Self-supervised Disentanglement of Disease Effects from Aging in 3D Medical Shapes

Self-sup ervised Disen tanglemen t of Disease Effects from Aging in 3D Medical Shap es Jak aria Rabbi 1 , Nilanjan Ray 1 , Dana Cobzas 2 1 Departmen t of Computing Science, Univ ersity of Alberta, Edmonton, Canada 2 Departmen t of Computer Science, MacEw an Universit y , Edmonton, Canada jakaria@ualberta.ca, nray1@ualberta.ca, cobzasd@macewan.ca Abstract. Disen tangling pathological c hanges from physiological aging in 3D medical shap es is crucial for developing in terpretable biomark ers and patient stratification. Ho wev er, this separation is c hallenging when diagnosis lab els are limited or unav ailable, since disease and aging often pro duce ov erlapping effects on shape changes, obscuring clinically rele- v an t shape patterns. T o address this c hallenge, w e propose a tw o-stage framew ork com bining unsup ervised disease discov ery with self-sup ervised disen tanglement of implicit shape r epresen tations. In the first stage, we train an implicit neural mo del with signed distance functions to learn stable shap e embeddings. W e then apply clustering on the shap e latent space, whic h yields pseudo disease labels without using ground-truth di- agnosis during discov ery . In the second stage, we disentangle factors in a compact v ariational sp ace using pseudo disease lab els disco vered in the first stage and the ground truth age lab els av ailable for all sub jects. W e enforce separation and controllabilit y with a m ulti-ob jective disen- tanglemen t loss com bining cov ariance and a sup ervised contrastiv e loss. On ADNI hippo campus and OAI distal femur shap es, we ac hieve near- sup ervised p erformance, improving disen tanglement and reconstruction o ver state-of-the-art unsup ervised baselines, while enabling high-fidelity reconstruction, controllable syn thesis, and factor-based explainabilit y . Co de and chec kp oin ts are av ailable at GitHub . Keyw ords: Disentanglemen t · Implicit Neural Representation · Inter- pretabilit y · V ariational Autoenco der · Self-supervised mac hine learning 1 In tro duction Ev aluating morphological v ariation in anatomical shapes is a crucial ob jective in computational medicine, where subtle changes can serve as imaging biomark- ers for diagnosis, prognosis, and patient stratification [6,10]. In neuro degenera- tion, hipp o campal atrophy patterns are widely studied in cohorts such as the Alzheimer’s Disease Neuroimaging Initiativ e (ADNI) [25]. Disease-related effects are strongly entangled b y physiological aging, as they may pro duce ov erlapping shap e c hanges, making it challenging to isolate clinically meaningful disease- asso ciated v ariations, esp ecially when diagnosis lab els are limited, noisy , or un- a v ailable [11]. Moreov er, separating disease effects from healthy controls is also crucial in diseases like osteoarthritis, where aging effects are less pronounced [2]. 2 Rabbi et al. Fig. 1: Stage 1: Learns p er-shap e co des ( z i ) and a INR-nased SDF deco der ( G θ ). Unsup ervised clustering is applied on the learned co des to create pseudo-lab els. Stage 2: A v ariational auto encoder (V AE) mo dels the distribution of shap e co des and learns latents ( z v i ). Pseudo-labels and age lab els are used for disentangling sp ecific laten t v ariables, while frozen G θ is used for reconstruction. Represen tation learning has shifted medical shape mo deling from hand-crafted descriptors and statistical mo dels to ward deep generative approac hes [22,9]. Im- plicit neural represen tations (INR) based on signed distance functions (SDF) pro- vide high-fidelit y con tinuous geometry and ha ve enabled strong reconstruction, in terp olation, and completion p erformance [3,24,21], but most implicit mo dels fo cus on reconstruction quality and do not directly address factor separation or lab el