Package 'autothresholdr'

Automatically threshold an array of non-negative integers.

Description

These functions apply the ImageJ "Auto Threshold" plugin's image thresholding methods. The available methods are "IJDefault", "Huang", "Huang2", "Intermodes", "IsoData", "Li", "MaxEntropy", "Mean", "MinErrorI", "Minimum", "Moments", "Otsu", "Percentile", "RenyiEntropy", "Shanbhag", "Triangle" and "Yen". Read about them at https://imagej.net/plugins/auto-threshold.

Usage

auto_thresh(
  int_arr,
  method,
  ignore_black = FALSE,
  ignore_white = FALSE,
  ignore_na = FALSE
)

auto_thresh_mask(
  int_arr,
  method,
  ignore_black = FALSE,
  ignore_white = FALSE,
  ignore_na = FALSE
)

auto_thresh_apply_mask(
  int_arr,
  method,
  fail = NA,
  ignore_black = FALSE,
  ignore_white = FALSE,
  ignore_na = FALSE
)

mask(
  int_arr,
  method,
  ignore_black = FALSE,
  ignore_white = FALSE,
  ignore_na = FALSE
)

apply_mask(
  int_arr,
  method,
  fail = NA,
  ignore_black = FALSE,
  ignore_white = FALSE,
  ignore_na = FALSE
)

Arguments

int_arr	An array (or vector) of non-negative integers.
method	The name of the thresholding method you wish to use. The available methods are "IJDefault", "Huang", "Huang2", "Intermodes", "IsoData", "Li", "MaxEntropy", "Mean", "MinErrorI", "Minimum", "Moments", "Otsu", "Percentile", "RenyiEntropy", "Shanbhag", "Triangle" and "Yen". Partial matching is performed i.e. method = "h" is enough to get you "Huang" and method = "in" is enough to get you "Intermodes". To perform manual thresholding (where you set the threshold yourself), supply the threshold here as a number e.g. method = 3; so note that this would not select the third method in the above list of methods.
ignore_black	Ignore black pixels/elements (zeros) when performing the thresholding?
ignore_white	Ignore white pixels when performing the thresholding? If set to TRUE, the function makes a good guess as to what the white (saturated) value would be (see 'Details'). If this is set to a number, all pixels with value greater than or equal to that number are ignored.
ignore_na	This should be TRUE if NAs in int_arr should be ignored or FALSE if you want the presence of NAs in int_arr to throw an error.
fail	When using auto_thresh_apply_mask(), to what value do you wish to set the pixels which fail to exceed the threshold? fail = 'saturate' sets them to saturated value (see "Details"). fail = 'zero' sets them to zero. You can also specify directly here a natural number (must be between 0 and 2^16 - 1) to use.

Details

• Values greater than or equal to the found threshold pass the thresholding and values less than the threshold fail the thresholding.

• For ignore_white = TRUE, if the maximum value in the array is one of 2^8-1, 2^12-1, 2^16-1 or 2^32-1, then those max values are ignored. That's because they're the white values in 8, 12, 16 and 32-bit images respectively (and these are the common image bit sizes to work with). This guesswork has to be done because R does not know how many bits the image was on disk. This guess is very unlikely to be wrong, and if it is, the consequences are negligible anyway. If you're very concerned, then just specify the white value as an integer in this ignore_white argument.

• If you have set ignore_black = TRUE and/or ignore_white = TRUE but you are still getting error/warning messages telling you to try them, then your chosen method is not working for the given array, so you should try a different method.

• For a given array, if all values are less than 2^8, saturated value is 2^8 - 1, otherwise, if all values are less than 2^16, the saturated value is 2^16 - 1, otherwise the saturated value is 2^32-1.

• For the auto_thresh() function, if you pass int_arr as a data frame with column names value and n, that's the same as passing an integer array having n entries of each value. For this form of int_arr, ignore_white and ignore_black are irrelevant.

