Meaning of the offset

[AlbertoPresta]

Hi,

Maybe is a stupid question, but what is the physical meaning of the value called self._offset?
You calculated in the following way:

self._offset = -minima

[YodaEmbedding]

_offset is set in update():

CompressAI/compressai/entropy_models/entropy_models.py

Lines 395 to 405 in 216af74

	medians = self.quantiles[:, 0, 1]
	minima = medians - self.quantiles[:, 0, 0]
	minima = torch.ceil(minima).int()
	minima = torch.clamp(minima, min=0)
	maxima = self.quantiles[:, 0, 2] - medians
	maxima = torch.ceil(maxima).int()
	maxima = torch.clamp(maxima, min=0)
	self._offset = -minima

And is later accessed during compress():

CompressAI/compressai/entropy_models/entropy_models.py

Lines 260 to 266 in 216af74

	rv = self.entropy_coder.encode_with_indexes(
	symbols[i].reshape(-1).int().tolist(),
	indexes[i].reshape(-1).int().tolist(),
	self._quantized_cdf.tolist(),
	self._cdf_length.reshape(-1).int().tolist(),
	self._offset.reshape(-1).int().tolist(),
	)

...and is immediately passed into the entropy coder, which subtracts the offset from the symbol it is trying to encode:

CompressAI/compressai/cpp_exts/rans/rans_interface.cpp

Line 128 in 216af74

int32_t value = symbols[i] - offsets[cdf_idx];

---

Each CDF has associated with it a single offset scalar value. This offset represents the smallest symbol that is encodable by our zero-mean distribution. (For even smaller symbols outside the distribution, we use a bypass coding engine.) Thus, offset ≤ 0.

ORIGINAL VALUES (FOR ZERO-MEAN SYMBOLS):

  ▲
  │            xxx
  │          xx │ xx
  │         x   │  xx
  │        x    │    x
  │       x     │    xx
  │      x      │      xx
  │     xx      │       xx
  │    xx       │       │xx
  │xxxx         │       │ xxxx
  ├─────────────┼───────┼───────►
  │             │       │

offset          0     symbol

MEMORY:

  ▲
  │            xxx
  │          xx │ xx
  │         x   │  xx
  │        x    │    x
  │       x     │    xx
  │      x      │      xx
  │     xx      │       xx
  │    xx       │       │xx
  │xxxx         │       │ xxxx
  ├─────────────┼───────┼───────►
  │             │       │

  0        -offset    (symbol - offset)

Notice how the "zero mean" symbol might be any number -- even negative! But we want to do an indexing operation on the CDF in memory, which only accepts positive numbers. That's what (symbol - offset) ensures.

[AlbertoPresta]

ok thanks got it! and just to be sure at 100%, the cdf_length simply represents the length of the cdf right? i know it can be seem a stupid question, but just to understan fully the code

[YodaEmbedding]

quantized_cdf is a 2D array. However, since CDFs are of different sizes, we use cdf_length[i] to represent the number of valid elements within the 1D array quantized_cdf[i]. Any element quantized_cdf[i][j] such that j ≥ cdf_length[i] is considered invalid, and thus will never be read/accessed.

CompressAI/compressai/entropy_models/entropy_models.py

Line 428 in 216af74

self._cdf_length = pmf_length + 2

Related: #146 (comment)