Simple Temporal Percentile Features Extraction

// Preprocessing step
var collection = ee.ImageCollection("COPERNICUS/S2_SR")
  .filterDate("2020-01-01", "2020-03-01")
  .filter(
    ee.Filter.lt('CLOUDY_PIXEL_PERCENTAGE', 50)
  )
  .map(function (image) {
      var qa = image.select('QA60');
      var cloudBitMask = 1 << 10;
      var cirrusBitMask = 1 << 11;
      var mask = qa.bitwiseAnd(cloudBitMask).eq(0)
                  .and(qa.bitwiseAnd(cirrusBitMask).eq(0));
      image = image.updateMask(mask).divide(10000);
      image = image.addBands(image.normalizedDifference(['B8', 'B4']).toFloat().rename('NDVI'))
                  .addBands(image.normalizedDifference(['B12', 'B4']).toFloat().rename('NDFI'))
      return image.select(["NDVI", "NDFI"]);
  });

// Foyou Tian, et al
// Add empty image to prevent null error when calculating percentile
var emptyImage = ee.Image().rename("NDVI").toFloat()
  .addBands(ee.Image().rename("NDFI").toFloat())
collection = ee.ImageCollection(ee.List([emptyImage])).merge(collection);

function percentile_transformation(data, bands) {
    function rename_bands(bands, suffix) {
        return bands.map(function (b) {
            return ee.String(b).cat(suffix)
        })
    }
    function get_interval_mean(img, bands, pstart, pend){
        return img
          .select(bands)
          .reduce(ee.Reducer.intervalMean(pstart,pend))
          .rename(rename_bands(bands, "_" + pstart + "-" + pend));
    }
    function get_percentile(img, bands, p){
        return img.select(bands).reduce(ee.Reducer.percentile(p));
    }

    return (
        get_interval_mean(data, bands, 0, 100)
        .addBands(get_interval_mean(data, bands, 10, 25))
        .addBands(get_interval_mean(data, bands, 10, 90))
        .addBands(get_interval_mean(data, bands, 10, 100))
        .addBands(get_interval_mean(data, bands, 25, 50))
        .addBands(get_interval_mean(data, bands, 25, 75))
        .addBands(get_interval_mean(data, bands, 50, 75))
        .addBands(get_interval_mean(data, bands, 75, 90))
        .addBands(get_interval_mean(data, bands, 90, 100))
        .addBands(get_percentile(data, bands, [10, 25, 50, 75, 95]))
    );
}

var resultImage = percentile_transformation(collection, ["NDVI", "NDFI"]);
Map.addLayer(resultImage)