I'm doing some image processing of some tidal lines that I'm trying to digitize from photographs using Matlab. The digitization is heavily dependent on the indexing of the image of x-values (time) and y-values (water level). After some initial processing based on pixel contrast, line continuity and minimum color (darkest) criteria, I need to fit a sinusoid to the resulting selected index pairs. For every x-value there is only one y-value.(adsbygoogle = window.adsbygoogle || []).push({});

The gist of the digitization procedure is that the contrast values are initially chosen to generate a series of line segments, which are then expanded upon by a forward and backward contrast trace (like the old-school video game Snake). It's an iterative process where some line segments get eliminated from the overall array based on length and RMSE criteria. However, the length criteria can be too restricted and eliminates lines that really are part of the tidal signal but they just don't fully connect to a larger line because of white space existing between the lines.

My problem is that I need to find a way of reintroducing these eliminated 'true' line segments without reintroducing 'false' tidal line segments. The method I came up with is to do a full image-scale sinusoidal curve fit using the fit and fitOptions functions. Then having the segments re-introduce if they intersect that fit line or have a similar slope over the line segment time domain.

This doesn't have to be a fit to determine the tidal constants as with most tidal harmonic analysis. Just accurate enough to get a precise fit. The problem, as with most harmonic analysis, is that the highs and lows are not really accurate. This accuracy is important for the image processing because it forces the ebb and flood regions to be constrained within the time of the extrema.

Is there a way to fix the high and low index values in place while the remaining points are fit to the curve?

Here is the set-up I have now:

xinput( yinput == 9999 ) = [];

yinput( yinput == 9999 ) = [];

% ffit = fittype('sin3');

fitOptions = fitoptions('sin5');

newOptions = fitoptions(fitOptions,'Robust','Bisquare','Normalize','on');

y_fit = fit( xinput, yinput, 'sin5', newOptions );

I have it at 'sin5' because it increases the accuracy of the fit and not because of the number of potential tidal constituents being 5 (i.e. M2, S1, K1, M4, P1 ).

However, I have also thought about establishing the relative deterministic frequencies of the above mentioned constituents in relation to the pixel span. This might cut down on the number of iterations required. Then again, this might decrease accuracy because the image only shows the tide signal for a day and a half rather than a month necessary to actually do harmonic analysis.

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# Sinusoidal fit with some points fixed

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