Adaptive　transform　coding　is　gaining　more　and　more　attention　for　better　mining　of　image　content　over　fixed　transforms　such　as　discrete　cosine　transform　(DCT).　As　a　special　case,　graph　transform　learning　establishes　a　novel　paradigm　for　the　graph-based　transforms.　However,　there　still　exists　a　challenge　for　graph　transform　learning-based　image　codecs　design　on　natural　image　compression,　and　graph　representation　cannot　describe　regular　image　samples　well　over　graph-structured　data.　Therefore,　in　this　article,　we　propose　a　cross-channel　graph-based　transform　(CCGBT)　for　natural　color　image　compression.　We　observe　that　neighboring　pixels　having　similar　intensities　should　have　similar　values　in　the　chroma　channels,　which　means　that　the　prominent　structure　of　the　luminance　channel　is　related　to　the　contours　of　the　chrominance　channels.　A　collaborative　design　of　the　learned　graphs　and　their　corresponding　distinctive　transforms　lies　in　the　assumption　that　a　sufficiently　small　block　can　be　considered　smooth,　meanwhile,　guaranteeing　the　compression　of　the　luma　and　chroma　signals　at　the　cost　of　a　small　overhead　for　coding　the　description　of　the　designed　luma　graph.　In　addition,　a　color　image　compression　framework　based　on　the　CCGBT　is　designed　for　comparing　DCT　on　the　classic　JPEG　codec.　The　proposed　method　benefits　from　its　flexible　transform　block　design　on　arbitrary　sizes　to　exploit　image　content　better　than　the　fixed　transform.　The　experimental　results　show　that　the　unified　graph-based　transform　outperforms　conventional　DCT,　while　close　to　discrete　wavelet　transform　on　JPEG2000　at　high　bit-rates.　©　2024　Copyright　held　by　the　owner/author(s).　Publication　rights　licensed　to　ACM.