how to find image surface normals for water surface? - graphics

I want to find surface normals for an image. I have 2 water surface images. First one is still water, and second one is a moving image.
I found each corrospondent pixels for both of images by using normalized correlation. therefore, I have displacement for all pixels in x and y direction.
what i am asking is how i can find the water surface normals for each point?
I think displacement in x and y direction can help me for finding surface normals, but I don't know how to move forward.
Thanks in advance.

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Reconstruction 3d for a rotation camera

I have rotating camera images and I'm trying this example of a MATLAB computer vision toolbox (https://www.mathworks.com/matlabcentral/fileexchange/67383-stereo-triangulation)
I have the calibration and rotation matrix for each image, however I always find 3d points equal to (0,0,0).
It is noted that the translation is null which makes the fourth column null.
You cannot reconstruct a 3D point from a rotating camera.
I suggest you try and draw an example. The idea of triangulation is to compute the intersection of two backprojection rays. These rays pass through the camera center and the point to be reconstructed. In your drawing, you'll find that the intersection becomes more and more accurate the larger the so-called stereo baseline is (that's the translation from one camera center to the other).
Now, for a rotating camera, the camera center remains the same and therefore, the two rays are identical. An intersection is not defined.

What is the reference point for measuring angles in OpenCV?

I'm trying to infer an object's direction of movement using dense optical flow in OpenCV. I'm using calcOpticalFlowFarneback() to get flow coordinates and cartToPolar() to acquire vector angles which would indicate direction.
To interpret the results I need to know the reference point for measuring the angle. I have found this blog post indicating that the range of angles is 360°. That tells me that the angle measurement would go along the lines of the unit circle. I couldn't make out much more than that.
The documentation for cartToPolar() doesn't cover this and my attempts at testing it have failed.
It seems that the angle produced by cartToPolar() is in reference to the unit circle rotated clockwise by 90° centered on the image coordinate starting point in the top left corner. It would look like this.
I came to this conclusion by using the dense optical flow example provided by OpenCV. I replaced the line hsv[...,0] = ang*180/np.pi/2 with hsv[...,0] = ang*180/np.pi to get correct angle conversion from radians. Then I tested a video with people moving from top right to bottom left and vice versa. I sampled the dominant color with GIMP and got RGB values which I converted to HSV values. Hue value corresponds to the angle in degrees.
People moving from top right to bottom left produced an angle of about 300° and people moving the other way round produced an angle of about 120°. This hinted at the way the unit circle is positioned.
Looking at the code, fastAtan32f is used to compute the angles. and that seems to be a atan2 implementation.

Algorithm to calculate and display a ribbon on a 3D triangle mesh

I am looking for an algorithm for the following problem:
Given:
A 3D triangle mesh. The mesh represents a part of the surface of the earth.
A polyline (a connected series of line segments) whose vertices are always on an edge or on a vertex of a triangle of the mesh. The polyline represents the centerline of a road on the surface of the earth.
I need to calculate and display the road i.e. add half of the road's width on each side of the center line, calculate the resulting vertices in the corresponding triangles of the mesh, fill the area of the road and outline the sides of the road.
What is the simplest and/or most effective strategy to do this? How do I store the data of the road most efficiently?
I see 2 options here:
render thick polyline with road texture
While rendering polyline you need TBN matrix so use
polyline tangent as tangent
surface normal as normal
binormal=tangent x normal
shift actual point p position to
p0=p+d*binormal
p1=p-d*binormal
and render textured line (p0,p1). This approach is not precise match to surface mesh so you need to disable depth or use some sort of blending. Also on sharp turns it could miss some parts of a curve (in that case you can render rectangle or disc instead of line.
create the mesh by shifting polyline to sides by half road size
This produces mesh accurate road fit, but due to your limitations the shape of the road can be very distorted without mesh re-triangulation in some cases. I see it like this:
for each segment of road cast 2 lines shifted by half of road size (green,brown)
find their intersection (aqua dots) with shared edge of mesh with the current road control point (red dot)
obtain the average point (magenta dot) from the intersections and use that as road mesh vertex. In case one of the point is outside shared mesh ignore it. In case both intersections are outside shared edge find closest intersection with different edge.
As you can see this can lead to serious road thickness distortions in some cases (big differences between intersection points, or one of the intersection points is outside surface mesh edge).
If you need accurate road thickness then use the intersection of the casted lines as a road control point instead. To make it possible either use blending or disabling Depth while rendering or add this point to mesh of the surface by re-triangulating the surface mesh. Of coarse such action will also affect the road mesh and you need to iterate few times ...
Another way is use of blended texture for road (like sprites) and compute the texture coordinate for the control points. If the road is too thick then thin it by shifting the texture coordinate ... To make this work you need to select the most far intersection point instead of average ... Compute the real half size of the road and from that compute texture coordinate.
If you get rid of the limitation (for road mesh) that road vertex points are at surface mesh segments or vertexes then you can simply use the intersection of shifted lines alone. That will get rid of the thickness artifacts and simplify things a lot.

Terrain tile scale in case of tilted camera

I am working on 3d terrain visualization tool right now. Surface is logically covered with square tiles. This tiling could be visualized as follows:
Suppose I want to draw a picture on these tiles. The level of detail for a picture is required to be selected according to the current camera scale which is calculated for each tile individually.
In case of vertical camera (no tilt, i.e. camera looks perpendicularly on the ground) all tiles have the same scale which is camera focal length divided on camera height above the ground.
Following picture depicts the situation:
where red triangle is camera which has no tilt, BG is camera height above the ground and EG is focal length, then scale = AC/DF = BG/EG
But if camera has tilt (i.e. pitch angle isn't 0) then scale is changed from tile to tile (even from point to point).
So I wonder if there any kind method to produce reasonable scale for each tile in that case ?
There may be (there almost surely is) a more straightforward solution, but what you could do is regular world to screen coordinate conversion.
You just take the coordinates of bounding points of the tile and calculate to which pixels on the screen these will project (you of course get floating point precision). From this, I believe you can calculate the "scale" you are mentioning.
This is applicable to any point or set of points in the world space.
Here is tutorial on how to do this "by hand".
If you are rendering the tiles with OpenGL or DirectX, you can do this much easier.

How to draw the heightmap onto the screen?

I'm using DirectX10 to simulate a water surface, and I'm now with a height map,which is a 2D array of the heights(y) at the points (x,z). But to draw it on the screen, I must turn it into a mesh or have a index to draw triangle topology.
But the data is too large to do it manually. Are there any methods for me to draw it on the screen. I hope it's easy to implement. If there is function included in DirectX10 which can make it, the it's the best one for me.
Create a mesh that format a grid of squares (each made of two triangles) and set all vertices y = 0. In the vertex shader sample the heightmap and add the value stored in the heightmap to the y of the vertice.
This might help you.
P.S: If the area you want it to cover is too big you should take a look at terrain LOD techniques (should work the same for water).
I'm sure you can make a mesh out of it. I doubt you can generate the heightmap for a water surface that is too large to "meshify".
Why are you looking at Diamond square. For a 512x512 heightmap all you need to do is define a set of point and then generate the triangles for it. Its really very simple.

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