Data visualization is an effective mechanism for identifying trends, insights, and anomalies in data. On large datasets, however, generating visualizations can take a long time, delaying the extraction of insights, hampering decision making, and reducing exploration time. One solution is to use online sampling-based schemes to generate visualizations faster while improving the displayed estimates incrementally, eventually converging to the exact visualization computed on the entire data. However, the intermediate visualizations are approximate, and often fluctuate drastically, leading to potentially incorrect decisions. We propose sampling-based incremental visualization algorithms that reveal the "salient" features of the visualization quickly---with a 46× speedup relative to baselines---while minimizing error, thus enabling rapid and error-free decision making. We demonstrate that these algorithms are optimal in terms of sample complexity, in that given the level of interactivity, they generate approximations that take as few samples as possible. We have developed the algorithms in the context of an incremental visualization tool, titled I nc V isage , for trendline and heatmap visualizations. We evaluate the usability of I nc V isage via user studies and demonstrate that users are able to make effective decisions with incrementally improving visualizations, especially compared to vanilla online-sampling based schemes.