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This chapter describes the filter algorithms that can be applied before compression. The purpose of these filters is to prepare the image data for optimum compression.

PNG filter method 0 defines five basic filter types:

Type Name 0 None 1 Sub 2 Up 3 Average 4 Paeth

(Note that filter method 0 in IHDR specifies exactly this set of five filter types. If the set of filter types is ever extended, a different filter method number will be assigned to the extended set, so that decoders need not decompress the data to discover that it contains unsupported filter types.)

The encoder can choose which of these filter algorithms to apply on a scanline-by-scanline basis. In the image data sent to the compression step, each scanline is preceded by a filter-type byte that specifies the filter algorithm used for that scanline.

Filtering algorithms are applied to **bytes**, not to
pixels, regardless of the bit depth or color type of the image. The
filtering algorithms work on the byte sequence formed by a scanline that
has been represented as described in Image
layout. If the image includes an alpha channel, the alpha data is
filtered in the same way as the image data.

When the image is interlaced, each pass of the interlace pattern is treated as an independent image for filtering purposes. The filters work on the byte sequences formed by the pixels actually transmitted during a pass, and the "previous scanline" is the one previously transmitted in the same pass, not the one adjacent in the complete image. Note that the subimage transmitted in any one pass is always rectangular, but is of smaller width and/or height than the complete image. Filtering is not applied when this subimage is empty.

For all filters, the bytes "to the left of" the first pixel in a scanline must be treated as being zero. For filters that refer to the prior scanline, the entire prior scanline must be treated as being zeroes for the first scanline of an image (or of a pass of an interlaced image).

To reverse the effect of a filter, the decoder must use the decoded values of the prior pixel on the same line, the pixel immediately above the current pixel on the prior line, and the pixel just to the left of the pixel above. This implies that at least one scanline's worth of image data will have to be stored by the decoder at all times. Even though some filter types do not refer to the prior scanline, the decoder will always need to store each scanline as it is decoded, since the next scanline might use a filter that refers to it.

PNG imposes no restriction on which filter types can be applied to an image. However, the filters are not equally effective on all types of data. See Recommendations for Encoders: Filter selection.

See also Rationale: Filtering.

With the None filter, the scanline is transmitted unmodified; it is only necessary to insert a filter-type byte before the data.

The `Sub()` filter transmits the difference between each byte
and the value of the corresponding byte of the prior pixel.

To compute the `Sub()` filter, apply the following formula to
each byte of the scanline:

Sub(x) = Raw(x) - Raw(x-bpp)

where `x` ranges from zero to the number of bytes
representing the scanline minus one, `Raw()` refers
to the raw data byte at that byte position in the scanline, and
`bpp` is defined as the number of bytes per complete pixel,
rounding up to one. For example, for color type 2 with a bit depth of
16, bpp is equal to 6 (three samples, two bytes per sample); for color
type 0 with a bit depth of 2, bpp is equal to 1 (rounding up); for color
type 4 with a bit depth of 16, bpp is equal to 4 (two-byte grayscale
sample, plus two-byte alpha sample).

Note this computation is done for each **byte**,
regardless of bit depth. In a 16-bit image, each MSB is predicted from
the preceding MSB and each LSB from the preceding LSB, because of the
way that `bpp` is defined.

Unsigned arithmetic modulo 256 is used, so that both the inputs and
outputs fit into bytes. The sequence of `Sub` values is
transmitted as the filtered scanline.

For all `x < 0`, assume `Raw(x) = 0`.

To reverse the effect of the Sub filter after decompression, output the following value:

Sub(x) + Raw(x-bpp)

(computed mod 256), where `Raw()` refers to the bytes
already decoded.

The `Up()` filter is just like the `Sub()` filter
except that the pixel immediately above the current pixel, rather than
just to its left, is used as the predictor.

To compute the `Up()` filter, apply the following formula to
each byte of the scanline:

Up(x) = Raw(x) - Prior(x)

where `x` ranges from zero to the number of bytes
representing the scanline minus one, `Raw()` refers
to the raw data byte at that byte position in the scanline, and
`Prior(x)` refers to the unfiltered bytes of the prior
scanline.

