The regionprops function in MATLAB returns a struct array containing various properties of the labeled regions in an image. The order of the objects detected by regionprops is determined by the order in which the objects appear in the labeled image.

If you want to control the order of the detected objects, you can modify the labeling process of the image. One approach is to use a different labeling algorithm that generates the labels in the order you desire. For example, you can use the bwlabel function with the 'linear' option, which labels the objects in the order they appear from left to right and top to bottom in the image.

Here's an example code snippet: 

% Load binary image
binaryImage = imread('example.png');

% Label objects using bwlabel with 'linear' option
labelImage = bwlabel(binaryImage, 8, 'linear');

% Get region properties in the desired order
props = regionprops(labelImage, 'Area', 'BoundingBox', 'Centroid');

In this example, bwlabel is used to label the objects in the binary image with the 'linear' option. The resulting label image is then passed to regionprops to get the region properties of the objects in the desired order.

Note that the labeling algorithm used depends on the specific requirements of your application, so you may need to experiment with different labeling options to get the desired result.