基於校正差異（Canonical Difference），我們發展了一套嶄新的核心鑑別式轉換（Kernel Discriminant Transformation，以下簡稱KDT）並應用在人臉辨識上。為了在不同的光線變化、人臉表情與姿勢下獲得更多的資訊，我們提出的人臉辨識系統使用一個多角度的人臉影像集（Multi-view Facial Image Set）來表示一個個體。由於多角度的人臉影像屬於非線性分布，每個影像集被套用一個非線性映像函式（Nonlinear Mapping Function）以映射至高維的特徵空間中，並且使用核心主要成分分析（Kernel Principal Component Analysis）產生對應的線性子空間，我們稱其核心子空間（Kernel Subspace）。基於另一種相似度比較法──校正角（Canonical Angle），我們提出了判別差異（Canonical Difference）以計算兩個核心子空間的相似度。此外，基於核心費雪鑑別式（Kernel Fisher’s Discriminant）所提供絕佳的分類效果， 我們藉由求相異種類（Between-class）與相同種類（Within-class）判節差異比值的最大值以推得KDT，並使用KDT 來讓兩兩核心子空間產生關聯。由實驗結果可看出，我們所提出的人臉辨識系統效能較其他的子空間比較方式優異。

A novel kernel discriminant transformation (KDT) algorithm based on the concept of canonical differences is presented for automatic face recognition applications. For each individual, the face recognition system compiles a multi-view facial image set comprising images with different facial expressions, poses and illumination conditions. Since the multi-view facial images are non-linearly
distributed, each image set is mapped into a high-dimensional feature space using a nonlinear mapping function. The corresponding linear subspace, i.e. the kernel subspace, is then constructed via a process of kernel principal component analysis (KPCA). The similarity of two kernel subspaces is assessed by evaluating the canonical difference between them based on the angle
between their respective canonical vectors. Utilizing the kernel Fisher discriminant (KFD), a KDT algorithm is derived to establish the correlation between kernel subspaces based on the ratio of the canonical differences of the between-classes to those of the within-classes. The experimental results demonstrate that the proposed classification system outperforms existing subspace comparison schemes and has a promising potential for use in automatic face recognition applications.

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