Value

auto_thresh() returns an object of class th containing the threshold value. Pixels exceeding this threshold pass the thresholding, pixels at or below this level fail.

auto_thresh_mask() returns an object of class masked_arr which is a binarized version of the input, with a value of TRUE at points which exceed the threshold and FALSE at those which do not.

auto_thresh_apply_mask() returns and object of class threshed_arr which is the original input masked by the threshold, i.e. all points not exceeding the threshold are set to a user-defined value (default NA).

mask() is the same as auto_thresh_mask() and apply_mask() is the same as auto_thresh_apply_mask().

Acknowledgements

Gabriel Landini coded all of these functions in Java. These java functions were then translated to C++.

References

• Huang, L-K & Wang, M-J J (1995), "Image thresholding by minimizing the measure of fuzziness", Pattern Recognition 28(1): 41-51

• Prewitt, JMS & Mendelsohn, ML (1966), "The analysis of cell images", Annals of the New York Academy of Sciences 128: 1035-1053

• Ridler, TW & Calvard, S (1978), "Picture thresholding using an iterative selection method", IEEE Transactions on Systems, Man and Cybernetics 8: 630-632

• Li, CH & Lee, CK (1993), "Minimum Cross Entropy Thresholding", Pattern Recognition 26(4): 617-625

• Li, CH & Tam, PKS (1998), "An Iterative Algorithm for Minimum Cross Entropy Thresholding", Pattern Recognition Letters 18(8): 771-776

• Sezgin, M & Sankur, B (2004), "Survey over Image Thresholding Techniques and Quantitative Performance Evaluation", Journal of Electronic Imaging 13(1): 146-165

• Kapur, JN; Sahoo, PK & Wong, ACK (1985), "A New Method for Gray-Level Picture Thresholding Using the Entropy of the Histogram", Graphical Models and Image Processing 29(3): 273-285

• Glasbey, CA (1993), "An analysis of histogram-based thresholding algorithms", CVGIP: Graphical Models and Image Processing 55: 532-537

• Kittler, J & Illingworth, J (1986), "Minimum error thresholding", Pattern Recognition 19: 41-47

• Prewitt, JMS & Mendelsohn, ML (1966), "The analysis of cell images", Annals of the New York Academy of Sciences 128: 1035-1053

• Tsai, W (1985), "Moment-preserving thresholding: a new approach", Computer Vision, Graphics, and Image Processing 29: 377-393

• Otsu, N (1979), "A threshold selection method from gray-level histograms", IEEE Trans. Sys., Man., Cyber. 9: 62-66, doi:10.1109/TSMC.1979.4310076

• Doyle, W (1962), "Operation useful for similarity-invariant pattern recognition", Journal of the Association for Computing Machinery 9: 259-267, doi:10.1145/321119.321123

• Kapur, JN; Sahoo, PK & Wong, ACK (1985), "A New Method for Gray-Level Picture Thresholding Using the Entropy of the Histogram", Graphical Models and Image Processing 29(3): 273-285

• Shanbhag, Abhijit G. (1994), "Utilization of information measure as a means of image thresholding", Graph. Models Image Process. (Academic Press, Inc.) 56 (5): 414–419, ISSN 1049-9652

• Zack GW, Rogers WE, Latt SA (1977), "Automatic measurement of sister chromatid exchange frequency", J. Histochem. Cytochem. 25 (7): 74153, PMID 70454

• Yen JC, Chang FJ, Chang S (1995), "A New Criterion for Automatic Multilevel Thresholding", IEEE Trans. on Image Processing 4 (3): 370-378, ISSN 1057-7149, doi:10.1109/83.366472

• Sezgin, M & Sankur, B (2004), "Survey over Image Thresholding Techniques and Quantitative Performance Evaluation", Journal of Electronic Imaging 13(1): 146-165

