The invention relates to a medical inspection apparatus (1), such as a microscope or endoscope, and to a medical inspection method such as microscopy or endoscopy. Visible image data (11) representing a visible-light image (49) and fluorescence image data (12) representing a fluorescent-light image (51) and a pseudocolor (70, 71) are merged to give an improved visual rendition of an object (2) which comprises at least one fluorophore (6) to mark special features of the object (2). This is accomplished in that an image processing unit (18) of the microscope (1) or endoscope is configured to compute a color (ro, go, bo) of an output pixel (54) in the pseudocolor image (53) from at least one pseudocolor (rp, gp, bp), a color (ri, gi, bi) of a first input pixel (50) in the visible-light image (49) and an intensity (f) of a second input pixel (52) in the fluorescent-light image (51). In particular, the color (ro, go, bo) may result from a linear interpolation in a color space (RGB) between the pseudocolor and the color of the first input pixel (50) of the visible-light image (49) depending on the intensity (f) of the second input pixel (52) in the fluorescent-light image.