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Eye tracking is an increasingly common technology with a variety of practical uses. Eye-tracking data, or gaze data, can be categorized into two main events: fixations represent focused eye movement, indicative of awareness and attention, whereas saccades are higher-velocity movements that occur between fixation events. Common methods to identify fixations in gaze data can lack sensitivity to peripheral points and may misrepresent positional and durational properties of fixations. To address these shortcomings, we introduce the notion of inner density for fixation identification, which concerns both the duration of the fixation and the proximity of its constituent gaze points. Moreover, we demonstrate how to identify fixations in a sequence of gaze data by optimizing for inner density. After decomposing the clustering of a temporal gaze data sequence into successive regions (chunks), we use nonlinear and linear 0–1 optimization formulations to identify the densest fixations within a given data chunk. Our approach is parametrized by a unique constant that adjusts the degree of desired density, allowing decision makers to have fine-tuned control over density during the process. Computational experiments on real data sets demonstrate the efficiency of our approach and its effectiveness in identifying fixations with greater density than existing methods, thereby enabling the refinement of key gaze metrics such as fixation duration and fixation center.

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