Examples

img_location <- system.file("extdata", "eg.tif", package = "autothresholdr")
img <- ijtiff::read_tif(img_location)
auto_thresh(img, "huang")
img_value_count <- magrittr::set_names(as.data.frame(table(img)),
                                      c("value", "n"))
print(head(img_value_count))
auto_thresh(img_value_count, "Huang")
auto_thresh(img, "tri")
auto_thresh(img, "Otsu")
auto_thresh(img, 9)
mask <- auto_thresh_mask(img, "huang")
ijtiff::display(mask[, , 1, 1])
masked <- auto_thresh_apply_mask(img, "huang")
ijtiff::display(masked[, , 1, 1])
masked <- auto_thresh_apply_mask(img, 25)
ijtiff::display(masked[, , 1, 1])

---

Masked array class.

Description

A mask of an array with respect to a given threshold is found by taking the original array and setting all elements falling below the threshold to FALSE and the others to TRUE. An object of class masked_arr has the attribute thresh detailing the threshold value that was applied.

Usage

masked_arr(arr, thresh)

Arguments

arr	An array of logicals (the mask).
thresh	The threshold. Either a scalar or an object of class th.

Value

An object of class masked_arr.

---

Threshold every image frame in an image stack based on their mean.

Description

An ijtiff_img is a 4-dimensional array indexed by img[y, x, channel, frame]. For each channel (which consists of a stack of frames), this function finds a threshold based on the sum all of the frames, uses this to create a mask and then applies this mask to every frame in the stack (so for a given pillar in the image stack, either all the pixels therein are thresholded away or all are untouched, where pillar ⁠x,y⁠ of channel ch is img[y, x, ch, ]).

Usage

mean_stack_thresh(
  img,
  method,
  fail = NA,
  ignore_black = FALSE,
  ignore_white = FALSE,
  ignore_na = FALSE
)

Arguments

img	A 4-dimensional array in the style of an ijtiff_img (indexed by img[y, x, channel, frame]) or a 3-dimensional array which is a single channel of an ijtiff_img (indexed by img[y, x, frame]).
method	The name of the thresholding method you wish to use. The available methods are "IJDefault", "Huang", "Huang2", "Intermodes", "IsoData", "Li", "MaxEntropy", "Mean", "MinErrorI", "Minimum", "Moments", "Otsu", "Percentile", "RenyiEntropy", "Shanbhag", "Triangle" and "Yen". Partial matching is performed i.e. method = "h" is enough to get you "Huang" and method = "in" is enough to get you "Intermodes". To perform manual thresholding (where you set the threshold yourself), supply the threshold here as a number e.g. method = 3.8 (so note that this would not select the third method in the above list of methods). This manual threshold will then be used to threshold the sum stack to create a 2D mask and then this mask will be applied to all frames in the stack. If you want a different method for each channel, specify this parameter as a vector or list, one element per channel.
fail	When using auto_thresh_apply_mask(), to what value do you wish to set the pixels which fail to exceed the threshold? fail = 'saturate' sets them to saturated value (see 'Details'). fail = 'zero' sets them to zero. You can also specify directly here a natural number (must be between 0 and 2^16 - 1) to use.
ignore_black	Ignore black pixels/elements (zeros) when performing the thresholding?
ignore_white	Ignore white pixels when performing the thresholding? If set to TRUE, the function makes a good guess as to what the white (saturated) value would be (see 'Details'). If this is set to a number, all pixels with value greater than or equal to that number are ignored.
ignore_na	This should be TRUE if NAs in int_arr should be ignored or FALSE if you want the presence of NAs in int_arr to throw an error.

Details

It's called mean_stack_thresh() and not sum_stack_thresh() because its easier for people to visualize the mean of an image series than to visualize the sum, but for the sake of this procedure, both are equivalent, except for the fact that the thresholding routine invoked inside this function prefers integers, which we get by using a sum but not by using a mean.

• Values greater than or equal to the found threshold pass the thresholding and values less than the threshold fail the thresholding.

