Abstract Data points situated near a cluster boundary are called boundary points and they can represent useful information about the process generating this data. The existing methods of boundary points detection cannot differentiate boundary points from outliers as they are affected by the presence of outliers as well as by the size and density of clusters in the dataset. Also, they require tuning of one or more parameters and prior knowledge of the number of outliers in the dataset for tuning. In this research, a boundary points detection method called BPF is proposed which can effectively differentiate boundary points from outliers and core points. BPF combines the well-known outlier detection method Local Outlier Factor (LOF) with Gravity value to calculate the BPF score. Our proposed algorithm StaticBPF can detect the top-m boundary points in the given dataset. Importantly, StaticBPF requires tuning of only one parameter i.e. the number of nearest neighbors $$(k)$$ ( k ) and can employ the same $$k$$ k used by LOF for outlier detection. This paper also extends BPF for streaming data and proposes StreamBPF. StreamBPF employs a grid structure for improving k-nearest neighbor computation and an incremental method of calculating BPF scores of a subset of data points in a sliding window over data streams. In evaluation, the accuracy of StaticBPF and the runtime efficiency of StreamBPF are evaluated on synthetic and real data where they generally performed better than their competitors.