thr_mblt: Calculate thresholds with the model-based method

In rcaiman: CAnopy IMage ANalysis

Calculate thresholds with the model-based method

Description

Transform background digital number into threshold values

Usage

thr_mblt(dn, intercept, slope)

Arguments

dn	Numeric vector or SpatRaster. Digital number of the background. These values should be normalized and, if they are extracted from a JPEG image, gamma back corrected.
intercept, slope	Numeric vector of length one. These are linear function coefficients.

Details

This function transforms background digital numbers into threshold values by means of the Equation 1 from \insertCiteDiaz2018;textualrcaiman, which is a linear function with the slope modified by a weighting parameter. This simple function was found by studying canopy models, also known as targets, which are perforated surfaces made of a rigid and dark material . These models were backlighted with homogeneous lighting, photographed with a Nikon Coolpix 5700 set to acquire in JPEG format, and those images were gamma back corrected with a default gamma value equal to 2.2 (see gbc()). Results shown that the optimal threshold value was linearly related with the background digital number (see Figure 1 and Figure 7 from \insertCiteDiaz2018;textualrcaiman). This shifted the aim from finding the optimal threshold, following \insertCiteSong2014;textualrcaiman method, to obtaining the background DN as if the canopy was not there, as \insertCiteLang2010;textualrcaiman proposed.

Working principle

\insertCite

Diaz2018;textualrcaiman observed the following linear relationship between the background value, usually the sky digital number (SDN), and the optimal threshold value (OTV):

IV = a + b \cdot SDN

(Equation 1a)

OTV = a + b \cdot w \cdot SDN

(Equation 1b)

were IV is the initial value \insertCiteWagner2001rcaiman, which is the boundary between SDN and the mixed pixels, i.e, the pixels that are neither Gap or Non-gap \insertCiteMacfarlane2011rcaiman, a and b are the intercept and slope coefficients, respectively, and w is a weighting parameter that takes into account that OTV is always lower than IV. If SDN is calculated at the pixel level, a local thresholding method can be applied by evaluating, pixel by pixel, if the below canopy digital number (CDN) is greater than the OTV. Formally, If CDN>OTV, then assign Gap class, else assign Non-gap class.

This conclusion drawn from an image processing point of view matches with previous findings drawn from a radiometric measurement paradigm, which are introduced next.

\insertCite

Cescatti2007;textualrcaiman posed that cameras can be used as a radiation measurement device if they are properly calibrated. This method, denominated by the author as LinearRatio, seeks to obtain the transmittance (T) as the ratio of below to above canopy radiation:

T = CDN/SDN

(Equation 2)

were CDN is below canopy digital number (DN), i.e., the DN extracted from a canopy hemispherical photograph.

The LinearRatio method uses T as a proxy for gap fraction. It requires twin cameras, one below and the other above the canopy. In contrast, \insertCiteLang2010;textualrcaiman proposed to obtain SDN by manually selecting pure sky pixels from canopy hemispherical photographs and reconstructing the whole sky by subsequent modeling and interpolating—this method is often referred to as LinearRatio single camera or LinearRatioSC.

Equation 2 can be seen as a standardization of the distance between CDN and SDN. With that in mind, it is useful to rewrite Equation 1b as an inequality that can be evaluated to return a logical statement that is directly translated into the desired binary classification:

CDN > a + b \cdot w \cdot SDN

(Equation 3)

Then, combining Equation 2 and 3, we find that \insertCiteDiaz2018;textualrcaiman parameters can be applied to T:

CDN/SDN > a + b \cdot w \cdot SDN/SDN

(Equation 4a)

T > a + b \cdot w

(Equation 4b)

From Equation 2 it is evident that any bias introduced by the camera optical and electronic system will be canceled during the calculation of T as long as only one camera is involved. Therefore, After examining Equation 4b, we can conclude that intercept 0 and slope 1 are theoretically correct.In addition, the w parameter can be used to filter out mixed pixels. The greater w, the greater the possibility of selecting pure sky pixels.

Value

An object of the same class and dimensions than dn.

Note

It is worth noting that Equation 1 was developed with 8-bit images, so calibration of new coefficient should be done in the 0 to 255 domain since that is what thr_mblt() expect, although the dn argument should be normalized. The latter, in spite of sounding counter intuitive, was a design decision aiming to harmonize the whole package.

Nevertheless, new empirical calibration on JPEG files may be unnecessary since the values -7.8 intercept and 0.95 slope that had been observed with back-gamma corrected JPEG files produced with the Nikon Coolpix 5700 camera are sufficiently close to the theoretical values that it sounds reasonable to interpret them as a confirmation of the theory.

Users are encouraged to adopt raw file acquisition (read_caim_raw()).

To apply the weighting parameter (w) from Equation 1, just provide the argument slope as slope \times w.

References

\insertAllCited

See Also

normalize(), gbc(), apply_thr() and regional_thresholding().

Other Binarization Functions: apply_thr(), obia(), ootb_mblt(), ootb_obia(), regional_thresholding(), thr_isodata()

Examples

thr_mblt(gbc(125), -7.8, 0.95 * 0.5)

rcaiman documentation built on Nov. 15, 2023, 1:08 a.m.