It is usually difficult to observe and compare the differences in colors perceived by different individuals. Recently, isometries or distance-preserving maps between psychophysical color spaces are proposed to compare and exchange color perceptions by different observers. On the other hand, existing ways to build isometries need to solve nonlinear equations and use a restricted form in order to obtain a unique solution. In this study, we show a new method to build an isometry between color spaces of different observers. We estimate local isometries using only color discrimination thresholds in a general form and with only computations of linear algebra. These local isometries are then combined by a convex interpolation to obtain a global isometry. The proposed method is then applied to visualize and compare the differences in color visions between different observers and exchange between them. In particular, we applied the method to color-weak compensation and color-weak simulation. Experiments shown that the proposed algorithm provides accurate estimates of the local isometries and is effective in color-weak compensation and simulation.