Issue with Consistent Value Reduction in 3D Point Interpolation Using MATLAB

I'm working on a geophysical project involving high-resolution topography and bathymetry measurements. Here's a brief overview of my process and the issue I'm encountering:

1. Data Set: My data consists of 3D scattered points (X, Y, Z) in a geophysical context. The points are closely packed, with the distance between any two points being no more than 0.1 meters.
2. Initial Step: Using MATLAB's ScatteredInterpolant function with 'natural' interpolation, I create an interpolated surface from these scattered points.
3. Extraction Process: I then extract values from this surface along several predefined, straight, and mostly parallel lines. These lines act as transects along a shoreline and are spaced appropriately. (the spacing of points in the line is 1m; can be changed if needed).
4. Regeneration of Points: The next step involves converting these lines back into a set of scattered points, effectively sampling the interpolated surface along the transects.

This process is repeated 10 times. However, I've noticed a consistent reduction in the values, particularly in the Z-axis measurements, which forms an oscillating pattern.

1. Primary Concern: My main goal is to maintain the original maximum Z values from the initial scattered points in the final set after interpolation.
2. Comparison: By subtracting the maximum Z values from the lines generated in the first iteration from those in the 10th iteration, I've observed a specific pattern, as shown in the attached photo. (Note, the section in the middle, I manually set to 0)

The image shows the line number vs (max_z_step10 -max_z_step1), for the middle points, I set the value manually to 0.

Question: Is there a more effective method to ensure the preservation of maximum Z values throughout this process? Any insights or alternative approaches would be greatly appreciated.

I need to either reduce the amount of z value (mainly the maximum values) reduction or at least make it consistent across all lines

Answer 1

[Hassaan]

I am gonna elaborate a bit on the post-processing correction with a code snippet:

% Assuming 'F' is your scatteredInterpolant object
Z_interpolated = F(Xq, Yq); % Interpolate Z values at query points (Xq, Yq)

% Assume 'original_maxima' is an array containing the original max Z for each line
for i = 1:numel(Xq)
    if Z_interpolated(i) < original_maxima(i)
        Z_interpolated(i) = original_maxima(i); % Enforce original maxima
    end
end

% Now Z_interpolated contains interpolated values with preserved maxima

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[Mohammad Traboulsi]

yes except that I dont want to force it like that.especially since I want to conserve the continuity of the profiles.

In reality I was looking to solve the problem itself instead of manually adjusting the values, since this is part of an iterative program and there are many other factors to consider.