scarcit y . In parallel, disen tanglement in generative mo dels has b een ex- tensiv ely studied using v ariational ob jectiv es and indep endence-promoting regu- larizers [5,7,16], yet purely unsup ervised disentanglemen t is fundamentally am- biguous without additional inductiv e biases or sup ervision [18]. Within medical imaging, weak or structured sup ervision has b een used to disen tangle disease [28,23], and supervised shap e disentanglemen t has been explored when lab els are av ailable [15,26]. Still, there remains a gap for shape frameworks that simul- taneously provide unsupervised/self-sup ervised disease disco very and disentan- glemen t within a single pip eline compatible with implicit representations. T o address these challenges, we introduce a t wo-stage framework that couples unsup ervised disease discov ery with self-sup ervised disen tanglement in implicit shap e represen tations. In the first stage, we train an INR model to learn stable laten t shap e embeddings and encourage a clustering organization of the shap e laten t space through a Gaussian mixture prior, yielding pseudo disease labels. Self-sup ervised Disentanglemen t of Disease Effects in 3D Medical Shap es 3 In the second stage, w e map learned shape codes in to a compact v ariational laten t space and disentangle disease and age using pseudo disease sup ervision and contin uous age lab els, with a m ulti-ob jectiv e loss [26]. W e v alidate our mo del on hippo campus meshes from ADNI [25] and OAI [2], sho wing that pseudo- lab els improv e disen tanglement in unlab eled and low-label settings and supp ort in terpretable tra v ersals that con trol disease and age-asso ciated morphology . Con tributions: (i) W e present the first INR-based self-supervised disease disen tanglement framew ork for 3D medical shap es. (ii) W e disentangle disease and age using a multi-ob jectiv e disentanglemen t loss. ( iii ) On ADNI hipp o cam- pus shapes, our metho d outp erforms unsup ervised baselines and also generalizes w ell to an osteoarthritis (OAI) dataset. 2 Metho d 2.1 Ov erview and Problem Setup W e prop ose a tw o-stage pip eline (Fig. 1) that first learns implicit shap e co des with an INR to disco ver healthy and diseased clusters, then trains a pseudo and age lab el-guided V AE on these co des while freezing the INR as a shap e renderer to preserve output shap e consistency from reconstructed shap e codes. W e represent each surface S i b y samples of a signed distance field. F or shap e i , let Ω i = { ( p ij , s ij ) } m j =1 denote m query p oin ts p ij ∈ R 3 with ground-truth signed distances s ij ∈ R . Stage-1 learns d dimensional co des, z i ∈ R d using an INR mo del [24]. Stage-2 learns a k ( k << d ) dimensional latents z v i ∈ R k o ver the shap e co des using a V AE. 2.2 Stage-1: Implicit Representation Learning W e represent each shap e as the zero lev el s et of a con tinuous SDF. Let G θ : R 3 × R d → R b e an implicit deco der that predicts the signed distance at a query p oin t p ∈ R 3 conditioned on a shap e code z i ∈ R d . Giv en SDF samples Ω i for shap e i , we learn θ and p er-shape codes b y minimizing L INR ( Z ; θ ) , Z ≡ { z i } N i =1 : L INR ( Z , θ ) = L SDF ( Z , θ ) | {z } SDF Loss + λ eik L eik ( Z , θ ) | {z } eikonal + λ gmm L GMM ( Z ) | {z } mixture prior . (1) F ollo wing DeepSDF [24], we use the same architecture for our INR mo del and fit the SDF v alues b y a point wise distance penalty for reconstruction: L SDF ( Z ; θ ) = 1 | Ω | X ( p ,s ) ∈ Ω ρ ( G θ ( p , Z ) − s ) + λ reg L SDF-reg ( Z ) , (2) where ρ ( · ) is a simple per-sample loss. W e keep a small ℓ 2 p enalt y , L SDF-reg ( Z ) on co des to preven t un b ounded growth and to stabilize optimization. W e also add Eikonal [12] loss that encourages the deco der to act lik e a distance field: L eik ( Z ; θ ) = 1 | Ω | X p ∈ Ω ( ∥∇ p G θ ( p , Z ) ∥ 2 − 1) 2 . (3) 4 