A Blind Watermarking Model of the 3D Object and the Polygonal Mesh Objects for Securing Copyright

Algorithm 2

Extraction function in the proposed method

(1)	Function [EW_img] = Extraction (W_3D_Obj,β, Key1, Key2, Key3)
(2)	//W_3D_Obj : Watermarked 3D object vertices, Key1, Key2 and Key3: Encryption keys
(3)	Normalized W_3D_Obj = Normalize(W_3D_Obj)
(4)	[Vertex x, Vertex y, Vertex z] = Preprocessing(Normalized W_3D_Obj)
(5)	for j = 1 to length(Msg vector) do
(6)
(7)	Extract the RecEncMsg value within the Coefficients values as the following equation system:
(8)	,
(9)	end
(10)	[Rec Msg1] = Decrypt(RecEncMsg1 vector, Key1)
(11)	[Rec Msg2] = Decrypt (RecEncMsg2 vector, Key2)
(12)	[Rec Msg3] = Decrypt (RecEncMsg3 vector, Key3)
(13)	Rec Msg vector = Average (Rec Msg1, Rec Msg2, Rec Msg3)
(14)	Rec Msg = Reshape to image(Rec Msg vector)
(15)	EW_img = DeNormalize(Rec Msg)
(16)	return Extracted Watermark grayscale image EW_img
(17)	end