# A Fragile Watermarking Scheme for Authenticity Verification of 3D Models in GLB Format
## 2 Related Works  
The watermarking of 3D models is mainly based on hiding the watermark in the object in the least noticeable way possible. Consequently, many steganographic methods are applicable in this domain [12]. [PERSON] et al. [21] proposed a method based on the Fuzzy C-Means Clustering (FCM) algorithm. The procedure involves determining a feature vector for vertices of degree 6 (i.e., vertices with six neighbours) that describes the local topology of the geometry (such as peak, plane, or moderate roughness). Based on this vector, a classification of vertices is carried out using the FCM technique, which allows the selection of suitable locations for watermark embedding. The embedding process itself involves moving the selected vertex from the six-element ring by the value of the standard deviation in that ring, depending on whether bit 0 or 1 is embedded. Solutions based on various transformations to spectral or frequency space can often be found [22] ([PERSON] and [PERSON]) and [17; 23; 24]. [PERSON] and [PERSON] used as a watermark a hash-based message authentication code (HMAC), generated from a set of all vertices and a texture. They investigated the possibility of placing this watermark in a spectral space to which the selected vertices were transformed using a discrete wavelet transform, specifically the lifting scheme algorithm [25]. After transforming the selected components of the chosen vertices into the spectral domain, the resulting wavelet coefficients (which are integers in this work) are altered. The watermark is embedded by incrementing or decrementing the coefficient values by one, based on the corresponding bit in the HMAC code. [PERSON] et al. [23] also used frequency space. The authors used spherical harmonics to transform a 3D mesh to spectral space for watermarking. They also used the concept of entropy to determine the appropriate level of reconstruction. [PERSON] et al. used hash functions to create the watermark, and the watermarking process involved substituting the least significant bits (LSBs) in the coordinates of the spherical harmonics according to accepted quantisation rules. In the paper [17], the model is watermarked by modifying the norm of the wavelet coefficient vectors (WCV), which are the result of applying the discrete wavelet transform. The watermark is placed in the low-frequency coefficients according to the accepted rules for quantising WCV norms. [PERSON] et al. [26] presented a watermarking method that involves embedding three watermarks into a single model. Each watermark is of a different nature: the first is related to the geometry of the model, the second to its topology, and the third was embedded in spectral space. This resulted in high resistance to various types of attacks. The authors used the Maximally Stable Meshes algorithm (which is an extension of Maximally Stable Extremal Regions for digital images) to select appropriate vertices. Some scholars use the Genetic Algorithm (GA) for watermarking purposes [18; 27]. In the work [28], the watermark bit string is embedded in a secret vector space defined by the Karhunen-Loeve transform (\(KTL\)), derived from a key that is an image. The marking process begins with creating an embedding unit (EU) (vertex position + special hash code), which has a size of 28 bytes. The GA then modifies eight LSBs in each coordinate \((x,y,z)\) of the vertex position in the selected EUs until the condition \((c_{1},c_{2},...,c_{28})=KLT(g_{1},g_{2},...,g_{28})\) is satisfied, where \((c_{1},c_{2},...,c_{28})\) are the predefined \(KTL\) coefficients and \((g_{1},g_{2},...,g_{28})\) are the bytes the EU consists of--\(g_{1}\)-\(g_{4}\) the \(x\)-coordinate, \(g5\)-\(g_{8}\) the \(y\)-coordinate, and \(g9\)-\(g_{12}\) the \(z\)-coordinate. It should be noted that watermarking is not only limited to ordinary 3D models: Ref. [29] ([PERSON] et al.) and [30; 31] presented a watermarking method for 3D Morphable Models. The authors designed and trained an advanced neural network model for overlay and watermark extraction.