Rabbi et al. Stage-1 shap e co des exhibit a bimo dal structure; therefore, we make this separa- tion stronger and improv e pseudo-lab el purity b y in tro ducing a tw o-comp onen t Gaussian mixture prior (GMM) ov er the co des: L GMM ( Z ) = − log 2 X m =1 π m N  Z | µ m , diag( σ 2 m )  ! . (4) Here, π m are mixture w eights ( P m π m = 1 ), and eac h comp onen t m has a learn- able mean µ m and diagonal cov ariance diag ( σ 2 m ) . Minimizing L GMM increases the likelihoo d of co des aligning with differen t clusters. Pseudo-lab el Disco v ery in Shap e Code: W e fit a 2-comp onen t GMM on the learned shap e co des ( z i ) and assign ˜ y i = arg max m p ( m | z i ) . 2.3 Stage-2: Self-sup ervised Disen tanglement and INR Stage-2 mo dels the distribution of stage-1 shap e codes with a V AE, learning a lo w-dimensional latent co de. The enco der E ϕ outputs Z v ≡ { z v i } N i =1 , and the deco der D ψ reconstructs the shape co de as ˆ Z ≡ { ˆ z i } N i =1 . W e use residual MLP stac ks for b oth enco der and deco der. Enco der contains hidden widths 256 and 128 that maps the input to V AE latent code. The detector consisting of hidden widths 128, 256, and 256 maps the laten t co de to the reconstructed input. Each stage con tains one residual blo ck with GeLU activ ations and La yerNorm. W e pass ˆ Z through the pretrained implicit deco der G θ with θ fixed. T raining ob jectiv e: Stage-2 optimizes a weigh ted sum of fiv e terms: L disentangle ( ϕ, ψ ) = L V AE  q ϕ ( Z v | Z ) , ˆ Z  | {z } V AE loss + λ snnl L SNNL ( Z v , ˜ y , c ) | {z } supervised loss + λ cov L cov ( Z v ) | {z } decorrelation + λ dis_sen L dis_sen ( Z v , ψ, c ) | {z } dist. & sens. + λ SDF L SDF ( ˆ Z ) | {z } SDF loss. . (5) Here, c are the designated co ordinates for sup ervised disentanglemen t. W e group co de reconstruction and KL regularization in to a single term, L V AE  q ϕ ( Z v | Z ) , ˆ Z  consisting of reconstruction loss, L code ( Z , ˆ Z ) and KL loss, L KL  q ϕ ( Z v | Z )  . The reconstruction part recov ers the shap e co de and is multiplied b y λ code , while the KL term regularizes the p osterior to w ard the unit Gaussian prior, m ultiplied b y β . W e apply a soft nearest-neigh b or loss (SNNL) [26] on Z v c : L SNNL ( Z v , ˜ y ; c, T h ) = X c − 1 b b X i =1 log P j ∈P i ( T h ) α c ij λ 1 P k  = i α c ik + λ 2 P j ∈P i ( T h ) α ¬ c ij ! . (6) Here, ˜ y is the label (for classification threshold T h = 0 ), P i ( T h ) = { j  = i : | ˜ y j − ˜ y i | ≤ T h } . W e define the affinit y α c ij = exp  − ∥ z v i,c − z v j,c ∥ 2 /T  and α ¬ c ij = exp  − [1 / ( |D ¬ t | T )] P d ∈D ¬ t ∥ z v i,d − z v j,d ∥ 2  , where T > 0 is an adaptive temp erature estimated from batch distances (low v ariance → small T ) and D ¬ t = Self-sup ervised Disentanglemen t of Disease Effects in 3D Medical Shap es 5 { 1 , . . . , k } \ { t } . The w eights λ 1 , λ 2 ≥ 0 balance (i) repulsion among all samples in the target co ordinate and (ii ) discouraging pseudo-lab el similarity leaking into non-target co ordinates. W e also penalize the off-diagonal entries (equation 7) for disen tanglement where C v = Co v ( Z v ) is the batc h cov ariance of Z v . L cov ( Z v ) = ∥ C v − diag( C v ) ∥ 2 F . (7) When SNNL is applied for disease disentanglemen t, we empirically observ ed tw o failure modes: v ariance collapse of Z v c to ward 0 [4], and co ordinate inactivity , where c hanging Z v c yields negligible change in the reconstructed co de [20]). W e therefore add a compact regularizer on the designated co ordinate in equation 8 inspired by isometric representation learning. [17]. L dis _ sen = ( s c − ¯ s ¬ c ) 2 +  max(0 , η − α c ) /η  2 . (8) Here s c = Std B ( Z v c ) , ¯ s ¬ c = 1 k − 1 P d  = c Std B ( Z v d ) , and α c = 1 b P b i =1   D ψ ( z v i + ε e c ) − D ψ ( z v i − ε e c )   2 is the av erage finite-difference effect of p erturbing only Z v c (with e c the c -th basis vector). W e reuse one of the INR losses ( L shape ( ˆ Z ; G θ ) ) from stage-1 on ˆ Z with θ fixed. 