This　paper　presents　a　spherical　measure　based　spherical　image　representation(SMSIR)　and　sphere-based　resampling　methods　for　generating　our　representation.　On　this　basis,　a　spherical　wavelet　transform　is　also　proposed.　We　first　propose　a　formal　recursive　definition　of　the　spherical　triangle　elements　of　SMSIR　and　a　dyadic　index　scheme.　The　index　scheme,　which　supports　global　random　access　and　needs　not　to　be　pre-computed　and　stored,　can　efficiently　index　the　elements　of　SMSIR　like　planar　images.　Two　resampling　methods　to　generate　SMSIR　from　the　most　commonly　used　ERP(Equirectangular　Projection)　representation　are　presented.　Notably,　the　spherical　measure　based　resampling,　which　exploits　the　mapping　between　the　spherical　and　the　parameter　domain,　achieves　higher　computational　efficiency　than　the　spherical　RBF(Radial　Basis　Function)　based　resampling.　Finally,　we　design　high-pass　and　low-pass　filters　with　lifting　schemes　based　on　the　dyadic　index　to　further　verify　the　efficiency　of　our　index　and　deal　with　the　spherical　isotropy.　It　provides　novel　Multi-Resolution　Analysis(MRA)　for　spherical　images.　Experiments　on　continuous　synthetic　spherical　images　indicate　that　our　representation　can　recover　the　original　image　signals　with　higher　accuracy　than　the　ERP　and　CMP(Cubemap)　representations　at　the　same　sampling　rate.　Besides,　the　resampling　experiments　on　natural　spherical　images　show　that　our　resampling　methods　outperform　the　bilinear　and　bicubic　interpolations　concerning　the　subjective　and　objective　quality.　Particularly,　as　high　as　2dB　gain　in　terms　of　S-PSNR　is　achieved.　Experiments　also　show　that　our　spherical　image　transform　can　capture　more　geometric　features　of　spherical　images　than　traditional　wavelet　transform.