Visual Place Recognition (VPR) is an image-based localization method that estimates the camera location of a query image by retrieving the most similar reference image from a map of geo-tagged reference images. In this work, we look into two fundamental bottlenecks for its localization accuracy: reference map sparseness and viewpoint invariance. Firstly, the reference images for VPR are only available at sparse poses in a map, which enforces an upper bound on the maximum achievable localization accuracy through VPR. We therefore propose Continuous Place-descriptor Regression (CoPR) to densify the map and improve localization accuracy. We study various interpolation and extrapolation models to regress additional VPR feature descriptors from only the existing references. Secondly, we compare different feature encoders and show that CoPR presents value for all of them. We evaluate our models on three existing public datasets and report on average around 30% improvement in VPR-based localization accuracy using CoPR, on top of the 15% increase by using a viewpoint-variant loss for the feature encoder. The complementary relation between CoPR and Relative Pose Estimation is also discussed.