Genotype-phenotype (G-P) analyses for complex morphological traits typically utilize simple, predetermined anatomical measures or features derived via unsupervised dimension reduction techniques (e.g. principal component analysis (PCA) or eigen-shapes). Despite the popularity of these approaches, they do not necessarily reveal axes of phenotypic variation that are genetically relevant. Therefore, we introduce a framework to optimize phenotyping for G-P analyses, such as genome-wide association studies (GWAS) of common variants or rare variant association studies (RVAS) of rare variants. Our strategy is two-fold: (i) we construct a multidimensional feature space spanning a wide range of phenotypic variation, and (ii) within this feature space, we use an optimization algorithm to search for directions or feature combinations that are genetically enriched. To test our approach, we examine human facial shape in the context of GWAS and RVAS. In GWAS, we optimize for phenotypes exhibiting high heritability, estimated from either family data or genomic relatedness measured in unrelated individuals. In RVAS, we optimize for the skewness of phenotype distributions, aiming to detect commingled distributions that suggest single or few genomic loci with major effects. We compare our approach with eigen-shapes as baseline in GWAS involving 8246 individuals of European ancestry and in gene-based tests of rare variants with a subset of 1906 individuals. After applying linkage disequilibrium score regression to our GWAS results, heritability-enriched phenotypes yielded the highest SNP heritability, followed by eigen-shapes, while commingling-based traits displayed the lowest SNP heritability. Heritability-enriched phenotypes also exhibited higher discovery rates, identifying the same number of independent genomic loci as eigen-shapes with a smaller effective number of traits. For RVAS, commingling-based traits resulted in more genes passing the exome-wide significance threshold than eigen-shapes, while heritability-enriched phenotypes lead to only a few associations. Overall, our results demonstrate that optimized phenotyping allows for the extraction of genetically relevant traits that can specifically enhance discovery efforts of common and rare variants, as evidenced by their increased power in facial GWAS and RVAS.

Human facial shape, while strongly heritable, involves both genetic and structural complexity, necessitating precise phenotyping for accurate assessment. Common phenotyping strategies include simplifying 3D facial features into univariate traits such as anthropometric measurements (e.g., inter-landmark distances), unsupervised dimensionality reductions (e.g., principal component analysis (PCA) and auto-encoder (AE) approaches), and assessing resemblance to particular facial gestalts (e.g., syndromic facial archetypes). This study provides a comparative assessment of these strategies in genome-wide association studies (GWASs) of 3D facial shape. Specifically, we investigated inter-landmark distances, PCA and AE-derived latent dimensions, and facial resemblance to random, extreme, and syndromic gestalts within a GWAS of 8,426 individuals of recent European ancestry. Inter-landmark distances exhibit the highest SNP-based heritability as estimated via LD score regression, followed by AE dimensions. Conversely, resemblance scores to extreme and syndromic facial gestalts display the lowest heritability, in line with expectations. Notably, the aggregation of multiple GWASs on facial resemblance to random gestalts reveals the highest number of independent genetic loci. This novel, easy-to-implement phenotyping approach holds significant promise for capturing genetically relevant morphological traits derived from complex biomedical imaging datasets, and its applications extend beyond faces. Nevertheless, these different phenotyping strategies capture different genetic influences on craniofacial shape. Thus, it remains valuable to explore these strategies individually and in combination to gain a more comprehensive understanding of the genetic factors underlying craniofacial shape and related traits.

