how to find the quadrant of the point in a image

Say you have a point in a bounding box and have to calculate which quadrant it lies in, in order to find the orientation of the next connected component. I have the centroid of the bounding box as well as the centroid of the point. Thanks

I have tried to find the directional vector of the two points but i dont think matlab has that functionality to find the oritentation of the next connected component.

[Ameer Hamza]

Please attach a sample image and clearly point out what you are trying to do?

[Joel Nunes]

[Joel Nunes]

I am trying to find the quadrant in which the point lies in the bouding box in order to find the next connected component

[Joel Nunes]

basically, the bouding boxes leads to a treasure , so i have to find the orientation of the next connected commponent, as one box leads to the next

[Ameer Hamza]

By quadrant do you mean which portion of the image the bounding box lie

[Joel Nunes]

No , i mean which quadrant of the boundung box the point lies ,for each bouding box.

[Ameer Hamza]

Which function are you using to calculate the bounding box?

[Joel Nunes]

i am using region props to get the porpoerties of the connected components

propsW = regionprops(whiteMask, 'BoundingBox', 'Centroid');

and

rectangle('Position', thisBB, 'EdgeColor', 'y', 'LineWidth', 1);

to draw the rectangle

[Guillaume]

Missing from your question is the definition of "quadrant". There are several ways you can divide a rectangle into 4 quadrants. The two simplest: you can use the diagonals, leading to 4 triangular quadrants or you can also divide the height and width by 2 leading to 4 rectangular quadrants. Both of these methods have the quadrants meet at the centre of the bounding box.

Either way, I'm not too sure what's the difficulty in identifying which quadrant a point lives in, you just take the angle of the vector defined by the centre and the point against an arbitrary line and compare that against the angle of the lines defining your quadrants.

[Joel Nunes]

if i consider two points, with the first being the centroid of the bouding box and the centroid of the white dot, how do you find the direction in which the line points to?

[Joel Nunes]

[Joel Nunes]

i had this, and i had to segement in order to extract the white dots which is in the figure above.

my task is to find the next arrow

Answer 1

[Ameer Hamza]

You can use atan2 to calculate the direction of the line connecting the center of the bounding box and dot.

center_bb = [0.1 0.3]; %
center_dot = [-0.5 0.5]; % 2nd quadrant with respect to center_bb
difference = center_dot - center_bb;
angle = atan2d(difference(2), difference(1)); % angles in degrees

Result

angle =

  161.5651
  

This assumes that you are using rectangular coordinates. So angle 161 degrees lies in the 2nd coordinate as we initially assumed.

Note that in case of an image, the y-axis might be inverted if the pixel coordinates start from the top-left of the image. In that case, 1st coordinate will be swapped with 4th and 2nd with 3rd.

[Joel Nunes]

"The y-axis might be inverted ", In that case, 1st coordinate will be swapped with 4th and 2nd with 3rd.

Could you pls give an example?

i didnt quite get you.

[Ameer Hamza]

Look at these two images.

For a regular rectangular coordinate (according to which atan2 works), x-value increase from left to right, and the y-value increases from bottom to top.

Whereas, we take image coordinate using pixel location (as you are doing with bounding box), the direction of y-axis reverse (it increase from top to bottom)

[Joel Nunes]

so once i getthe pixel coordinates, in order to adapt it in the arctan2 fucntion , what has to be changed to get the right angle?

[Ameer Hamza]

atan2d gives the angles in the range [-180 to 180]. According to the first picture above

[-180 -90] -> 3d quadrant (lower left direction)

[-90 0] -> 4th quadrant (lower right direction)

[0 90] -> 1st quadrant (upper right direction)

[90 180] -> 2nd quadrant (upper left direction)

In case of an image

[-180 -90] -> 2nd quadrant (upper left direction)

[-90 0] -> 1st quadrant (upper right direction)

[0 90] -> 3rd quadrant (lower right direction)

[90 180] -> 4th quadrant (lower left direction)

I specided the directions along with quadrant number to avoid confusion.

[Guillaume]

I thought Ameer's explanation and drawing were very clear. I'd recommend you spend a bit of time drawing axes on a paper. This is really basic geometry.

_"what has to be changed to get the right angle?"

The sign of y or the sign of the angle... or nothing at all if you use the same coordinate system to define all your angles/coordinates.

[Joel Nunes]

thanks soo much