Skin cancer is among the most common and potentially lethal malignancies worldwide, so early and accurate detection is essential for reducing morbidity and mortality. Clinical decision support systems based on machine learning have shown strong promise for automating the analysis of dermoscopic images, with deep models approaching dermatologist-level performance on lesion classification tasks~\cite{codella2018skin,tang2020automated}. However, conventional CNN and transformer architectures are driven primarily by local pixel and texture cues and may underutilize global properties such as lesion shape, connectivity patterns, and boundary irregularities that often distinguish malignant from benign lesions~\cite{gutman2016skin}.

Topological data analysis (TDA) offers a complementary perspective by extracting stable, multiscale descriptors of an image’s geometric and connectivity structure~\cite{carlsson2009topology}. Persistent homology summarizes how features such as connected components and holes appear and disappear across a filtration, yielding signatures that are robust to small deformations and illumination changes. Prior work has demonstrated the value of TDA in medical imaging, including tumor characterization and histopathology~\cite{hofer2017deep}, but almost all existing approaches rely on single-parameter filtrations and therefore cannot directly capture how multiple imaging cues interact across scales.


In this paper, we introduce \emph{cubical multiparameter persistence} for dermoscopic image analysis and, to our knowledge, provide the first systematic study of multipersistence for skin cancer detection. We build coupled cubical filtrations that jointly encode intensity, scale, and simple texture surrogates, producing multiparameter Betti summaries that reflect cross-parameter interactions that single-parameter pipelines can miss. To fuse these topological signals with modern vision backbones, we integrate the multipersistence descriptors with a Vision Transformer (ViT) using \emph{supervised contrastive learning}, encouraging class-consistent agreement between image features and topological structure in a shared representation space.

We evaluate our method, TopoCon-MP, on three publicly available skin lesion datasets that include melanoma, basal cell carcinoma, squamous cell carcinoma, and benign nevi. Experiments show that multipersistence alone is competitive with strong pretrained baselines, and that topology-aware contrastive fusion improves AUC, accuracy, and balanced accuracy over both CNN and ViT models, with particularly clear gains in cross-dataset transfer. In addition, the learned topological channels provide interpretable cues that co-localize with clinically meaningful structures such as pigment networks and irregular lesion borders.

Our contributions are:
\begin{itemize}
\item We present the first application and systematic evaluation of \emph{cubical multiparameter persistence} for automated skin lesion classification.
\item We propose a topology and vision fusion strategy that aligns multipersistence descriptors with a ViT using supervised contrastive learning to obtain joint representations.
\item We demonstrate consistent performance gains over strong pretrained CNN and ViT baselines across multiple datasets, including a cross-dataset transfer setting, with ablations showing the advantage of multipersistence over single-parameter cubical persistence.
\item We provide qualitative evidence that topological signals highlight clinically relevant morphology, supporting interpretability for dermatological imaging.
\end{itemize}