3 Exp erimen ts 3.1 Datasets W e use tw o datasets: hipp ocampal shap es from the ADNI-1 3T MRI dataset [25] (1 mm isotropic), including left/right segmen tation masks with ground-truth v ol- umes, and distal femur shapes from the Osteoarthritis Initiativ e (O AI) dataset (with fem ur segmentation) [2] for cross-disease ev aluation. F or ADNI, we gen- erate 3D meshes using marc hing cub es [19] follo wed by smoothing. W e v alidate 819 ADNI (AD and cognitive normal - CN) and 191 (h ealth y and O A) O AI scans with patient-disjoin t, stratified splits of 80%/10%/10% (train/v al/test), preserving age, sex, and diagnosis ratios. All scans are used for representation learning, and unsupervised/self-sup ervised disentanglemen t following Horan et al. [13], while the splits are used for sup ervised ablation. 3.2 Implemen tation Details and Metrics W e train a t wo-stage pip eline on three NVIDIA Titan R TX (24 GB) GPUs. Stage-1 is trained for 2000 ep o c hs on SDF samples (16 shapes/batch, 16,384 samples/shap e; clamping=0.1; grad-clip=1.0) with λ eik = λ reg = 10 − 4 , λ g mm = 10 − 3 ( K =2 ), and step LR decay (lr=0.001). Stage-2 trains a V AE with the shap e co des as input/output while keeping the SDF deco der frozen as a renderer; it runs for 2000 ep ochs (32 shap es/batc h, 16,384 samples/shap e) with λ reg = 10 − 4 , λ code = 0 . 44 , β = 0 . 008 , λ snnl = 0 . 77 , ( λ 1 = λ 2 = 0 . 5) , T h = . 05 , λ cov = 0 . 007 , and λ dis _ sen = 0 . 56 ( ε = 0 . 02 , η = 0 . 02 ). 6 Rabbi et al. T able 1: Stage-1 ablation: purity (Pur (%) ↑ ), and mean-v olume gap ( ∆V ↑ , mm 3 ) for shap es b et ween the t wo clusters. A verage volume of AD is lo wer compared to CN which is clearly represen ted by stage-1 clusters. Losses Pur (%) ↑ ∆V ( mm 3 ) ↑ Recon. ↓ Rec + ℓ 2 72.43 1154 0.0014 + Eikonal 80.19 1317 0.0013 + GMM prior 82.37 1401 0.0015 Fig. 2: V olume distribution of shap es in stage-1 cluslters. W e find the best parameters by using the Optuna framework [1] and for Stage-2 ablations, run eac h setting with three random seeds, reporting a v er- age p erformance. W e ev aluate disentanglemen t using SAP [18] and correlations b et w een laten t dimensions and co v ariates (age, diagnosis), with diagnosis clas- sification, age regression, and shape reconstruction. All metho ds use the laten t co des from our stage-1 because most unsupervised disen tanglement methods p erform p o orly on the shap e space. W e rep ort all comparisons and ablations on ADNI, and include OAI results for our method only in the last row of T able 2 due to space constrain ts. 4 Results 4.1 Clustering quality , V olume analysis and Disentanglemen t W e ev aluate stage-1 INR training in T able 1. Cluster purit y ( Pur ) is com- puted with AD/CN lab els only for ev aluation b y a veraging the ma jorit y-class fraction per cluster. A dding Eik onal impro ves Pur (72.43 → 80.19) and recon- struction (0.0014 → 0.0013), indicating smo other SDF geometry . A dding a GMM prior giv es the b est purity (82.37) and largest mean volume difference of shap es ( ∆V = 1401 mm 3 ) b et ween tw o clusters with a small reconstruction error us- ing the chamfer distance (CD) increase (0.0015). Fig. 2 sho ws that the mean v olumes differ and the distributions ov erlap, implying clustering is not based on v olume. Cluster 1 represen ts CN and cluster 2 represen ts AD, as CN co- horts ha v e higher hippo campal volumes [8]. Similar process is follo w ed for O AI dataset. Shap e-space clustering and HLLE+ICA [13], do es not pro duce mean- ingful disentanglemen t; therefore, we adopt our Stage-1 metho d. In stage-2 , w e report disen tanglement and do wnstream prediction in T a- ble 2 using an 8D V AE latent co de for ADNI dataset. W e sup ervise z v i, 0 with pseudo disease lab els and