We use the Millennium Galaxy Catalogue ( MGC ) to study the effect of compact galaxies on the local field galaxy luminosity function .
Here we observationally define as ‘ compact ’ galaxies that are too small to be reliably distinguished from stars using a standard star-galaxy separation technique .
In particular , we estimate the fraction of galaxies that are misclassified as stars due to their compactness .

We have spectroscopically identified all objects to B _ { \mbox { \tiny \sc MGC } } = 20 mag in a 1.14 deg ^ { 2 } sub-region of the MGC , regardless of morphology .
From these data we develop a model of the high surface brightness incompleteness and estimate that \sim 1 per cent of galaxies with B _ { \mbox { \tiny \sc MGC } } < 20 mag are misclassified as stars , with an upper limit of 2.3 per cent at 95 per cent confidence .
However , since the missing galaxies are preferentially sub- L ^ { * } their effect on the faint end of the luminosity function is substantially amplified : we find that they contribute \sim 6 per cent to the total luminosity function in the range -17 < M _ { B } < -14 mag , which raises the faint end slope \alpha by 0.03 ^ { +0.02 } _ { -0.01 } .
Their contribution to the total B -band luminosity density is \sim 2 per cent .
Roughly half of the missing galaxies have already been recovered through spectroscopy of morphologically stellar targets selected mainly by colour .
We find that the missing galaxies mostly consist of intrinsically small , blue , star-forming , sub- L ^ { * } objects .

In combination with the recent results of Driver et al .
( 29 ) we have now demonstrated that the MGC is free from both high and low surface brightness selection bias for giant galaxies ( M _ { B } \la - 17 mag ) .
Dwarf galaxies , on the other hand , are significantly affected by these selection effects .
To gain a complete view of the dwarf population will require both deeper and higher resolution surveys .