Note this is done for each **byte**, regardless of bit
depth. Unsigned arithmetic modulo 256 is used, so that both the inputs
and outputs fit into bytes. The sequence of `Up` values is
transmitted as the filtered scanline.

On the first scanline of an image (or of a pass of an interlaced
image), assume `Prior(x) = 0` for all `x`.

To reverse the effect of the `Up()` filter after decompression,
output the following value:

Up(x) + Prior(x)

(computed mod 256), where `Prior()` refers to the decoded
bytes of the prior scanline.

The `Average()` filter uses the average of the two neighboring
pixels (left and above) to predict the value of a pixel.

To compute the `Average()` filter, apply the following formula
to each byte of the scanline:

Average(x) = Raw(x) - floor((Raw(x-bpp)+Prior(x))/2)

where `x` ranges from zero to the number of bytes
representing the scanline minus one, `Raw()` refers
to the raw data byte at that byte position in the scanline,
`Prior()` refers to the unfiltered bytes of the prior
scanline, and `bpp` is defined as for the Sub filter.

Note this is done for each **byte**, regardless of bit
depth. The sequence of `Average` values is transmitted as
the filtered scanline.

The subtraction of the predicted value from the raw byte must be
done modulo 256, so that both the inputs and outputs fit into bytes.
However, the sum `Raw(x-bpp)+Prior(x)` must be formed without
overflow (using at least nine-bit arithmetic). `floor()`
indicates that the result of the division is rounded to the next lower
integer if fractional; in other words, it is an integer division or
right shift operation.

For all `x < 0`, assume `Raw(x) = 0`. On the first
scanline of an image (or of a pass of an interlaced image),
assume `Prior(x) = 0` for all `x`.

To reverse the effect of the `Average()` filter after decompression,
output the following value:

Average(x) + floor((Raw(x-bpp)+Prior(x))/2)

where the result is computed mod 256, but the prediction is
calculated in the same way as for encoding. `Raw()` refers to
the bytes already decoded, and `Prior()` refers to the decoded
bytes of the prior scanline.

The Paeth filter computes a simple linear function of the three neighboring pixels (left, above, upper left), then chooses as predictor the neighboring pixel closest to the computed value. This technique is due to Alan W. Paeth [PAETH].

To compute the `Paeth()` filter, apply the following formula
to each byte of the scanline:

Paeth(x) = Raw(x) - PaethPredictor(Raw(x-bpp), Prior(x), Prior(x-bpp))

where `x` ranges from zero to the number of bytes
representing the scanline minus one, `Raw()` refers
to the raw data byte at that byte position in the scanline,
`Prior()` refers to the unfiltered bytes of the prior
scanline, and `bpp` is defined as for the Sub filter.

Note this is done for each **byte**, regardless of bit
depth. Unsigned arithmetic modulo 256 is used, so that both the inputs
and outputs fit into bytes. The sequence of `Paeth` values
is transmitted as the filtered scanline.

The `PaethPredictor()` function is defined by the following
pseudocode:

function PaethPredictor (a, b, c) begin ; a = left, b = above, c = upper left p := a + b - c ; initial estimate pa := abs(p - a) ; distances to a, b, c pb := abs(p - b) pc := abs(p - c) ; return nearest of a,b,c, ; breaking ties in order a,b,c. if pa <= pb AND pa <= pc then return a else if pb <= pc then return b else return c end

The calculations within the `PaethPredictor()` function must
be performed
exactly, without overflow. Arithmetic modulo 256 is to be used only for
the final step of subtracting the function result from the target byte
value.

**Note that the order in which ties are broken is critical and
must not be altered.** The tie break order is: pixel to the left,
pixel above, pixel to the upper left. (This order differs from that
given in Paeth's article.)

For all `x < 0`, assume `Raw(x) = 0`
and `Prior(x) = 0`. On the first
scanline of an image (or of a pass of an interlaced image), assume
`Prior(x) = 0` for all `x`.

To reverse the effect of the `Paeth()` filter after decompression,
output the following value:

Paeth(x) + PaethPredictor(Raw(x-bpp), Prior(x), Prior(x-bpp))

(computed mod 256), where `Raw()` and `Prior()`
refer to bytes already decoded. Exactly the same `PaethPredictor()`
function is used by both encoder and decoder.

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