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

Algorithm 1

Embedding function in the proposed method

(1)	Function [W_3D_Obj] = Embedding (Obj, Msg,α, β, Key1, Key2, Key3)
(2)	//Obj : Original 3D object vertices, Msg : Secret grayscale image, Key1, Key2 and Key3: Encryption keys
(3)	//Control parameters: α ∈ [0, 0.5], β ∈ [1000, 9000]
(4)	Normalized Obj = Normalize(Obj)
(5)	[Vertex x, Vertex y, Vertex z] = Preprocessing(Normalized Obj, α)
(6)	Normalized Msg = Normalize(Msg)
(7)	Msg vector = Reshape to vector(Normalized Msg)
(8)	[Enc Msg1] = Encrypt(Msg vector, Key1)
(9)	[Enc Msg2] = Encrypt(Msg vector, Key2)
(10)	[Enc Msg3] = Encrypt(Msg vector, Key3)
(11)	for j = 1 to length(Msg vector) do
(12)
(12)	Embed the Enc Msg value within the Coefficients values as the following equation system:
(13)	,
(14)
(15)	end
(16)	W_3D_object = DeNormalize(Vertex x’, Vertex y’, Vertex z’)
(17)	return Watermarked 3D object W_3D_Obj
(18)	end