В вашем коде есть несколько ошибок,
(i) Используйте ng-click вместо click с angularjs
(ii) Поместите ng-repeat снаружи так, чтобы изменения с фильтром получилиотражение
(iii) Используйте фильтр Angularjs вместо создания собственного
DEMO
"use strict";
angular.module('myApp',[]);
angular.module('myApp').controller('MainController', function($scope) {
var vm = this;
vm.selectCategory=selectCategory;
vm.options = {
imageList:[
{
name: 'Fluffy',
images: 'images/Fluffy.jpeg',
caption: 'cuddly',
category: 'lake'
},
{
name: 'Blacky',
images: 'images/blacky.jpeg',
caption: 'cuddly',
category: 'lake'
},
{
name: 'Tabby',
images: 'images/tabby.jpeg',
caption: 'sleepy',
category: 'family'
},
{
name: 'Cleo',
images: 'images/Cleo.jpeg',
caption: 'sleepy',
category: 'family',
},
{
name: 'Fluffy',
images: 'images/Fluffy.jpeg',
caption: 'cuddly',
category: 'family'
},
{
name: 'Blacky',
images: 'images/blacky.jpeg',
caption: 'cuddly',
category: 'lake'
},
{
name: 'Tabby',
images: 'images/tabby.jpeg',
caption: 'sleepy',
category: 'lake'
},
{
name: 'Cleo',
images: 'images/Cleo.jpeg',
caption: 'sleepy',
category: 'lake'
}
],
};
function selectCategory(pos) {
vm.selectedCategory = pos;
};
});
<script src="https://ajax.googleapis.com/ajax/libs/angularjs/1.2.23/angular.min.js"></script>
<!DOCTYPE html>
<html ng-app = "myApp">
<head>
<meta charset="UTF-8">
<title>AngularJS Picture Gallery</title>
<div ng-controller = "MainController as vm">
<div class = "container">
<div class = "row">
<div class = "col-md-12" id ="myBtnContainer">
<button class = "btn active" ng-click =
"vm.selectCategory('all')"> Show all </button>
<button class = "btn active" ng-click =
"vm.selectCategory('lake')"> Lake Pics </button>
<button class = "btn active" ng-click =
"vm.selectCategory('family')"> Family Pics </button>
<button class = "btn active" ng-click =
"vm.selectCategory('kids')"> Kid Pics </button>
</div>
<div class = "row">
<div class = "col-md-12">
<div class = "thumbnail">
</div>
</div>
<div ng-repeat = "image in vm.options.imageList | filter: { category: vm.selectedCategory }">
<img ng-src="{{image.images}}" hspace ="15" vspace ="10">
</div>
</div>
</div>
</div>
</body>
</html>