z v i, 1 with av ailable ages for our mo del. F or β -V AE/ β - TCV AE/DIP-V AE [18], we rep ort disease metrics on the latent dimension with the strongest disease association and k eep age sup ervision fixed to z v i, 1 . F or PCA/ICA and HLLE+ICA [13], we do the same as for the V AEs, although it is not p ossible to em bed age lab els there. Our method impro ves disease and Self-sup ervised Disentanglemen t of Disease Effects in 3D Medical Shap es 7 T able 2: Comparison of representation methods, unsup ervised disentanglemen t mo dels, and our metho d. ↑ / ↓ indicates higher / low er is b etter, resp ectiv ely . All rows except the last one show the results of the ADNI dataset. The last row sho ws the results from the OAI dataset with the p ercen tage increase or decrease from the second-b est or best method. Method Disease Age Recon. ↓ SAP ↑ Correlation ↑ Accuracy ↑ SAP ↑ Correlation ↑ RMSE ↓ PCA 0.14 0.57 67.38 0.03 0.22 0.162 0.0020 ICA 0.14 0.61 63.15 0.02 0.20 0.162 0.0021 HLLE+ICA 0.18 0.67 71.76 0.02 0.18 0.161 N/A β -V AE 0.15 0.47 51.27 0.61 0.79 0.065 0.0016 β -TCV AE 0.16 0.49 51.94 0.64 0.82 0.068 0.0017 DIP-V AE 0.18 0.48 53.61 0.63 0.86 0.062 0.0017 w/ fixed T 0.30 0.69 76.31 0.63 0.82 0.065 0.0018 w/o cov 0.34 0.73 76.55 0.63 0.83 0.068 0.0018 Ours 0.38 0.73 78.67 0.67 0.86 0.061 0.0019 Ours (OAI ) 0.25 (+32%) 0.55 (+1%) 63.67 (+2%) 0.41 (+5%) 0.52 (+7%) 0.091 (+5%) 0.0016 (-10%) age separation (SAP) while maintaining reconstruction quality (CD) compara- ble to other V AEs. W e report P earson correlation, disease accuracy , and age RMSE from the designated disease and age latent dimensions using original la- b els, with a simple kNN [14] classifier and regressor ev aluated on train and test splits. Ablations show that an adaptiv e SNNL temp erature impro v es SAP o v er a fixed temp erature and that co v ariance regularization improv es factor separa- tion. The last row rep orts O AI results for our metho d only , with p ercen tages indicating improv emen t o v er the second-b est model or reduction relative to the b est model. Our mo del p erforms strongly on all metrics except reconstruction, whic h is exp ected under additional latent-space constraints [26]. 4.2 Shap e Generation through Latent T ra v ersal and Lab el Mixing Fig. 3 illustrate the mo del’s generative control. W e sample multiple v alues along the age axis ( z v i, 1 ) and, for each fixed z v i, 1 , generate tw o shap es by setting z v i, 0 to its minimum and maxim um v alues. This yields paired AD/CN shap es at matched ages, demonstrating controllable synthesis along both factors. Qualitativ ely , the generated pairs show volume ( ∼ 30% shrink age due to AD) and disease-asso ciated morphological differences aligning with known anatomical progression patterns rep orted in prior clinical shap e studies [10]. Our self-sup ervised mo del closely follo ws the sup ervised mo del in terms of volume and shap e changes [10]. In OAI, distal femur shap e sho w limited c hange o ver time [27], which is consisten t with our observ ation that age-related femoral deformation is not clearly separated in this cohort. W e v ary the fraction of real disease labels in Stage-2 (T able 3) for the ADNI dataset. Compared to leaving the remaining samples unlab eled, pseudo lab els pro vide the largest b enefit in lo w-lab el settings (0–30% real lab els: SAP 0.29– 0.32 vs. 0.17–0.21). As real sup ervision increases ( ∼ 80%), the gain from pseudo- lab els diminishes, and the results are rep orted on the test split. Here, our mo del 8 Rabbi et al. Fig. 3: Rendering healthy and diseased shap es at different ages b y laten t tra versal (trained b y both real pseudo lab els) sho ws consisten t v olume changes in ADNI (left) and deformation in OAI (righ t) that reflect the original dataset. T able 3: Disease SAP across v arying fractions of real AD labels used in Stage-2 training (first