A Novel Evolutionary Method for Automated Skull-Face Overlay in Computer-Aided Craniofacial Superimposition

TL;DR

Lilium is introduced, an automated evolutionary method to enhance the accuracy and robustness of Skull-Face Overlay, and outperform the state-of-the-art method in terms of both accuracy and robustness.

Abstract

Craniofacial Superimposition is a forensic technique for identifying skeletal remains by comparing a post-mortem skull with ante-mortem facial photographs. A critical step in this process is Skull-Face Overlay (SFO). This stage involves aligning a 3D skull model with a 2D facial image, typically guided by cranial and facial landmarks' correspondence. However, its accuracy is undermined by individual variability in soft-tissue thickness, introducing significant uncertainty into the overlay. This paper introduces Lilium, an automated evolutionary method to enhance the accuracy and robustness of SFO. Lilium explicitly models soft-tissue variability using a 3D cone-based representation whose parameters are optimized via a Differential Evolution algorithm. The method enforces anatomical, morphological, and photographic plausibility through a combination of constraints: landmark matching, camera parameter consistency, head pose alignment, skull containment within facial boundaries, and region parallelism. This emulation of the usual forensic practitioners' approach leads Lilium to outperform the state-of-the-art method in terms of both accuracy and robustness.

Figures (6)

• Figure 1: Overview of the CFS process comprising three main stages.
• Figure 2: Cone-based soft-tissue modeling approach for 3D facial landmark estimation. The volume defines an anatomically plausible conical search region with a $40^\circ$ angular aperture, originating from a cranial landmark (left). The soft-tissue depth ($||\vec{ST}_i||$) is calculated as a linear interpolation between population-based minimum ($minP_i$) and maximum ($maxP_i$) values using the parameter $p_1$ (second from left). The angular aperture ($\alpha$) of the cone is scaled by $p_2$, and the rotation angle ($\theta$) about the cranial vector is controlled by $p_3$, which allows rotation across the entire $360^\circ$ range (third and fourth from left, respectively). Together, these parameters define a constrained 3D region where the facial landmark is likely to be found.
• Figure 3: This figure illustrates the Lilium pipeline. The process begins with the random initialization of a solution population, which is then iteratively refined by the DE algorithm through mutation, crossover, and selection. A key element in this refinement is Lilium's powerful composite fitness function (see Section \ref{['sec:opt']}). This iterative process continues until the defined stopping criterion is met, at which point the vector with the best fitness score represents the optimal SFO solution.
• Figure 4: Contour extraction for the parallelism term $\text{P}_{\text{pll}}$. The regions of interest are isolated from the skull and the facial meshes using anatomically defined cutting planes (top). The boundary of each segmented region is extracted, cleaned, ordered, and merged into a single continuous curve. The curves are then trimmed using averaged endpoint normals to ensure consistent and comparable extents between skull and face (bottom).
• Figure 5: Real facial photographs are replaced by synthetic renderings generated from 3D facial models, where landmarks are precisely defined. These 3D landmarks are projected into 2D using known camera parameters, eliminating annotation errors.