To convert a grayscale image to binary by threshold command and to measure fractal dimension

Hi all
I am working with a 8-bit grayscale image. I would like to convert it to binary image to measure its fractal dimension. By two ways I converted the grayscale image to binary one and then calculate the fractal dimension. Would you please let me know which of the way is correct for thresholding as well as measuring the fractal dimension?

  1. Process>Enhanced contrast> then Image>Adjust>Threshold (upper value: 23 and lower value: 185) then analyze> tools> Fractal box count
    Fractal dimension: 1.7800
  2. I used the same way to threshold the grayscale image same as 1 and then I used the Fraclac and box counting scan to measure the fractal dimension and the results is as below:

    Fractal dimension: 1.78 for each grid orientation

I want to know which process is more correct although the results are the same?
and also, in the second way, I used the Autoconvert to binary image for the image type. Would you please let me know I can try it with Gray 1 or Gray 2 Or Gray 3? If I need to change the other parameters in Fraclac setting please let me know that. Finally, is using thresholding my image enough to convert that image to binary one or I need to use the other command such as make binary or convert to mask?

Thank you for your response. I hope I can receive help from all of you.