ro w). In the Real+No Lab el setting, the remaining samples are unlab eled, whereas in the Real+Pseudo setting, they are assigned pseudo-lab els. Real lab els (%) 0 10 20 30 40 50 60 70 80 90 100 SAP (Real + No lab el) - 0.19 0.21 0.21 0.25 0.29 0.32 0.35 0.38 0.39 0.40 SAP (Real + Pseudo) 0.29 0.29 0.30 0.32 0.32 0.34 0.35 0.37 0.37 0.38 - sup ervised with 100% real lab els gives the upp er-bound as we improv e sup ervised disen tanglement b y incorporating recen t metho ds. 5 Conclusion W e prop ose a tw o-stage, lab el-efficient framework for 3D shap e disen tanglement with limited or no diagnosis lab els. Stage-1 INR learns clusterable implicit co des and yields pseudo disease lab els through tw o-cluster dis co v ery , and a stage-2 V AE separates disease and age into fixed laten t dimensions while freezing the INR deco der as a renderer to preserve reconstruction. On ADNI hipp ocampus and OAI distal fem ur shap es, we outp erform unsup ervised baselines, enable con- trollable healthy and diseased shap e generation across ages, and show pseudo lab els help most in low-label settings but fade as real sup ervision increases in ADNI. In future work, w e will study different diseases across diverse anatomical shap es. Self-sup ervised Disentanglemen t of Disease Effects in 3D Medical Shap es 9 References 1. Akiba, T., Sano, S., Y anase, T., Ohta, T., Ko y ama, M.: Optuna: A next- generation hyperparameter optimization framework. In: Pro ceedings of the 25th A CM SIGKDD international conference on knowledge disco very & data mining. pp. 2623–2631 (2019) 2. Am b ellan, F., T ac k, A., Ehlke, M., Zacho w, S.: Automated segmen tation of knee b one and cartilage combining statistical shap e knowledge and conv olutional neural net works: Data from the osteoarthritis initiative. Medical image analysis 52 , 109– 118 (2019) 3. Amiranash vili, T., Lüdke, D., Li, H.B., Zacho w, S., Menze, B.H.: Learning con tin- uous shap e priors from sparse data with neural implicit functions. Medical image analysis 94 , 103099 (2024) 4. Bardes, A., P once, J., LeCun, Y.: Vicreg: V ariance-in v ariance-co v ariance regular- ization for self-sup ervised learning. arXiv preprint arXiv:2105.04906 (2021) 5. Burgess, C.P ., Higgins, I., Pal, A., Matthey , L., W atters, N., Desjardins, G., Ler- c hner, A.: Understanding disentangling in β -v ae. arXiv preprint (2018) 6. Cerrolaza, J.J., Picazo, M.L., Humbert, L., Sato, Y., Rueck ert, D., Ballester, M.Á.G., Linguraru, M.G.: Computational anatom y for multi-organ analysis in medical imaging: A review. Medical image analysis 56 , 44–67 (2019) 7. Chen, R.T., Li, X., Grosse, R.B., Duvenaud, D.K.: Isolating sources of disentan- glemen t in v ariational auto encoders. A dv ances in neural information processing systems 31 (2018) 8. Ch upin, M., Gérardin, E., Cuingnet, R., Boutet, C., Lemieux, L., Lehéricy , S., Benali, H., Garnero, L., Colliot, O.: F ully automatic hipp ocampus segmentation and classification in alzheimer’s disease and mild cognitiv e impairmen t applied on data from adni. Hippo campus 19 (6), 579–587 (2009) 9. Dannec ker, M., Kyriak op oulou, V., Cordero-Grande, L., Price, A.N., Ha jnal, J.V., Ruec kert, D.: Cina: Conditional implicit neural atlas for spatio-temp oral represen- tation of fetal brains. In: International Conference on Medical Image Computing and Computer-Assisted Interv en tion. pp. 181–191. Springer (2024) 10. F rankó, E., Joly , O., Initiative, A.D.N.: Ev aluating alzheimer’s disease progression using rate of regional hipp ocampal atrophy . PloS one 8 (8), e71354 (2013) 11. Gerardin, E., Chételat, G., Chupin, M., Cuingnet, R., Desgranges, B., Kim, H.S., Niethammer, M., Dub ois, B., Lehéricy , S., Garnero, L., et al.: Multidimen- sional classification of hipp ocampal shap e features discriminates alzheimer’s disease and mild cognitive impairment from normal aging. Neuroimage 47 (4), 1476–1486 (2009) 12. Gropp, A., Y ariv, L., Haim, N., A tzmon, M., Lipman, Y.: Implicit geometric reg- ularization for learning shapes. arXiv preprin t arXiv:2002.10099 (2020) 13. Horan, D., Richardson, E., W eiss, Y.: When is unsupervised disen tanglement p os- sible? Adv ances in Neural Information Pro cessing Systems 34 , 5150–5161 (2021) 14. Imandoust, S.B., Bolandraftar, M., et al.: Application of k-nearest neigh b or (knn) approac h for predicting economic even ts: Theoretical background. International journal of engineering researc h and applications 3 (5), 605–610 (2013) 15. Kiec hle, J., Miller, D., Slessor, J., Pietrosanu, M., K ong, L., Beaulieu, C., Cobzas, D.: Explaining anatomical shape v ariabilit y: sup ervised disentangling with a v ari- ational graph autoenco der. In: 2023 IEEE 20th International Symp osium on Biomedical Imaging (ISBI). pp. 1–5. IEEE (2023) 10 Rabbi et al. 16. Kumar, A., Sattigeri, P ., Balakrishnan, A.: V ariational inference of disentangled la- ten t concepts from unlab eled observ ations. arXiv preprint arXiv:1711.00848 (2017) 17. Lee, Y., Y o on, S., Son, M., Park, F.C.: Regularized auto encoders for isometric represen tation learning. In: In ternational Conference on Learning Represen tations (2022) 18. Lo catello, F., Bauer, S., Lucic, M., Raetsc h, G., Gelly , S., Schölk opf, B., Bachem, O.: Challenging common assumptions in the unsup ervised learning of disentangled represen tations. In: international conference on machine learning. pp. 4114–4124. PMLR (2019) 19. Lorensen, W.E., Cline, H.E.: Marching cubes: A high resolution 3d surface con- struction algorithm. In: Seminal graphics: pioneering efforts that shap ed the field, pp. 347–353 (1998) 20. Lucas, J., T uck er, G., Grosse, R., Norouzi, M.: Understanding p osterior collapse in generativ e laten t v ariable mo dels; 2019. In: URL https://openreview. net/forum (2019) 21. Mesc heder, L., Oec hsle, M., Niemeyer, M., Now ozin, S., Geiger, A.: Occupancy net works: Learning 3d reconstruction in function space. In: Proceedings of the IEEE/CVF conference on computer vision and pattern recognition. pp. 4460–4470 (2019) 22. Molaei, A., Aminimehr, A., T av akoli, A., Kazerouni, A., Azad, B., Azad, R., Mer- hof, D.: Implicit neural representation in medical imaging: A comparative survey . In: Pro ceedings of the IEEE/CVF International Conference on Computer Vision. pp. 2381–2391 (2023) 23. Ouy ang, J., Zhao, Q., Adeli, E., Zaharch uk, G., P ohl, K.M.: Disentangling normal aging from sev erit y of disease via w eak sup ervision on longitudinal mri. IEEE transactions on medical imaging 41 (10), 2558–2569 (2022) 24. P ark, J.J., Florence, P ., Straub, J., New combe, R., Lov egrov e, S.: Deepsdf: Learning con tinuous signed distance functions for shap e representation. In: Pro ceedings of the IEEE/CVF conference on computer vision and pattern recognition. pp. 165– 174 (2019) 25. P etersen, R.C., Aisen, P .S., Beck ett, L.A., Donoh ue, M.C., Gamst, A.C., Harvey , D.J., Jac k Jr, C.R., Jagust, W.J., Shaw, L.M., T oga, A.W., et al.: Alzheimer’s disease neuroimaging initiative (adni) clinical c haracterization. Neurology 74 (3), 201–209 (2010) 26. Rabbi, J., Kiechle, J., Beaulieu, C., Ray , N., Cobzas, D.: Disen tangling hipp ocam- pal shape v ariations: A study of neurological disorders using mesh v ariational au- to encoder with contrastiv e learning. arXiv preprint arXiv:2404.00785 (2024) 27. Wise, B.L., Niu, J., Zhang, Y., Liu, F., Pang, J., Lync h, J.A., Lane, N.E.: Pat- terns of c hange o v er time in knee b one shap e are associated with sex. Clinical Orthopaedics and Related Researc h ® 478 (7), 1491–1502 (2020) 28. Zhang, J., Shi, Y.: Surface-based m ulti-axis longitudinal disentanglemen t using con trastive learning for alzheimer’s disease. In: International Conference on Medi- cal Image Computing and Computer-Assisted Interv en tion. pp. 585–594. Springer (2025)