• For ignore_white = TRUE, if the maximum value in the array is one of 2^8-1, 2^16-1 or 2^32-1, then those max values are ignored. That's because they're the white values in 8, 16 and 32-bit images respectively (and these are the common image bit sizes to work with). This guesswork has to be done because R does not know how many bits the image was on disk. This guess is very unlikely to be wrong, and if it is, the consequences are negligible anyway. If you're very concerned, then just specify the white value as an integer in this ignore_white argument.

• If you have set ignore_black = TRUE and/or ignore_white = TRUE but you are still getting error/warning messages telling you to try them, then your chosen method is not working for the given array, so you should try a different method.

• For a given array, if all values are less than 2^8, saturated value is 2^8 - 1, otherwise, saturated value is 2^16 - 1.

Value

An object of class stack_threshed_img which is the thresholded image (an array in the style of an ijtiff_img). Pillars not exceeding the threshold are set to the fail value (default NA).

Examples

img <- ijtiff::read_tif(system.file("extdata", "50.tif",
  package = "autothresholdr"
))
ijtiff::display(img[, , 1, 1])
img_thresh_mask <- mean_stack_thresh(img, "Otsu")
ijtiff::display(img_thresh_mask[, , 1, 1])
ijtiff::display(img[, , 1, 1])
img_thresh_mask <- mean_stack_thresh(img, "Huang")
ijtiff::display(img_thresh_mask[, , 1, 1])

---

Threshold every image frame in a stack based on their median.

Description

An ijtiff_img is a 4-dimensional array indexed by img[y, x, channel, frame]. For each channel (which consists of a stack of frames), this function finds a threshold based on all of the frames, then takes the median of all the frames in the stack image, uses this to create a mask with the found threshold and then applies this mask to every frame in the stack (so for a given pillar in the image stack, either all the pixels therein are thresholded away or all are untouched, where pillar ⁠x,y⁠ of channel ch is img[y, x, ch, ]).

Usage

med_stack_thresh(
  img,
  method,
  fail = NA,
  ignore_black = FALSE,
  ignore_white = FALSE,
  ignore_na = FALSE
)

Arguments

img	A 3-dimensional array (the image stack, possibly a time-series of images) where the $n$th slice is the $n$th image in the stack.
method	The name of the thresholding method you wish to use. The available methods are "IJDefault", "Huang", "Huang2", "Intermodes", "IsoData", "Li", "MaxEntropy", "Mean", "MinErrorI", "Minimum", "Moments", "Otsu", "Percentile", "RenyiEntropy", "Shanbhag", "Triangle" and "Yen". Partial matching is performed i.e. method = "h" is enough to get you "Huang" and method = "in" is enough to get you "Intermodes". To perform manual thresholding (where you set the threshold yourself), supply the threshold here as a number e.g. method = 3 (so note that this would not select the third method in the above list of methods). This manual threshold will then be used to threshold the median stack to create a 2D mask and then this mask will be applied to all frames in the stack. If you want a different method for each channel, specify this parameter as a vector or list, one element per channel.
fail	When using auto_thresh_apply_mask(), to what value do you wish to set the pixels which fail to exceed the threshold? fail = 'saturate' sets them to saturated value (see 'Details'). fail = 'zero' sets them to zero. You can also specify directly here a natural number (must be between 0 and 2^32 - 1) to use.
ignore_black	Ignore black pixels/elements (zeros) when performing the thresholding?
ignore_white	Ignore white pixels when performing the thresholding? If set to TRUE, the function makes a good guess as to what the white (saturated) value would be (see 'Details').
ignore_na	This should be TRUE if NAs in int_arr should be ignored or FALSE if you want the presence of NAs in int_arr to throw an error.

Details

• Values greater than or equal to the found threshold pass the thresholding and values less than the threshold fail the thresholding.

