Looks to me like there is no lobe above 3 dB. If you mean -3 dB then there is one or maybe 2 peaks. How do you define width? Do you want just the x and y widths at the -3 dB level, or do you want to extend out, or "fall down," the lobe well past the -3 dB cutting level? If it's the latter you might need some kind of region growing process. If it's the former, simply threshold and call regionprops() asking for the bounding box. Two lines of code.
binaryImage = H > -0.3;
measurements = regionprops(binaryImage, 'BoundingBox');
Here's a full blown demo:
clc; % Clear the command window.
close all; % Close all figures (except those of imtool.)
workspace; % Make sure the workspace panel is showing.
fontSize = 20;
% Create sample data.
H = peaks(90);
H = 11*mat2gray(H) - 13;
% Display it.
subplot(2, 2, 1);
surf(H);
xlabel('Azimuth [deg]', 'FontSize', fontSize);
ylabel('Elevation [deg]', 'FontSize', fontSize);
% Enlarge figure to full screen.
set(gcf, 'units','normalized','outerposition',[0 0 1 1]); % Maximize figure.
set(gcf,'name','Demo by ImageAnalyst','numbertitle','off')
% Threshold the image
binaryImage = H > -3;
% Display it.
subplot(2, 2, 2);
imshow(binaryImage);
axis on;
xlabel('Azimuth [deg]', 'FontSize', fontSize);
ylabel('Elevation [deg]', 'FontSize', fontSize);
measurements = regionprops(binaryImage, 'BoundingBox');
bb = [measurements.BoundingBox]
x1 = bb(1);
x2 = x1 + bb(3);
y1 = bb(2);
y2 = y1 + bb(4);
% Plot box over image.
hold on;
plot([x1 x2 x2 x1 x1], [y1 y1 y2 y2 y1], 'r-', 'LineWidth', 2);
message = sprintf('The Azimuth Width at -3 dB = %.1f\nThe Elevation Width at -3 dB = %.1f', ...
bb(3), bb(4));
msgbox(message);