A genome-wide association study (GWAS) of a complex, multi-dimensional morphological trait, such as the human face, typically relies on predefined and simplified phenotypic measurements, such as inter-landmark distances and angles. These measures are predominantly designed by human experts based on perceived biological or clinical knowledge. To avoid use handcrafted phenotypes (i.e., a priori expert-identified phenotypes), alternative automatically extracted phenotypic descriptors, such as features derived from dimension reduction techniques (e.g., principal component analysis), are employed. While the features generated by such computational algorithms capture the geometric variations of the biological shape, they are not necessarily genetically relevant. Therefore, genetically informed data-driven phenotyping is desirable. Here, we propose an approach where phenotyping is done through a data-driven optimization of trait heritability, defined as the degree of variation in a phenotypic trait in a population that is due to genetic variation. The resulting phenotyping process consists of two steps: 1) constructing a feature space that models shape variations using dimension reduction techniques, and 2) searching for directions in the feature space exhibiting high trait heritability using a genetic search algorithm (i.e., heuristic inspired by natural selection). We show that the phenotypes resulting from the proposed trait heritability-optimized training differ from those of principal components in the following aspects: 1) higher trait heritability, 2) higher SNP heritability, and 3) identification of the same number of independent genetic loci with a smaller number of effective traits. Our results demonstrate that data-driven trait heritability-based optimization enables the automatic extraction of genetically relevant phenotypes, as shown by their increased power in genome-wide association scans.

The relationship between the shape and gender of a face, with particular application to automatic gender classification, has been the subject of significant research in recent years. Determining the gender of a face, especially when dealing with unseen examples, presents a major challenge. This is especially true for certain age groups, such as teenagers, due to their rapid development at this phase of life. This study proposes a new set of facial morphological descriptors, based on 3D geodesic path curvatures, and uses them for gender analysis. Their goal is to discern key facial areas related to gender, specifically suited to the task of gender classification. These new curvature-based features are extracted along the geodesic path between two biological landmarks located in key facial areas. Classification performance based on the new features is compared with that achieved using the Euclidean and geodesic distance measures traditionally used in gender analysis and classification. Five different experiments were conducted on a large teenage face database (4745 faces from the Avon Longitudinal Study of Parents and Children) to investigate and justify the use of the proposed curvature features. Our experiments show that the combination of the new features with geodesic distances provides a classification accuracy of 89%. They also show that nose-related traits provide the most discriminative facial feature for gender classification, with the most discriminative features lying along the 3D face profile curve.

Advances in 3D imaging have recently made 3D surface scanners, capable of capturing textured surfaces at video rate, affordable and common in computer vision. This is a relatively new source of data, the potential of which has not yet been fully exploited as the problem of non-rigid registration of surfaces is difficult. While registration based on shape alone has been an active research area for some time, the problem of registering surfaces based on texture information has not been addressed in a principled way. We propose a novel, efficient and reliable, fully automatic method for performing groupwise non-rigid registration of textured surfaces, such as those obtained with 3D scanners. We demonstrate the robustness of our approach on 3D scans of human faces, including the notoriously difficult case of inter-subject registration. We show how our method can be used to build high-quality 3D models of appearance fully automatically.

The groupwise approach to non-rigid image registration, solving the dense correspondence problem, has recently been shown to be a useful tool in many applications, including medical imaging, automatic construction of statistical models of appearance and analysis of facial dynamics. Such an approach overcomes limitations of traditional pairwise methods but at a cost of having to search for the solution (optimal registration) in a space of much higher dimensionality which grows rapidly with the number of examples (images) being registered. Techniques to overcome this dimensionality problem have not been addressed sufficiently in the groupwise registration literature. In this paper, we propose a novel, fast and reliable, fully unsupervised stochastic algorithm to search for optimal groupwise dense correspondence in large sets of unmarked images. The efficiency of our approach stems from novel dimensionality reduction techniques specific to the problem of groupwise image registration and from comparative insensitivity of the adopted optimisation scheme (simultaneous perturbation stochastic approximation (SPSA)) to the high dimensionality of the search space. Additionally, our algorithm is formulated in way readily suited to implementation on graphics processing units (GPU). In evaluation of our method we show a high robustness and success rate, fast convergence on various types of test data, including facial images featuring large degrees of both inter- and intra-person variation, and show considerable improvement in terms of accuracy of solution and speed compared to traditional methods.