Marked point processes have received a great attention in the re- cent years, for their ability to extract objects in large data sets as those obtained in biological studies or hyperspectral remote sens- ing frameworks. This paper focuses on an original Bayesian point process estimation for the detection of galaxies from the hyperspec- tral data 'cubes' provided by the Multi Unit Spectroscopic Explorer (MUSE) instrument. It is shown that this approach allows to obtain a synthetic representation of the detection problem and circumvent the computational complexity inherent to high dimensional pixel based approaches. The reversible jump Monte Carlo Markov Chain imple- mented to sample the parameters is detailed, and the results obtained on benchmark data mimicking the real instrument are provided.