Aims: According to some estimations, there are as many as 100000 open clusters in the Galaxy, but less than 2000 of them have been discovered, measured, and cataloged. We plan to undertake data mining of multiwavelength surveys to find new star clusters. Methods: We have developed a new method to search automatically for star clusters in very large stellar catalogs, which is based on convolution with density functions. We have applied this method to a subset of the Two Micron All Sky Survey catalog toward the Galactic anticenter. We also developed a method to verify whether detected stellar groups are real star clusters, which tests whether the stars that form the spatial density peak also fall onto a single isochrone in the color-magnitude diagram. By fitting an isochrone to the data, we estimate at the same time the main physical parameters of a cluster: age, distance, color excess. Results: For the present paper, we carried out a detailed analysis of 88 overdensity peaks detected in a field of $16\times16$ degrees near the Galactic anticenter. From this analysis, 15 overdensities were confirmed to be new open clusters and the physical and structural parameters were determined for 12 of them; 10 of them were previously suspected to be open clusters by Kronberger (2006) and Froebrich (2007). The properties were also determined for 13 yet-unstudied known open clusters, thus almost tripling the sample of open clusters with studied parameters in the anticenter. The parameters determined with this method showed a good agreement with published data for a set of well-known clusters.