Object Modelling by Registration of Multiple Range Images
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βππ β π, βππ β π | πππ β ππ = 0
D π, π = Ξ©
ππ(π’, π£) β π(π π’, π£ , π(π’, π£)) 2 ππ’ππ£ = 0
π(π’, π£) β π, π(π’, π£) β π π’, π£ β β Γβπ π
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T =
ππΌππ½π πΌππ½βπ π½0
ππΌπ π½π πΎ β π πΌππΎπ πΌπ π½π πΎ + ππΌππΎππ½π πΎ0
ππΌπ π½ππΎ + π πΌπ πΎπ πΌπ π½ππΎ β ππΌπ πΎππ½ππΎ0
π‘π₯π‘π¦π‘π§1
πΌ, π½, πΎ, π‘π₯, π‘π¦ , π‘π§
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ππ·
ππΌ= 0,
ππ·
ππ‘π₯= 0,
ππ·
ππ½= 0,
ππ·
ππ‘π¦= 0,
ππ·
ππΎ= 0,
ππ·
ππ‘π§= 0
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π =
π=1
π
πππ β ππ2
ππ π π ππ π π π = 1β¦π
π =
π=1
π
πππ β ππ2, with ππ = |π min
ππππππ β π
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ππ =
π=1
π
ππππ β πππ 2 , with ππ
π = |π minπππππβ1ππ β π
πππ
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ππ =
π=1
π
ππππ β ππβ²π 2 , with ππ
β²π = ππβ1βπ β© π
where βπ = π| ππ β π Γ πππ = 0
πβπ β© π βπ π
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π
where ππ is the tangent plane of π at ππ
π =
π=1
π
πππ β ππβ² 2 , with ππ
β² = |π minπππππππ β π
π =
π=1
π
πππ β ππ2
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π
ππ =
π=1
π
ππ 2 ππππ , ππ
π
with πππ = π | πππ
π β ππβ²π β π = 0 , ππ
β²π = ππβ1βπ β© π
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π π
π¬
π«
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π π
π¬
ππβ1π«
ππ ππ
πππ
ππ
ππ = π=1π ππ
2 ππππ , πππ
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π
π«
π¬
π = (π₯, π¦, π(π₯, π¦))π
- β π ππ
π§
π₯0 = π₯ π¦0 = π¦
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π
π«
π¬
π0
πππ = π₯π, π¦π, π§π
βπ ππβ1
π«
π1
ππ β ππβ1 < ππ ππ > 0
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ππ = π=1π ππ
2 π β ππβ1ππ , πππ
πΌ, π½, πΎ π
where π β ππβ1 = ππ
πππ π ππ
π
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ππ π0 π0π
ππ
ππβ1 ππ πππ ππβ² πππ
β²
πππ π
πππ π ππ
β²
π ππ
ππ = π β ππβ1
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πΏ =ππβππ+1
πβ²β€ ππ , ππ > 0
ππ
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π₯ π’, π£ , π¦ π’, π£ πππ π§(π’, π£)
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