My dog Jules barks and howls at cats and will chase them if able, completely fenced in at home, but he has never caught one, possibly because he gives them plenty of warning.
But, once I heard him barking up by the swimming pond and on investigation found him shouting at a little cat which was soaking wet and I assumed had fallen in. But it wasn’t running and, although the 2 were only a few centimetres apart, he wasn’t attacking.
Today I had a similar experience. Heading into the field, the grass of which is mainly eye high (my eye), with Jules about 10 metres ahead, out of the corner of my eye I saw a dark figure less then 6 inches from my foot. It was the little brown/black cat that we have seen in there before and which Jules has chased and howled at when seen from 20 metres or so. Taken by surprise, I stopped and looked down and said ‘hello’. It immediately ran away soon out of sight.
Surely Jules with his roving eye could not have missed it. Even if he had, his super sensitive nose would not have. Is it possible that, because it did not run, he had not reacted and instead the two had stared at each other while only millimetres apart before moving on?
Perhaps he is only movement activated, it is true that he sometimes stares at cats outside the fence and only barks when they move. If so, if this little chap(ess), had responded to my voice by remaining for one of his treats, he might have had a friend to talk to in the garden later. What a shame.
BTW I saw a piece on TV last night from the States where a lizard, with one leg frozen in the air remained motionless as a snake wriggled by. It knows that snakes have poor eyesight and only responds to movement, hence his behaviour, but then another snake approached and would have touched him on it’s progress so he took the decision to burst into rapid running flight. Soon many snakes came racing out of the rocks and he only escaped by the skin of his teeth. Could Jules have a similar bent, only reacting to movement? If so and a cat coming into the garden was brave enough, we could have a cosy coexistence in the house. 
Sorry, no photos, but I thought this was the best place to catch interest. 