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Minor edits and punctuation fixes in sato examples
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SHA: e352a2f
Reason: push, by wantehchang

Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com>
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wantehchang and github-actions[bot] committed Oct 23, 2024
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<mn>2</mn>
</msub>
</math>
<p>Each output sample is equal to the sum of a sample of the first input image item shifted to the left by 8 bits and of a sample of the second input image item. This can be viewed as a bit depth extension of the first input image item by the second input image item. The first input image item contains the 8 most significant bits and the second input image item contains the 8 least significant bits of the output reconstructed image item which has a bit depth of 16, something that is impossible to achieve with a single <a data-link-type="dfn" href="#av1-image-item" id="ref-for-av1-image-item②⑥">AV1 image item</a>.</p>
<p>Each output sample is equal to the sum of a sample of the first input image item shifted to the left by 8 bits and of a sample of the second input image item. This can be viewed as a bit depth extension of the first input image item by the second input image item. The first input image item contains the 8 most significant bits and the second input image item contains the 8 least significant bits of the 16-bit output reconstructed image item. It is impossible to achieve a bit depth of 16 with a single <a data-link-type="dfn" href="#av1-image-item" id="ref-for-av1-image-item②⑥">AV1 image item</a>.</p>
<p class="note" role="note"><span class="marker">NOTE:</span> If the first input image item is the <a data-link-type="dfn" href="https://www.iso.org/standard/74417.html" id="ref-for-something②⑤⑤">primary image item</a> and is enclosed in an <code>'<a data-link-type="dfn" href="https://www.iso.org/standard/68960.html" id="ref-for-something②⑤⑥">altr</a>'</code> group (see <a href="#altr-group">§ 5.1 'altr' group</a>) with the <a data-link-type="dfn" href="#sample-transform-derived-image-item" id="ref-for-sample-transform-derived-image-item①⑥">Sample Transform Derived Image Item</a>, the first input image item is also a backward-compatible 8-bit regular coded image item that can be used by readers that do not support <a data-link-type="dfn" href="#sample-transform-derived-image-item" id="ref-for-sample-transform-derived-image-item①⑦">Sample Transform Derived Image Items</a> or do not need extra precision.</p>
<p class="note" role="note"><span class="marker">NOTE:</span> The second input image item can be marked as <a data-link-type="dfn" href="https://www.iso.org/standard/66067.html" id="ref-for-something②⑤⑦">hidden</a> to prevent readers from surfacing it to users.</p>
<p class="note" role="note"><span class="marker">NOTE:</span> The second input image item loses its meaning of least significant part if any of the most significant bits changes, so the first input image item has to be losslessly encoded. The second input image item supports reasonable loss during encoding.</p>
<p class="note" role="note"><span class="marker">NOTE:</span> The second input image item loses its meaning of the least significant part if any of the most significant bits changes, so the first input image item has to be losslessly encoded. The second input image item supports reasonable loss during encoding.</p>
<p class="note" role="note"><span class="marker">NOTE:</span> This pattern can be used for reconstructed bit depths beyond 16 by combining more than two input image items or with various input bit depth configurations and operations.</p>
<h4 class="heading settled" id="sato-example-residual-bit-depth-extension"><span class="content">Residual bit depth extension</span><a class="self-link" href="#sato-example-residual-bit-depth-extension"></a></h4>
<p>The following example describes how to leverage a <a data-link-type="dfn" href="#sample-transform-derived-image-item" id="ref-for-sample-transform-derived-image-item①⑧">Sample Transform Derived Image Item</a> on top of a regular 12-bit <a data-link-type="dfn" href="https://www.iso.org/standard/74417.html" id="ref-for-something②⑤⑧">MIAF image item</a> to extend the decoded bit depth to 16 bits.<br> It differs from the <a href="#sato-example-suffix-bit-depth-extension">Suffix bit depth extension</a> by its slightly longer series of operations allowing its first input image item to be lossily encoded.</p>
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<mo>-</mo>
<mn>128</mn>
</math>
<p>Each output sample is equal to the sum of a sample of the first input image item shifted to the left by 4 bits and of a sample of the second input image item offset by -128. This can be viewed as a bit depth extension of the first input image item by the second input image item which contains the residuals to correct the precision loss of the first input image item.</p>
<p>Each output sample is equal to the sum of a sample of the first input image item shifted to the left by 4 bits and of a sample of the second input image item offset by -128. This can be viewed as a bit depth extension of the first input image item by the second input image item, which contains the residuals to correct the precision loss of the first input image item.</p>
<p class="note" role="note"><span class="marker">NOTE:</span> If the first input image item is the <a data-link-type="dfn" href="https://www.iso.org/standard/74417.html" id="ref-for-something②⑥⑧">primary image item</a> and is enclosed in an <code>'<a data-link-type="dfn" href="https://www.iso.org/standard/68960.html" id="ref-for-something②⑥⑨">altr</a>'</code> group (see <a href="#altr-group">§ 5.1 'altr' group</a>) with the derived image item, the first input image item is also a backward-compatible 12-bit regular coded image item that can be used by decoding contexts that do not support <a data-link-type="dfn" href="#sample-transform-derived-image-item" id="ref-for-sample-transform-derived-image-item②⓪">Sample Transform Derived Image Items</a> or do not need extra precision.</p>
<p class="note" role="note"><span class="marker">NOTE:</span> The second input image item can be marked as <a data-link-type="dfn" href="https://www.iso.org/standard/66067.html" id="ref-for-something②⑦⓪">hidden</a> to prevent readers from surfacing it to users.</p>
<p class="note" role="note"><span class="marker">NOTE:</span> The first input image item supports reasonable loss during encoding because the second input image item "overlaps" by 4 bits to correct the loss. The second input image item supports reasonable loss during encoding.</p>
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