\subsection{How did the HOG features of your face compare to those of a car/truck?}
+The HOG features of the face were significantly noisier, had greater curvature, and were less regular than the HOG features of the truck image due to one being a natural object and the other being man-made.
+
+\subsection{Which parameter settings do you think would work best for distinguishing between different types of images?}
+We would recommend the 8$\times$8 cell size with 2$\times$2 block size as it captures the important details \& overall structure of the face without introducing too much noise into the visualisation, without losing too much detail.
+
+\end{document}