• For ignore_white = TRUE, if the maximum value in the array is one of 2^8-1, 2^16-1 or 2^32-1, then those max values are ignored. That's because they're the white values in 8, 16 and 32-bit images respectively (and these are the common image bit sizes to work with). This guesswork has to be done because R does not know how many bits the image was on disk. This guess is very unlikely to be wrong, and if it is, the consequences are negligible anyway. If you're very concerned, then just specify the white value as an integer in this ignore_white argument.

• If you have set ignore_black = TRUE and/or ignore_white = TRUE but you are still getting error/warning messages telling you to try them, then your chosen method is not working for the given array, so you should try a different method.

• For a given array, if all values are less than 2^8, saturated value is 2^8 - 1, otherwise, saturated value is 2^16 - 1.

Value

An object of class stack_threshed_img which is the thresholded image (an array in the style of an ijtiff_img). Pillars not exceeding the threshold are set to the fail value (default NA).

Examples

img <- ijtiff::read_tif(system.file("extdata", "50.tif",
  package = "autothresholdr"
))
ijtiff::display(img[, , 1, 1])
img_thresh_mask <- med_stack_thresh(img, "Otsu")
ijtiff::display(img_thresh_mask[, , 1, 1])
ijtiff::display(img[, , 1, 1])
img_thresh_mask <- med_stack_thresh(img, "Triangle")
ijtiff::display(img_thresh_mask[, , 1, 1])

---

Stack-thresholded image class.

Description

A stack-thresholded array is an array which has had stack-thresholding applied to it. See mean_stack_thresh(). It has 3 necessary attributes:

• thresh is the threshold that was applied. This is either a number or an object of class th. Values in the original array which were less than this value are deemed to have failed the thresholding.

• fail_value is the value to which elements of the array which failed the thresholding were set. This could be something like 0 or NA.

• stack_thresh_method details which stacked-thresholding method was employed; this is either "mean" or "median".

Usage

stack_threshed_img(img, thresh, fail_value, stack_thresh_method)

Arguments

img	A 4-dimensional array in the style of an ijtiff_img (indexed by img[y, x, channel, frame]) or a 3-dimensional array which is a single channel of an ijtiff_img (indexed by img[y, x, frame]).
thresh	The threshold that was used. Either a number or an object of class th.
fail_value	The value to which elements of the array which failed the thresholding were set.
stack_thresh_method	This must be set to either "mean" or "median" to tell which stacked-thresholding method was employed.

Value

An object of class stack_threshed_img.

See Also

threshed_arr, mean_stack_thresh(), med_stack_thresh().

---

Automatically found threshold class.

Description

A threshold found automatically via auto_thresh(). It is a number (the value of the threshold) with 4 attributes:

• ignore_black is TRUE if black values were ignored during the thresholding and FALSE otherwise.

• ignore_white is TRUE if white values were ignored during the thresholding and FALSE otherwise.

• ignore_na is TRUE if NAs were ignored during the thresholding and FALSE otherwise.

• autothresh_method details which automatic thresholding method was used.

Usage

th(thresh, ignore_black, ignore_white, ignore_na, autothresh_method)

Arguments

thresh	A scalar. The threshold.
ignore_black	TRUE if black values were ignored during the thresholding and FALSE otherwise.
ignore_white	TRUE if white values were ignored during the thresholding and FALSE otherwise.
ignore_na	TRUE if NA values were ignored during the thresholding and FALSE otherwise.
autothresh_method	The name of the automatic thresholding method used.

Value

An object of class th.

---

Thresholded array class.

Description

A thresholded array is an array which has had a threshold applied to it. It has an attribute thresh which is the threshold that was applied which can be a number or an object of class th.

Usage

threshed_arr(arr, thresh)

Arguments

arr	The thresholded array (not the original array).
thresh	The threshold that was used. Either a number or an object of class th.

Details

The term 'array' is used loosely here in that vectors and matrices qualify as arrays.

Value

An object of class threshed_arr.

See Also

stack_threshed_img, apply_mask().

---